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STUDIES IN CHEMICAL DYNAMICS.

-STUDIES

CHEMICAL DYNAMICS

J. H. v A N 'T H O F F

REVISED AND ENLARGED BY

DR. ERNST COHEN

Assistant in the Chemical Laboratory of the University of Amsterdam
TRANSLATED BY

THOMAS EWAN M. Sc., Ph. D.

Demonstrator of Chemistry in the Yorkshire College, Leeds

WITH A PREFACE BY PROFESSOR J. H. VAN 'T HOFF

AND
49 FIGURES IN THE TEXT

AMSTERDAM

FREDERIK MULLER & Co

LONDON

WILLIAMS & NORGATE

I 896

Printed by the Amst. Boek- en Steendrukkerij v/h. Ellerman, Harms & Co.

PREFACE I.

The ,, Etudes de Dynamique Chimique" being out of print, the
desirability of a new edition was suggested by the publisher.

This, however, gave rise to a difficult problem : the ' 'Etudes'
represented, at the time of their publication, a certain stage in
my chemical thinking, beyond which, doubtless, everyone is now
advanced. To introduce many changes would, however, take
away from the original work its desired documentary character,
while to change nothing would be to contribute nothing to
making the contents acceptable to the public.

Dr. E. COHEN'S proposal to revise the 'Etudes' in the form
of the old laboratory programme, in ' carrying out which he has
very successfully assisted, came just at the right moment, and
so, may this work serve as a suitable record of our little labora-
tory history.

Stuhlingen, October 1895.

J. H. VAN 'T HOFF.

PREFACE II.

The first edition of this work was published about twelve
years ago under the title 'Etudes de Dynamique ChimiqueS

Since then many of the views put forward in it have proved
to be uncommonly fruitful, on the one hand in explaining
known facts, on the other, by suggesting new directions for
investigation.

The object of the present German edition is not merely to
reproduce the original book, but also to present the researches
which have been engendered by it together with the parent
memoir as a homogeneous whole ; in doing this, much which has
not hitherto been published has been included.

Amsterdam, October 1895.

ERNST COHEN.

NOTE BY THE TRANSLATOR.

The appearance of a revised edition of Professor VAN 'T HOFF'S
classical 'Etudes de Dynamique Chimique'1 seemed to provide a
wished-for opportunity of introducing it to a wider circle of
English readers by means of a translation; the paucity of works
in our language dealing with the subject made this the more
desirable.

The simplicity and originality of the treatment of chemical
change and affinity make the book of the greatest value to the
student seeking clear views on the fundamental problems of our
science, whilst the fertility in ideas makes it uncommonly suggestive
to the chemist already familiar with the outlines of the subject.

The nature of the contents is sufficiently indicated in the
preceding prefaratory notes. The translation adheres closely to
the sense of the original, occasional notes having been added
for the sake of greater clearness.

I am greatly indebted to my friend A. C. WEIGHT M. A., B. Sc.
for his kindness in reading the revised proofs.

May 1896.

THOS. EWAN.

UNIVERSITY"
C*7

CONTENTS,

THE COURSE OF CHEMICAL CHANGE.

First Part. THE FORMAL CHEMICAL REACTION.

Page.

I. The monomolecular reaction. Decomposition of arsenic

hydride 1

II. The bimolecular reaction. Hydrolysis of esters ... 4

III. ,, ,, „ Effect of molecular volume . 15

IV. The polymolecular reaction. Slow oxidation of phosphine,

Simplicity of many reactions. ......... 25

Second Part. DISTURBING ACTIONS.
Chapter I. Disturbing actions in liquids.

I. Effect of the medium on the velocity of reaction. Action

of contact 26

II. Influence of pressure on the velocity of reaction . . 30

Chapter II. Disturbing actions in gaseous systems.

I. The order of magnitude of the disturbing actions in
gaseous systems . ., . . 31

II. The nature of the disturbing actions in gaseous systems.
Action of the walls of the vessel. Formation of cya-
melide and of water; decomposition of phosphine . . 43

III. The nature of the disturbing actions in gaseous systems.

a. The rate of oxidation of phosphine 50

b. The rate of oxidation of phosphorus, sulphur,

and aldehyde 61

II CONTENTS.

Page.

Chapter III. Elimination of the disturbing actions

I. Methods of eliminating the disturbing actions. Form
and dimensions of the apparatus. Use of a solvent.

Moistening the walls of the vessel 86

II. The first period of chemical change. Chemical induction 91

Third Part. APPLICATIONS.

I. Determination of the number of molecules which take
part in a chemical reaction. A. Method in which the

volume remains constant 99

II. Determination of the number of molecules which take
part in a chemical reaction. B. Method in which the

volume varies 101

1. Action of bromine on fumaric acid 105

.2. Polymerisation of cyanic acid. . . . -. . . .107
3. The action of stannous chloride mi ferric chloride . 110

III. Recognition of mixtures. Decomposition of dibrom-
succinic, and iso-dibromsuccinic acids 113

IV. Comparison of the velocities of different reactions.

a. Hydrolysis of esters by bases 115

b. Hydrolysis of esters by acids .... . . .116

THE INFLUENCE OF TEMPERATURE ON
CHEMICAL CHANGE.

First Part. THE RELATION BETWEEN THE VELOCITY CONSTANT K

AND THE TEMPERATURE.

a. Application of thermodynamics 122

b. Experimental treatment of the subject . . ... . . .127

1. Influence of the temperature on the rate of decompos-
ition of dibromsuccinic acid. . 127

CONTENTS. Ill

Page.

-. Influence of the temperature on the rate of the reaction

between sodiumchloracetate and caustic soda . . .129

:l. Influence of the temperature on the rate of change of

chloracetic acid in aqueous solution 130

4. Influence of the temperature on the rate of hydrolysis

of ethyl acetate by caustic soda 130

5. Influence of the temperature on the velocity of the

reaction between potassium chlorate and ferrous

sulphate in presence of sulphuric acid 132

<). Influence of the temperature on the rate of hydrolysis

of ethyl acetate by caustic soda 133

7. Influence of the temperature on the inversion of cane

sugar 133

8. Influence of the temperature on the action of sodium

ethylate on methyl iodide 133

9. Influence of the temperature on the formation of nitriles

from syn-aldoxime acetates and on the change of

the latter into the anti-modifications 133

10. Influence of the temperature on the rate of decomposition

of the hydrides of arsenic and phosphorus. . . . 134

Second Part. THE TEMPERATURE OF IGNITION . . .136

CHEMICAL EQUILIBRIUM.
First Part. THE THREE FORMS OF EQUILIBRIUM.

I. Homogeneous systems.

a. At constant temperature 143

b. The temperature is variable 148

Application of thermodynamics 148

Applications 150

II. Heterogeneous systems 155

Cases i/tcextif/ated ....156

IV CONTENTS.

Page.

III. 1. Condensed systems 163

2. Cases investigated 167

a. The transition temperature of polymorphous

bodies 1 67

b. The transition temperature of salts containing

water of crystallisation 168

c. The transition temperature in the formation

.and decomposition of double salts . . . .169

d. The transition temperature in cases of double

decomposition 173

e. The transition temperature of isomeric com-

pounds 173

3. Solubility and vapour pressure at the transition

temperature 174

4. Relation between the transition temperature of a

hydrated salt and the vapour pressures of the
salt and of solutions of it 179

5. Methods of determining the transition temperature 180

a. The dilatometric method 181

b. The thermometric method ] 84

c. The crystallisation method 186

d. The identity methods . 186

os,. Determination of solubility 186

(B. Determination of vapour pressure.

1. Vapour pressures of solutions 187

2. Pressure of dissociation 188

7. The solution pressure methods.

1. Solutions 188

2. Solution pressure of dissociation . . . .192
2. Electrical methods.

1. Electrical method with both stable and

meta- stable phases 193

2. Electrical method with stable and without

meta-stable phases 198

Further methods .... 203

CONTENTS. V

Page.

Second part. THE THREE FORMS OF PHYSICAL EQUILIBRIUM.

I. Homogeneous systems 205

II. Heterogeneous systems 205

III. Condensed systems 210

Third par t. DIAGRAM OF THE INFLUENCE OF TEMPERATURE

ON EQUILIBRIUM. DETERMINATION OF THE TRANSITION POINT OF
SULPHUR 212

Fourth part. DISPLACEMENT OF EQUILIBRIUM WITH THE

TEMPERATURE. PRINCIPLE OF MOBILE EQUILIBRIUM 217

I. The principle of mobile equilibrium applied to hetero-
geneous systems.

a. Physical equilibrium in heterogeneous systems.

Evaporation and condensation 217

b. Chemical equilibrium in heterogeneous systems. 218

II. The principle of mobile equilibrium applied to con-
densed systems.

a. Physical equilibrium in condensed systems. Fusion

and solidification 219

b. Chemical equilibrium in condensed systems. In-

compatible systems 219

III. The principle of mobile equilibrium applied to homo-
geneous systems 222

AFFINITY.

I. The comparison of chemical affinities 229

II. Measurement of affinity. The magnitude of the affinity

which retains the water of crystallisation in salts. . 230

III. Determination of the work done by affinity .... 235

VI CONTENTS.

Page.

IV. Applications.

1. Work done by affinity at absolute zero. Diagram

of the work done . 241

2. Influence of pressure on the transition point. 242

3. Calculation of the transition point.

a. The allotropic modifications of sulphur . 248

b. The transformation of a mixture of sodium

ammonium laevo- and dextro-tartrates
into sodium and ammonium racemates . 250
V. The electrical work performed by a chemical change.

1. General considerations 251

2. Thermodynamics of the transition cell. . . . 254

3. Equilibrium- constant and electromotive force . 267

Appendix ... * 274

Name index 276

Subject index 279

THE COURSE OF CHEMICAL CHANGE.

FIRST PART.

THE NORMAL CHEMICAL REACTION.
I. THE MONOMOLECULAR REACTION.

Decomposition of Arsenic Hydride.

The most simple chemical change is that which can be
accomplished within a single molecule, a change for the accomp-
lishment of which the mutual action of several molecules is not
requisite.

Whether it^be a question of isomeric change, or of decompos-
ition, the process is subject to the same law.

On these grounds we will call the chemical reaction of this
kind the monomolecular reaction.

Experiment will show us that in this case there is proportio-
nality between the quantity of substance still decomposable, and
the quantity which undergoes decomposition in each instant,
which may be represented by the following equation,

where C is the concentration, (quantity in unit volume),

t, the time, and k a constant \ which we will call the velocity
constant.

1 It is of course assumed here that the reaction takes place at constant tempera-
ture, and consequently the heat evolved or absorbed by it may be neglected.

2 THE MONOMOLECULAR REACTION.

The decomposition which was studied in order to test this
equation is the following; —

As H3 = As + 3 H.

If we assume that the arsenic hydride decomposes in accord-

ance with the simple equation just given \ it will be easy,

by determining the pressure of the decomposing gas (at constant

volume), to calculate the undecomposed part of it in unit volume.

Let C0 and P0 be the concentration of the arsenic hydride,

and the total pressure at the beginning,
Ct and Pt the values after a partial decomposition.

and
Then

P . . p

*t — -t

Ct = C0 (3

+ p

n 2

~ " Ct).

2 Pt

(1)

The apparatus for making the determinations of the pressure
will be fully described later, (p. 41).

The results obtained are given in the following table.

Time in hours
t

Pressure in mm.
P

1 po

k — f log o p 9P

o r0 - - <L rt

784.84

878.50

0.09076

904.05

0.09051

928.02

0.09079

949.28

0.09051

969.08

0.09056

987.19

0.09060

To control the accuracy of the differential equation

it must be integrated.

1 That this is really the case will be shown later.

2 See appendix, note 1.

THE MONOMOLECULAH REACTION.

We find

— log C — kt + constant.

Eliminating the integration constant by means of equation
(1), we get: -

1 C0 1

k = -- log -£ = -- log -

t • > G; - I J * 3P0-2Pt

These values of k have been calculated, and are set down
in the third column of the table; [their constancy shows that
the requirements of the differential equation are satisfied.

A further example of a monomolecular reaction is the decom-
position of phosphine, which will be considered later.

From the preceding we may draw the following general con-
clusion, which however contains nothing unexpected in the case
of a monomolecular reaction.

The quantity decomposed in unit time is independent of the
volume of the decomposing substance.

This proposition may also be proved in the following way:

Suppose that two equal quantities Q occupy at the beginning
of two experiments two different volumes Vi and V2, it is easy
to see that the corresponding quantities Xx and X2, which remain
undecomposed at the end of the same interval of time t, will
be the same in both cases.

Applying the equation

kt = log I
we obtain

__ __

kt = log -^ - ^g r = log -J2- = loS I

AI AI A2 A

from which -=r- = -=-, or Xi = X2.

II. THE BIMOLECULAR REACTION.
Hydrolysis of Esters.

We will call a change in which the interaction of several
molecules is required, poly molecular.

The most simple case of this sort is the reaction between two
molecules, or the bimolecular reaction.

If we call the concentrations of the two reacting substances
G! and C2, the decrease of concentration which the substances
undergo in each instant, will be proportional to the concentrations
of both of them, that is

= kj CJL C2 and - ^ = k2 d C2

—

at at

where t is the time, and ki and k2 are constants.

As the unit of concentration of a body we will choose the
molecular weight of it, in kilograms in a cubic metre. If we
are considering, for example, the hydrolysis of ethyl acetate by
jaaustic soda, the concentration is unity when 40 kgrms of caustic
soda and 88 kgrms of the ester are present in a cubic metre.

As will be seen in what follows, the accuracy of the equations
has been confirmed by experiment ; the experiments on this point
were carried ont by L. T. REICHER. l

The hydrolysis of ethyl acetate by caustic soda, represented
by the equation

NaOH H- CaHBOOCH8 = CH3COONa + C2H5OH,

was studied.

WARDER 2 had already found that this reaction takes place
at the ordinary temperature with a velocity which allows of its
course being followed.

It is thus a question in this case of verifying the equation

d Ci , i p p

- K \Ji L»2.

1 LIES. Ann. 228, 257, 1885.
a Berichte. 14, 1361, 1881.

HYDROLYSIS OF ESTEES. :>

where Ci is the concentration of the caustic soda, C% that of
the ester, t the time, and k some constant.

Consider now an aqueous solution of base and ester, which
are acting on each other at a given temperature; then at any
moment during the reaction the concentration of the base, C1?
can be determined by titration with an acid ; from this the
concentration of the ester, €2, may be calculated if the base be
used in excess and its concentratration, Cw, be determined after
the reaction is complete. We have then,

Substituting this value in the original equation, we obtain
_ d_Ci = k Ci (Ci _ CA

from which by integration

1 C
^— log ~ -~— = kt + constant.

^w VI v^a>

If we make two determinations, say Ci and Ct, and if the
time intervening between them is t, we find, eliminating the
constant of integration;

1 Ct (d — CCQ)

k = p 7 log p-7p p-ri

Ow t bi (Ut - • ^v>)

or introducing common logarithms in place of the Naperian,

2.3025 _ Ct (Ci — Ceo)
k = -» Log ^

t d (Ct - C«o)'

As the apparatus used will be referred to again, it is fully
described here. (Fig. 1).

In order to obtain a constant temperature the essential part
of the apparatus, A, is placed within two glass cylinders F and
G; into the first of these water at a high pressure from the
water supply is conducted by two fine jets from the tubes L

THE BIMOLECULAR REACTION.

und Ly ; by means of the currents produced in this way a
uniform temperature is maintained.

This temperature is determined by means of a thermometer
N which allows J/io of a degree to be read.

The second vessel G, contains ice water, or warm water,

Fig. 1.

according as the temperature of the water supply is too high
or too low.

To prevent evaporation of the ester during the reaction the
liquid is placed in the glass vessel A, which may be closed by
the glass tap C, and which it completely fills; liquid may be

APPARATUS. 7

removed from A for the titrations, by displacing it through C
by means of mercury, which is allowed to run in from the
funnel B.

The manipulation of the experiments~requires the cooperation
of two observers, and consists of three operations ; filling, mixing,
and drawing off samples.

A quantity of the aqueous solution of the ester is first placed in
the apparatus, such that when the latter is subsequently wholly
filled by the addition of the alkaline solution, a small excess of
alkali shall be present. It is therefore necessary to know to
begin with, the concentrations of the solutions of ester and soda,
and also the capacity of A.

The apparatus is then filled with the solution of ester, placed
in position as shown in the figure, and the solution of the base,,
(protected from the carbon dioxide of the air), introduced gradu-
ally through H in such a way that the solutions of ester and
alkali form separate layers over each other. During the time
which is needed for the filling, the temperature in F is regulated
in the way described, so that when the apparatus is quite full
the temperature of the liquid in it is about 0°.4 below that
desired; this will be indicated by the thermometer D.

In order to mix the liquids thus introduced, some mercury is
allowed to flow through B into A, the tap C closed, the appa-
ratus removed from the cylinder, and shaken uniformly several
times so that the mercury effects the mixture of the liquids; if
necessary the temperature is then raised to the desired point by
warming with the hand. The apparatus is now placed in its
original position and the real experiment may be begun as soon as
the temperature of the water in the cylinder F has reached the
desired point.

Before drawing of a sample, a volume of mercury correspon-
ding to the part of the apparatus which projects above the
water in F, is poured in through the funnel B, on opening the
tap C this displaces the liquid in that part of the apparatus
which possibly does not possess the correct temperature. When
the mercury has fallen to the mark E, the tap is closed again,
and 100 cc. of mercury poured into B. The one observer then

THE BIMOLECULAR REACTION.

brings a measured quantity, R, of sulphuric acid of known
strength under the opening K, and quickly opens the tap C com-
pletely; the time is noted by the second observer on a chrono-
meter indicating seconds, and also the moment at which the
mercury has fallen very nearly to the mark E. By partially
closing C the last small quantity flows out slowly until E is
reached, when the tap is closed completely. This manipulation is
repeated each time a sample is drawn off, and since the
sulphuric acid employed is amply sufficient to neutralise the alkali
present, the hydrolysis taking place in 100 cc. of the liquid is
stopped at a given time, in the space of a few seconds (about 9).

If time allows, the excess of sulphuric acid is at once titrated
with baryta water of known strength using phenol-phthalem
as indicator (or rosolic acid in experiments with ammonia).

Samples are drawn off at intervals of some minutes until only
about 100 cc. of the mixture are left in the apparatus, which
serve for the determination of the final titre after the reaction
may be regarded as complete (viz. after at least 24 hours).
It is obvious that after the last sample has been taken the tem-
perature need no longer be regulated.

The results obtained are contained in the following table : l

Time in minutes.

Titre of base in
the mixture. T.

61.95

4.89

50.59

2.31

11.36

42.40

2.33

29.18

29.35

2.28

14.92

—

In calculating the values of k it is to be noticed that in the
expression given on page 5,

k =

1 The tempei'ature was 9°. 4.

2.3025

Qt (Ci-C,)

Cl (ct - cw)

CALCULATION OF RESULTS. 9

the quotient, the logarithm of which occurs, may be written thus

m /rp rp \

T! (Tt - Tw)'

since the values of C (the concentrations, in kgrm. mols. per
cubic metre, of the free caustic soda) are proportional to those
of T (the quantities of free caustic soda expressed in cc. of
the baryta solution employed).

Co, is the final concentration (in kgrm. mols. per cubic metre)
of the caustic soda in the mixture in which the reaction has
taken place, the concentration being unity when 40 kgrms NaOH
are present in each cubic metre.

If the baryta solution is N times normal we have

C--T, N

100
The value of k becomes therefore

2.3025 X 100 , Tt (T! — TM)
Tw Nt °g T! (Tt - T«)'

These values of k are entered in the third column of the
table \ their practical identity shows that the requirements of
the original differential equation are satisfied.

The equation

- f = k Cl C,

leads us to the conclusion, that each of the bodies taking part
in the reaction has an equal influence on its velocity.

L. TH. REICHER 2 has confirmed this experimentally, and has
shown that the same value of the constant k is obtained, whether
excess of caustic soda, or of the ester, be employed.

In this case also, the hydrolysis of ethyl acetate by caustic
soda was studied.

2 LIEB. Ann. 238, 276, 1887.

THE BIMOLECULAR REACTION.

X)-

The apparatus used is shown in fig. 2.

The most important condition to be fulfilled in these experi-
ments, is that the free soda contained in the mixture, must not
be exposed to the air either during its intro-
duction, or afterwards within the apparatus
itself.

The apparatus consists of two fairly strong
vessels, P and Q, which communicate by a
thick-walled tube, and which may be closed
above by taps R and S. At U and T there
are two marks. The volume from R to
the mark U was 125.7 ccv from U to T
100.2 cc.

In order to find the final titre, the apparatus,
after being carefully cleaned and dried, is
exactly filled from R to U with the alkaline
solution of known strength through the tube V;
the piece of tube V R is then cleaned and filled
with mercury, and finally, through S, so much
more of this metal introduced that in all 10 cc.
of it have been employed. The exit tube K
of the apparatus A (fig. 1) which has already been described,
is now united to V by a short india rubber tube, and with the
help of mercury which is poured into the funnel B, the mixture
of caustic soda and ester is allowed to flow into P so slowly
that it remains as a separate layer over the solution of soda ;
this can be plainly seen by the sharp boundary between the
two layers.

The apparatus being filled in this way to the mark T, the
taps are closed, and the liquids mixed by transferring the mercury
alternately from one vessel to the other 100 times, shaking
vigorously meanwhile. The contents are then allowed to stand
for at least 24 hours, after which the titration is proceeded with.
This is done by first pouring in some mercury above S, and
attaching a tube for drawing off the liquid at V; W is then
connected to a gas holder containing air and the liquid driven
out to the mark T, after which (from T to U) 100.2 cc. of the

rig, 2.

EXCESS OF BASE OR ESTER.

mixture are allowed to flow into a measured quantity of sul-
phuric acid which must be in excess. This is then titrated back.

A second 100.2 cc. of liquid is now driven out of the appa-
ratus after running mercury into Q through S up to the mark
T, in the way just described.

The results obtained with this apparatus are contained in the
following table: —

(Temperature 15°. 8).

a. Experiments with excess of caustic soda.1

Time in minutes,
t

Titre of the base
in the mixture. (T)

62.09

—

3.74

54.33

3.47

6.28

50.60

3.48

10.48

46.28

3.43

13.59

43.87

3.44

33.06

—

b. Experiments with excess of ester.2

Time in minutes,
t

Titre of the base
in the mixture. (T)

38.94

—

2.52

, 31.32

3.47

5.04

25.92

3.43

8.34

20.74

3.41

10.71

17.85

3.42

23.65

—

In both cases the values of the constants agree together
very well; k, in the last column of table a, is calculated in the
way described on page 9. In the second table, &, where excess

2 N =

12 THE BIMOLECULAK KEACTION.

of ester was used, the sign of Tw must be changed in the formula
for k (page 9) so that in table b

2. 3025X100 T TX (Tt + TM)

TCO Nt og Tt (Tx + Tc«y

At the present time a considerable number of researches on
this subject are in existence; as further examples of bimolecular
changes the action of acids on acetamide (OSTWALD) \ and that
of bases on lactones studied by P. HENEY 2, are to be mentioned.

A simplification which may be introduced by using the react-
ing substances in equivalent quantities will now be pointed out.

In this special case, the ratio of the concentrations of the sub-
stances does not change during the reaction; by choosing the
units in a suitable way, only one single concentration need be
taken into account.

This concentration, which refers to both bodies, will be called
the concentration of the system.

In place of the equations

- ^ = k, Cx C2 and - ~ = k, C, C2

we may write the following,

d C

= k C2

0 being the concentration of the system.
Integrating we obtain

p- = kt + constant (1)

Considering for example the hydrolysis of an ester by caustic
soda, (in equivalent quantities), the concentration of the system is
proportional to the titre of the alkali in the solution, therefore

n . f» ±!

Ct - Cx |-

where GX and T! are the original values of the concentration and
titre, Ct and Tt their values after a partial decomposition.

1 Journ. prakt. Chem. (2), 27, 1, 1883.

2 Zeit. phys. Chem. 10, 96, 1892.

INFLUENCE OF VOLUME. 13

Eliminating by means of this equation the constant of integration
in equation (1), we get

k . I (L IV JL

t \Ct ' d/ "id

On comparing this expression with that which was obtained
for the monomolecular reaction, (page 3),

3T.-2TY

a great difference is apparent. l

While in the case of a monomolecular reaction the value of
k depends exclusively on the choice of the unit of time (t), in
the case of the bimolecular reaction its value is also a function
of the unit of concentration (C).

The following statement indicates the difference in the courses
of the mono- and bi-molecular reactions : -

In a bimolecular reaction the quantity decomposed depends on
the volume of the decomposing system.

This proposition is obvious, when one remembers that the bimole-
cular reaction differs from the monomolecular, in the fact that
in the former, the encounter of the reacting molecules must occur.

A further simplification takes place if in a bimolecular reaction
one of the reacting bodies is present in great excess. For since its
concentration, C2, is then not perceptibly changed during the
reaction, C2 in the equation

d C, , „ „
IT kl Cl °2

is to be considered as a constant, so that

that is the process takes place in the^same way as a mono-
molecular reaction.

Processes of this kind have been examined in great number. 2

1 This expression corresponds in every way to that obtained on page 3, —

3 P0 - 2 Ft

2 WILHELMI, Ostwald's Klassiker der exacten Wissenschaften, No. 29. — WITTWKR,
Pogg. Ann. 94, 593 (1855). — HARCOURT and ESSON, Phil. Trans. (1866) 193; (1867)
117. __ OSTWALD, Journ. prakt. Chem. 28, 449 (1883); 29. 385; 31.307.

THE BIMOLECULAR REACTION.

BUCHANAN l has studied the action of a large excess of water on
monochloracetic acid at 100°, and found that it takes place
according to the following equation: —

C2 H3 Cl 02 + H2 0 = C2 H, 03 + H Cl.

As may be foreseen, the reaction in this case goes forward
as if it were monomolecular, because the concentration of the
water may be regarded as constant.

In order to confirm this, a solution containing 4 grams
of chloracetic acid per litre was heated for a definite time in
sealed tubes, (of 15 cc. capacity), which were suspended in boil-
ing water. The reaction was then stopped by sudden cooling,
and the titre of the acid in the solution determined by means
of N/io ammonia.

Ci and TI being the concentration and titre respectively at
the beginning, and Ct and Tt the same quantities after partial
decomposition, we have the relationship

2 Tx — Tt

ct = c,

The following table contains the experimental results.

Time in hours,
t
60

Titre of the
solution. T

k— — 1 *"irj* . — lr\rr

— 4. 1O5 p 4- °e 9 T T
I L*t T, & li — It

12.90

. —

13.45

0.000158

13.90

0.000195

14.20

0.000192

14.60

0.000170

15.80

0.000184

16.40

0.000176

17.60

0.000173

18.50

0.000165

34.5

20.50

0.000187

20.65

0.000155

21.30

0.000159

Obviously the reaction takes place as if it were monomolecular.

Berichte, 4, 340, 1871.

III. THE BIMOLECULAR REACTION.

Effect of molecular volume.

In order to determine this, SCHWAB investigated the following
process which is analogous to a hydrolysis,

C2 H2 Cl 02 Na + NaOH = C2 H3 03 Na -f- NaCl. l

Assuming that the change takes place in accordance with the
'^^^s^ above chemical equation, the quantity

of the undecomposed compound in unit
volume, may be determined by means
of the titre of the alkali in the
solution which is undergoing the
change.

If the sodium chloracetate and the
caustic soda be used in molecular pro-
portions, the simplification before men-
tioned may be employed.

We have then only to take into
consideration the concentration of the
system, which refers both to the sodium
Fig. 3. chloracetate, and to the caustic soda.

The experiments were
made with the apparatus shown in fig. 3.

The large flask contained initially 553 . 9 cc. of a
caustic soda solution (containing 1.9935 grams
NaOH)2 at a temperature of 100°; the small flask
B in which there were 2.3542 grams of chlo-
racetic acid 3 could be shattered at a given
moment.

Since the molecular ratio between the quantity
of the acid and of the soda was 1 : 2, a mixture
of sodium chloracetate and caustic soda in the F)'s- 4-

1 See also BUCHANAN, Berichte. 4. 863, 1871.

2 Prepared from sodium amalgam.

3 1.3879 grams of this acid required 18.18 cc. of 0.8077 N caustic soda solution
for saturation, the calculated quantity being 18.2 cc.

THE BIMOLECULAR REACTION.

desired proportions is produced by bringing the two liquids to-
gether.

After a suitable interval the titre of 17.75
cc. of the liquid was determined in the follow-
ing way : — The liquid was expelled at C by
blowing, and poured through a funnel into
the tube D, which was surrounded by ice in
order to stop the reaction.

The funnel was then removed and the li-
quid transferred to the vessel in which the
titration was to take place by means of the
pipette E. (fig. 5).

The results obtained are given in the fol-
lowing table. l

Time in minutes,
t

Titre of 17.75 cc.
in terms of N/20
sulphuric acid = T

1 / T^ T^ \
lr 1 2 ~~ M

(tt-t2)c2V Tt ;

t2 = 4, T2 = 14.9, C2= 0.042

15.97 (calculated)

(0.399)

14.9

—

14.1

0.15

13.3

0.15

12.75

0.138

11.15

0.136

10.0

0.131

123

8.95

0.133

153

0.138

183

7.3

0.138

258

5.95

0.141

318

5.15

0.144

378

4.55

0.145

1 In calculating the value of k the initial concentration has not been used, that
observed after 4 minutes had elapsed being taken (viz. C2 = 0.042); in this way we
eliminate an irregularity in the course of the reaction which exists in the first period
and which is due partly to the incomplete mixture of the substances and partly to the
heat evolved by the neutralisation. The change is accelerated by these causes to such
an extent, that the value of k is trebled (0.399).

ACTION OF SODA ON CHLORACETIC ACID. 17

It is obvious that the course of the reaction here investigated
is not normal. The values of k obtained at the beginning of
the reaction, refer in fact to an aqueous solution, whilst those
which were obtained later are affected by the action of the sod-
ium chloride formed during the reaction.

SCHWAB l has avoided this difficulty by studying the decompos-
ition in very dilute aqueous solution; with this object he used
solutions of different initial concentrations.

Chloracetic acid was mixed with caustic soda in dilute solution
in the ratio C2 H3 Cl 02 : 2 Na OH; the formation of sodium
glycolate being prevented by cooling.

From this solution five others were prepared which contained
respectively 32, 16, 8, 4, and 2 grams of chloracetic acid per
litre. These solutions were brought into glass tubes which were
then sealed. Six tubes of each series were kept for a certain
time in boiling water, after which the titre of their contents was
determined by means of N/2o sulphuric acid. From this the
quantity undecomposed was calculated.

The following mean values of k were, found in this way.

Value of k. Concentration.
0.18 0.2

0.163 0.099

0.14 0.059

0.128 0.038

0.131 0.015

A deviation comes to light in these numbers which was
concealed in the experiments described on p. 16, and which "is
nevertheless of a fundamental character. The value of k decreases
icith decreasing concentration to a certain limit (0.13), after
irhich it remains constant.

We see accordingly, that here the equation for the bimole-
cular reaction,

— - = kt + const,
L»

is only true for small concentrations.

1 Inaugural Dissertation, Amsterdam 18S8.

THE BIMOLECULAR REACTION,

The agreement between the requirements of the formula and
the numbers found experimentally is sufficiently good for concen-
trations smaller than 0.038.

This concentration may be called the gaseous concentration,
because it is not very far removed from that which the mixture
of sodium chloracetate and caustic soda would have at normal
temperature and pressure in the gaseous condition viz : - - 0.023.

This experimental result was the origin of a series of experi-
ments on the course of the decomposition in a very weak solution
(initial concentration = 0.04984); they were carried out with
great care in sealed tubes.

The following are the results.

Time in minutes,
t

Titre of 30 cc.
in terms of
N/2o H2SO, = T.

1 /Ti-TA

~tCA Tt /

25.25

19.55

0.1300

0.1289

180

11.7

0.1291

The constancy of k leaves nothing to be desired.

Owing to the fundamental nature of the deviation just described,
it is of interest to trace its origin.

We assumed, in deducing the equation for the bimolecular
reaction, that the quantity of the two bodies decomposed in unit
time was proportional to the quantities of each of them in unit
volume; this assumption includes another which is not fulfilled
in the experiments, namely, the volume of the reacting substances
themselves must be zero.

The non-fulfilment of this condition appears to be the cause
of the irregularity observed. On the one hand the irregularity
disappears when the concentration becomes small, that is, when the

THE POLYMOLECULAR EEACTION. 19

space occupied by the reacting bodies vanishes in comparison
with the whole volume, on the other hand the deviation changes
in the way which might be expected, k increasing with the con-
centration.

IV. THE POLYMOLECULAR REACTION.

We may now go a step further and write down the differen-
tial equations for more complicated cases. If we consider a
reaction which may be ascribed to the mutual action of n mole-
cules, we have

^ = k, d (V . . .Cn; etc.; - - ^ = kn C, C2. . . .Cn;

where C1? C2 . . . . Cn, are the concentrations of the substances
reacting on each other, kx . . . . kn are constants, and t is the time.
When the reacting bodies are present in the proportions in
which they take part in the reaction, the equations may be
simplified to one single expression,

where C is the concentration of the system.
Integrating this, we find l

—£ — k t + constant,

in which the value of k is (n — 1) times that which it had in
the differential equation.

It would be interesting if it were possible to realise the differ-
ent cases which follow from this equation, that is if it were
possible to study the course of a tri- (n — 3), or quadri- (n = 4),
molecular reaction.

It is not difficult to find chemical equations which represent

1 V is supposed to be constant.

THE POLYMOLECULAR EEACTION.

three, four, or more molecules as interacting; as for example
4 P H3 = Pi + 6 H2

or the case investigated by HOOD *,

KC10, + 6FeO =: KC1

3 Fe20,.

Researches on this subject have, however, shown that the
greater number of such equations give an entirely false idea of
the mechanism of the reactions, only expressing the quantitative
aspect of them.

This mechanism is generally very simple, in almost all cases

it is mono- or bi molecular,
rarely trimolecular.

So for example the decom-
position of phosphorus (or
arsenic) hydride takes place
as if it were monomolecular,
that is according to the equation,

PH3 = P 4- Ha

whilst Hood's reaction appears
to be bimolecular.

According to the researches
of J. VAN DE STADT 2, which
will be described below, the
slow oxidation of phosphine
may, under certain circum-
stances, follow a very simple
course, namely that of a bi-
molecular reaction.
He found that the following are the principal changes which
may occur during this slow oxidation: —

(1) 2 P H3 + 4 02 = P2 05 + 3 H2 0

(2) 2 P H3 + 3 02 = 2 H3 P 03

(3) P H3 4- 02 = H P 02 + H2

Fig. 6.

1 Phil. Mag, (5). 20, 323, 1885.

2 Zeit. phys. Chem. 12, 322. 1893. Inaugural Dissertation. Amsterdam, 1893.

OXIDATION OF PHOSPHINE. 21

Equation (1) represents the change which occurs in the ordinary
combustion of phosphine.

By means of the apparatus shown in figure 6, changes (2) or
(3) could be brought about at will, and so could be separately
studied; metaphosphorous acid which was previously unknown
was prepared in the course of this investigation.

Oxidation to phosphorous acid.

The principal condition which must be fulfilled if reaction (1)
is to be excluded; is that the gases must be brought together in
a suitably dilute condition and as dry as possible ; instantaneous
oxidation can be insured, and excess of one or other avoided,
only in this way

The flask V is evacuated at d by means of the air pump, and
c closed; e is connected to the phosphine, f to the oxygen gas-
holder, while p acts as a gas pipette the contents of which may
be transferred to V by turning a. The tap a is so arranged
that V may be placed in communication with the manometer M
or with the pipette p; the tap b allows the apparatus to be
placed in communication with e or with f, or to be closed entirely.

In the dark room the gas required is admitted, one pipette full
at a time, into the flask until its admission fails to produce any
further luminosity, showing it to be present in excess. The
following results were obtained, the + sign indicates that lumi-
nosity was observed after admission of the gas;

P H3 02

1 + 1 - 1 + 1 + 1

1 + 1 — 1 + 1+1

13 X-

1 + 1 — 1 + 1 + 1 —

26 39

The manometer remained stationary during these 65 admissions
of gas, although one pipette full alone produced a pressure of
0.7 mm. in the flask.

The flask was covered with a coating which became solid and

22 THE POLYMOLECULAR REACTION.

crystalline on standing over night, and then melted at 63° and
gave the reactions of phosphorous acid, (melting point 70°).
Everything points therefore to the change having taken place
entirely according to equation (2).

Oxidation accompanied by liberation of hydrogen.

If in the experiment just described the admission of the gas
to V be brought about slowly by opening the tap a gradually,
a greenish blue flame, which is frequently intermittent and which
in daylight only betrays its existence by the formation of a
cloud, is seen instead of the phosphorous acid flame which in
the dark is almost blinding and often accompanied by a slight
explosion.

The reaction accompanying it is quite different from the former
one; a quantitative experiment carried out in the apparatus
already described (fig. 6) gave the following result;

PH3 02

1 + 1 + 1- 1 + 1 + 1

The manometer now indicates an evolution of gas, corres-
ponding to an increase of pressure of 53/4 mm., that is, since one
pipette full gave 0.7 mm., nearly 9 pipettes full. Therefore the
gases react together in equal volumes, and leave behind a third
gaseous substance equal in volume to either of them. A very
accurate confirmation of this may be obtained by adding oxygen
carefully to phosphine in excess; the addition of 17 consecutive
pipettes full of oxygen, each of which produced a blue flame on
entering the flask, left the level of the manometer unchanged
at 281/4 mm.

Formation of metaphosphorous acid.

Although the gas produced in the last experiments was found
to be hydrogen, and the equation for the change was therefore
probably PH3 + 02 = H2 + HP02, the compound HP02, the

OXIDATION OF PHOSPHINE. 23

formation of which is assumed, could not be isolated with the
experimental arrangements described.

In place of it a yellow or brown deposit was formed, which
was partly moist and soluble in water, and in short was evidently
a non-homogeneous product of secondary reactions.

A good result was however at once obtained when the two
gases were mixed by diffusion instead of by allowing them to
flow into each other. They must also be very dilute; at a
pressure of 50 mm., even when the gases diffuse into each other
the action is too violent, and no pressures greater than about
25l/2 mm. are suitable. To obtain the necessary quantity under
these circumstances, the flask V was allowed to remain in connexion
with the air pump, and filled with phosphine at a pressure of
25i-'2 mm.; the air pump was filled with oxygen at 251/2 mm.,
and the tap a opened.

The manometer indicated the gradual combination by a decrease
of pressure.

This was ,

after 2 hours 3 1/3 mm.

» 21 11

,, 24 „ 91/2 „

This decrease corresponds to the desired change, for as the
volumes of the flask and of the air pump were in the ratio
0.69 : 1, a decrease in pressure of about 101/2 mm. would be
anticipated.

The flask had in the meantime become covered with glittering,
feathery crystals which were at once seen to differ from
phosphorous acid; they did not melt at 80°. (H3P03 melts at
70°, H3P02 at 17°).

In addition, their behaviour with aqueous vapour was very
characteristic ; on admitting a very little water through a, the
coating of crystals first liquefied, and then after a few minutes
solidified entirely, forming long needles, which plainly consisted
of phosphorous acid,

HP02 + H20 - H3P03

24 THE POLYMOLECULAE KEACTION.

subsequently these again liquefied, and the aqueous solution now
formed showed the well known reaction of phosphorous acid
with silver nitrate.

The change ivhich occurs during slow oxidation.

The question as to which of the above changes occurs during
the slow oxidation of phosphorus hydride, and to what extent it
occurs, still remained to be answered.

11.89 cc. of phosphine and 6.69 cc. of oxygen were mixed
together in a eudiometer and heated in a water bath to 50°
until the pressure no longer decreased.

The volume of gas remaining, 10.3 cc., was free from oxygen,
and contained 6.2 cc. phosphine and 4.1 cc. hydrogen.

11.89 6.2 - 5.69 cc. P H3 and 6.69 cc. 02 had thus

disappeared forming 4.1 cc. H2. Assuming that the latter had
been formed in the same way as before, that is from 4.1 cc. P H3
and 4.1 cc. 02, we have 5.69 4.1 = 1.59 cc. P H3 and

6.69 — 4.1 — 2.59 cc. 02 which have reacted together in some
other way, probably to form phosphorous acid as their volumes
are approximately in the ratio 2:3.

In the slow oxidation, therefore, we are dealing with the two
processes

2 PH3 + 3 02 = JB3P03 .... (a)
and PH3 f Oa = HP02 + H2 . . . . (ft)

That the latter does not occur alone is doubtless due to the
very considerable concentration (the pressure was approximately
one atmosphere) at which this slow oxidation took place.

The following observations, made by VAN 'T HOFF, confirm this
result. Oxygen and phosphine in the ratio of 361 : 177 were allowed
to react partly at the ordinary temperature, but for the greater
part at 50°. A residue of 196 mm. 02 and 42 mm. PH3 was
left unchanged, 70 mm, H2 being produced at the same time. 1

Therefore,

177 - - 42 = 135 PH3, and 361 - - 196 = 165 02
had undergone change.

1 The volume of the gases being constant, the quantity is measured by the pressure.

SIMPLICITY OF MANY REACTIONS. 25

According to equation (&), 70 mm. of hydrogen are formed
from equal amounts of phosphine and oxygen, so that after
subtracting 70 from each of the above quantities in order to
allow for the formation of the 70 mm. of hydrogen, we obtain
65 mm. PH3 and 95 mm. 02, quantities which are nearly in
the ratio 2:3.

This result agrees very well with the hypothesis that the
oxidation takes place partly according to equation (a), partly
according to (b) ; only in this case, owing to the greater quantity
of oxygen, rather more of the phosphine (just half of it) is
changed into phosphorous acid than in the first experiment.

The slow oxidation therefore takes place approximately ac-
cording to the equation

4 PH3 4- 5 02 = 2 HP02 + 2 H3P03 + 2 H2,

in which the phosphorous acid might occur as the pyro-acid
H4P205.

As bearing on the simplicity of many reactions the results of
SMITHELLS and DENT 1 are interesting ; they found that the com-
bustion of cyanogen takes place in two phases, viz : —

C2N2 + 02 = 2 CO + N2,

whilst in the second phase the carbon monoxide is oxidised to
carbon dioxide.

We are dealing therefore, in this case, not with a trimolecular
reaction represented by the equation

C2N2 + 2 02 = N2 + 2 C02,

but with a bimolecular reaction.

The trimolecular reactions with which we are at present
acquainted will be more fully treated later. At present it may
be mentioned that their number is small.

1 Jonrn. Chem. Soc. 1894. 603.

THE COURSE OF CHEMICAL CHANGE.

SECOND PART.
DISTURBING ACTIONS.

Chapter I.
Disturbing actions in liquids.

I. EFFECT OF THE MEDIUM ON THE VELOCITY OF
REACTION. ACTION OF CONTACT.

It is only in rather rare cases that a chemical change takes
place in the simple way indicated. The influences to which it
is subject are so manifold, that the study of the course of a
reaction resolves itself to a great extent into that of the
disturbing effects. For this reason these secondary actions will
be separately considered here.

In this special chapter such obvious causes of irregularity as
lack of homogeneity of the reacting substances, evolution of
heat by the reaction, occurrence of secondary transformations and
so on, will not be considered.

Attention will rather be directed to less evident disturbances.
As we have chosen the normal course of change for our point
of departure, we shall first turn to the reactions which take
place in liquids in order to study these phenomena, because in
liquids the influences under consideration are very little felt and
are easily eliminated, whilst the study of the gases presents
much greater difficulties in this respect and can only be taken
up later.

If a reaction take place in a liquid there is only one cause

INFLUENCE OF THE MEDIUM. 27

of irregularity which merits special attention here, namely the
influence of the medium on the velocity of the reaction.

It is evident that if this influence really exist, the data
relating to the reaction will not be comparable with each other in
the different periods of its course, because the medium is grad-
ually modified in consequence of the accumulation of the products
of the reaction.

Such an influence of the medium on the velocity of the reaction
quite certainly exists, and is of considerable magnitude even in
those cases in which a chemical, or any analogous process which
might be supposed to produce such effects, appears to be ex-
cluded; that which is called action of contact, therefore, really
exists.

The numerous observations which have been made on the
influence of the medium on the velocity of a reaction can be
referred in the majority of cases to actions which are due to the
nature af the medium ; they do not in the least compel us to
admit the reality of the mysterious action of contact.

Thus the following two categories of observations appear to
be wholly unsuited to solve the question.

(1) There are in the first place those actions of the medium
which are evidently of a chemical nature.

• (2) We have secondly those observations in which the reacting
bodies were not in a homogeneous condition ; these cannot be
regarded as decisive.

The effects produced by spongy platinum may perhaps be
classed with these, though this is a point which is not yet
completely elucidated. }

Further, (and this remark applies to the experiments of
BOGUSKI 2 on the rate at which marble is dissolved by dilute
acids), an alteration of the medium (such as the addition of
certain salts to it) may favour the renewal of the decomposed
acid near the marble and thus may influence the velocity of the
reaction in a way differing entirely from a contact action.

The following observations, against which the objections men-

l See also OSTWALD, Lehrbuch der Allgem. Chemie, II. 512 et seq.

a Berichte 9, 1646, 1876; see also SPRING, Zeit. phys. Chem. 1, 209, 1887.

28 DISTURBING ACTIONS IN LIQUIDS.

tioned cannot be raised, seem to establish the action of the
medium in virtue of its presence alone: —

(1) BERTHELOT and PEAN DE ST. GILLES l found that an excess
of alcohol retards the etherification of acetic acid in such a way
that a gram molecule of it was transformed in 4 hours at 100°

[28 per cent

to the extent of 118
1 1

molecules of alcohol.

(2) A thorough investigation of the subject has recently been
made by MENSCHUTKIN 3, who has shown by means of an extended
series of experiments, that the so called chemically indifferent
solvents influence the velocity of chemical reactions in very
different degrees.

Whilst for example the combination of triethylamine and ethyl
iodide takes place with a velocity — 1 when they are dissolved
in hexane, the same combination occurs with benzyl alcohol for
solvent with a velocity which is 742.2 times greater.

It may therefore also happen that one of the liquid bodies
which is taking part in the reaction is itself an unfavourable
medium.

An excess of aniline for example retards its own action on
acetic acid in such a way that, of a gram, molecule of acetic acid

35 percent! . [ 1 ]

9Q Ms changed by < > molecules of aniline

^y ,, I 1^1

into acetanilide in 15 minutes at 155°.

(3) L. MEYER 4 has drawn attention to the fact that the
velocity of nitration of benzene increases proportionately to the
square of the quantity of nitric acid used, whereas it is diminished
by excess of benzene.

Along with these phenomena we may here mention the
researches of LANDOLT 5 on the change in the optical rotatory

1 Ann. Chim. Phys. (3), 66, 90, 1862.

2 SCHWAB, Inaugural Dissertation p. 37; cf. p. 17.

3 Zeit. phys. Chem. 1. 627, 1887; 6, 41, 1890; Berichte, 15, 1618, 1882.

4 Zeit. phys. Chem. 2. 713, 1888; Berichte, 22, 18, 1889.

5 Das optische Drehungsvermogen.

CONTACT ACTION. 29

power of a substance when it is dissolved in liquids with which
there is little probability of a chemical reaction, for example
turpentine dissolved in alcohol, benzene, or acetic acid.

To those who regard the rotativity as a function of the con-
stitution of the molecule, (without regard to any special hypothesis),
an alteration in it will be an indication of some displacement
of the molecular equilibrium.

The velocity of a reaction is very much affected by such
small displacements; the slow course of the monomolecular
reactions proves, for example, that the different molecules, although
apparently placed in identical conditions, still differ from each
other in such a way that in a given time only a part of them
undergoes change.

LANDOLT expresses himself as follows: -

"It is conceivable that when molecules of a foreign body
(alcohol) come between the molecules of an active substance
(turpentine) a certain modification is produced in the structure
of the latter, so that in each molecule the distances between
the atoms, their arrangement in space, and also the nature of
the atomic movements are changed."

In connexion with the experiments which he has recently
made MENSCHUTKIN l says : —

"This behaviour shows that a certain contact action occurs
between the so called indifferent solvent and the dissolved body,
in consequence of which solutions of a body exhibit different
chemical behaviour with regard to the changes in the velocity
of chemical reactions taking place in such solutions, according*
to the composition and structure of the indifferent solvent.11

On the whole, experience forces us to admit that contact action
exists, that is, that the medium may by its mere presence influence
the velocity of a reaction. The greatest attention must therefore
be paid to this influence in studying the course of a reaction.

Zeit. phys. Chem. I, 627 et seq. 1887; fi. 41 et seq. 1890.

II. INFLUENCE OF PRESSURE ON THE VELOCITY
OF REACTION.

That the rate of reaction is influenced by pressure is proved by
many of the researches which have been made on the subject.

REISER l has shown that the transformation of moriosymmetric
into rhombic sulphur takes place at 96°. 2 under a pressure of 16
atmospheres, whilst at atmospheric pressure the change in the
opposite direction occurs at this temperature. Later, SPRING and VAX
'T HOFF found that copper calcium acetate, which decomposes into
its constituents at 77° under atmospheric pressure, undergoes this
same decomposition at 40° when the pressure is 6000 atmospheres.

SPRING 2 has prepared compounds of sulphur and arsenic with
various metals by using very high pressures. A great number
of reactions may be brought about by sudden pressure 3.

These effects of pressure will, however, be considered below,
for the present it is sufficient to point out their existence.

The influence of pressure on the rate of reactions taking place
in liquid media has only been examined in a few cases.

BERTHELOT and PEAN DE ST. GILLES 4 could find no difference in the
rate of etherification of an alcohol by an acid at different pressures.

VAN 'T HOFF also found that the rate at which dibromsuc-
cinic acid, when dissolved in water, is transformed at 100°, is in-
dependent of the pressure.

Finally some recent experiments by RONTGEN 5 may be men-
tioned, in which the influence of pressure on the rate at which
cane sugar is inverted by hydrochloric acid was studied. The
pressure used was 500 atmospheres, whilst BERTHELOT and PEAN
DE ST. GILLES worked at 50, and VAN 'T HOFF at 6 atmospheres.

RONTGEN concludes that the rate of inversion is diminished
by pressure. He is, however, not justified in drawing this con-
clusion from his experiments.

l GROTH'S Zeitschrift fur Krystallographie, Vol. 8. p. 593, 1884. Inaugural Dissertation,
Amsterdam, 1883.

2 Bulletins de 1'Academie royal de Belgique, [2] vols. 45 and 49. Berichte 15. 595, 1882.

3 MEYER. Dynamik der Atome. 1883, 393.

4 Ann. Chim. Phys. (3) 66. 45, 1862.

5 WIED. Ann. 45, 98, 1892.

DISTURBING ACTIONS IN GASEOUS SYSTEMS. 31

For if the velocity constants for the inversion be calculated
from his numbers, it is found that the values of the constants
obtained in different experiments with the same solution differ
from each other more considerably, than do the constants ob-
tained • with solutions which have undergone inversion on the
one hand at the ordinary pressure, on the other under a pres-
sure of 500 atmospheres.

The differences observed by RONTGEN in the course of the in-
version under different pressures are accordingly smaller than
the errors in the experiments, which are of not inconsiderable
magnitude, and which can be completely accounted for by the
variations of the temperature of the solutions *.

A measurable acceleration of the reaction should however
occur with weak acids or acids of intermediate strength, as in
such cases, according to the calculations of TAMMANN 2, the external
pressure exerts a very considerable influence on the degree of
electrolytic dissociation of the acid.

Chapter II.
Disturbing actions in gaseous systems.

I. THE ORDER OF MAGNITUDE OF THE DISTURBING
ACTIONS IN GASEOUS SYSTEMS.

While it is fairly easy to eliminate the disturbances which
occur in the course of reactions in liquid systems, and to lay
bare the true character of the course of the reaction in all its
simplicity, so that reactions of this kind form the most convenient
material for studies in chemical dynamics, it is quite different
with gaseous systems. There the irregularities of the reactions
are of such importance that it is frequently difficult to realise
the normal course of the reaction.

When this work originally appeared there was in existence
a number of researches, by other chemists, on the course of

1 See TAMMANN, Zeit. pliys. Chem., 14, 444, 1894.

2 See TAMMANN, Zeit. phys. Chem., 17, 725, 1895.

32 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

reactions in liquid systems, the results of which agreed more or
less with the requirements of the equations which have been
deduced above.

This was the case with the researches of BUCHANAN 1 on the
decomposition of chloracetic acid by caustic soda, and of aqueous
solutions of chloracetic acid; with those of URECH on the birot-
ation of milk sugar 2 and on the inversion of cane sugar 3 ; and
also with those of WARDER4 on hydrolysis; since then they have
become innumerable.

The position is, however, quite different when we turn to
chemical reactions in gaseous systems ; the only researches in this
department, which up to the present time have been brought to
a satisfactory conclusion are those on the rate of change of
arsine and phosphine (VAN 'T HOFF, Koou), and of hydriodic acid
(BODENSTEIN). On the other hand our experimental knowledge of
the disturbances which affect reactions in gaseous systems has
greatly increased without any comprehensive explanation of the
greater part of the phenomena having, so far, been given.

The following observations appear to point to a contact action
of the medium, though other hypotheses have been proposed to
account for them.

(1) The rate of oxidation of phosphorus is affected in a
remarkable way by various gases.

For example the oxidation in air is prevented by mixing the
air with 1/3 of its volume of H2S, 1/50 of ether vapour, x/45o of
ethyl ene, Viooo of PH3, 1/18W of petroleum vapour, or 1/uu of
turpentine vapour 5.

(2) In recent years a great number of cases have been investi-
gated, more especially by DIXON and BAKER, in which the influence of
minute traces of aqueous vapour on chemical changes is apparent G.

1 Berichte 4, 863, 1871.

2 „ 15, 2457, 1882.

3 „ 16, 2270, 1883.

4 Amer. chem. Journ. 3, 1881—82; Berichte 14, 1361, 1881.

5 According to GRAHAM, Phil. Mag. 5, 408, 1834, liquid hydride of phosphorus
shows a similar behaviour.

6 The literature of this subject is given in the Journal of the Chemical Society
1894. (Trans.) p. 623.

INFLUENCE OF MOISTURE. 33

According to DIXON l a perfectly dry mixture of carbon mon-
oxide and oxygen cannot be exploded at all, or only with great
difficulty, by the electric spark. If a minute trace of moisture
be brought into the mixture, the explosion occurs at once without
difficulty. The explosion may also be induced by other gases
such as H2S, NH3, HC1, C2H4, i.e., such as contain hydrogen,
while S02, CS2, C02, C2N2 are without action.

Furthermore the quantity of the aqueous vapour present has a very
great effect on the velocity with which the explosion is propagated.

It is in place, however, to point out here that in other reactions
the presence of aqueous vapour may retard the change; the
rate of decomposition of ammonia at high temperatures according
to THAN ' is diminished by about 98 per cent by the presence of
aqueous vapour , and according to VAN DE STADT 3 the rate of
oxidation of gaseous phosphine is also diminished by it.

Among BAKER'S numerous observations, the experiment in which
phosphorus was found not to burn in very carefully dried
oxygen even when heated to 150° , may be pointed out as par-
ticularly interesting ; it was only after the admission of a small
quantity of moist air that inflammation occurred. 4 Similar results
were obtained with sulphur, carbon, etc.

(3.) Whilst studying the action of hydrogen on chlorine under
the influence of light, BUNSEN and ROSCOE 5 found that the rate
of change was diminished

37.8 per cent ) f 3/iooo of hydrogen,

to the extent of

9.7
60.2

Viooo of oxygen,
'/iooo of chlorine.

PRINGSHEIM 6, DIXON and HARKER 7, and also BAKER 8 have further

1 Phil. Trans. 1884, 618.

2 LIEB. Ann. 131, 121, 1864.

3 Zeit. phys. Cbem. 12, 329, 1893.

4 BAKER unfortunately does not mention the pressure of the oxygen used. See
EWAN'S experiments on p. 68.

5 POGG. Ann. 100, 499, 501, 502, 1857. Also OSTWALD'S Klassiker der exact. Wissen-
schaften, No. 34. p. 81.

6 WIED. Ann. 32, 384, 1887.

7 Manchester Lit. ami Phil. Soc. 1890. OWENS College Researches, 1.

8 Journ. Chem. Soc. 1894, p. 623.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

shown that this change takes place much more slowly when
aqueous vapour is excluded than when it is present.

(4.) The formation of ozone by the electric discharge is com-
pletely stopped by the addition of traces of chlorine, while nitrogen,
hydrogen, and fluoride of silicon are favourable to it !. In this
case aqueous vapour has no effect according to
SHENSTONE 2 and BAKER 3.

A reaction which was carefully studied by VAN
'T HOFF is closely allied to these so called catalytic
actions; he found that the formation of ammonium
carbamate was accelerated by the presence of aqueous
vapour whilst alcohol vapour retards it.

It is to be noticed that the acceleration produced
by the aqueous vapour is not be ascribed to the
simultaneous formation of ammonium carbonate
though this certainly occurs.

Special experiments on this point have shown
that the mixture of steam, ammonia, and carbon
dioxide which may be obtained according to the
equation

NH4.HC03 = C02 -f NH3 + H20,

by volatilising ammonium carbonate, forms in the
first place ammonium carbamate with very great
velocity,

C02 + NH3 = NH2.COOHN,,
and then, very slowly, ammonium carbonate,

NH2.COONH4 + H20 = NH4.HC03 + NH3.

Fig. 7.

The apparatus which was used in the ob-
servations on the acceleration produced by aqueous vapour
and the retarding effect of alcohol vapour is represented in
figure 7.

1 Compt. Rend. 91, 762, 1880.

2 Journ. Chem. Soc. 1888, 53.

3 Ibid. 1894, 617.

FORMATION OF AMMONIUM CAKBAMATE. 35

The side tube C was filled with carbamate und closed before the
blowpipe. The whole apparatus was then filled with mercury and
placed in position in the burette D which also contained mercury.
On heating the salt, the mixture of carbon dioxide and ammonia
produced displaces the mercury from the vessels A and B. When
a sufficient quantity of the mixture is obtained the formation
of the carbamate may be allowed to begin, and the velocity
with which it takes place in the two vessels compared.

This is done by determining the pressures of the gaseous
mixture in the two vessels from time to time, the volume being
maintained constant. This is accomplished by allowing mercury
to flow out of the burette whenever it is on the point of rising
into A or B.

If the apparatus has been properly filled, the velocities of the
reaction in the two divisions of it are found to be exactly equal.

A small quantity of water is then introduced in a little glass
bulb into A. The quantity used is that which can evaporate at
the ordinary temperature into the space available (0.0004 gram,
or 4 per cent, of the carbamate employed).

Both vessels are then warmed in an air bath so as to decompose
the carbamate which has deposited on their walls. In this way
the mixture of carbon dioxide and ammonia is regenerated in A and
B, but with the difference that water vapour is now present in A.

When the two divisions of the apparatus are brought back to
the initial temperature a decided difference in the rates at which
the reaction occurs in them is evident.

The rate in A is approximately doubled by the introduction
of the aqueous vapour.

The retarding influence of alcohol vapour was established in
a similar way, while air had no effect even when present in
fairly large quantities.

Since the existence of these disturbances in the course of a
reaction is proved experimentally in such a variety of cases, it
is not surprising that the greater part of the reactions occurring
in gaseous systems which have been studied up to now do not
follow the equations which we have deduced. l This is the case

1 Sec the exceptions on p. 32.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

with the experiments of BERTHELOT and PEAN DE SAINT GILLES on
etherification, and with those of LEMOINE on the formation and
decomposition of hydriodic acid.

The following changes also, which were investigated by VAN
'T HOFF, lead to similar results : —

1. The polymerisation of formaldehyde.

2. The polymerisation of cyanic acid.

3. The transformation of moist electrolytic gas
into water.

4. The transformation of dry electrolytic gas into
water.

1. Polymerisation of formaldehyde.

Through the researches of HOFMANN l we know
that gaseous formaldehyde possesses the formula
CH^O, and that this body gradually changes into
a solid polymeric substance, the formula of which
is very probably C3H603.

This reaction was investigated as it is of special
interest, being probably trimolecular.

The apparatus used (fig. 8) consists of a large
round flask A, attached to a barometer tube B.
After evacuating it as far as possible with the air pump, (to
about 2.01 mm.), the gaseous formaldehyde, evolved by heating
the compound C3H603 in a small retort, was admitted over
mercury.

Having thus filled the apparatus it is placed in position in
the mercury of the burette C 2 ; the volume is maintained con-
stant and the pressure of the unchanged formaldehyde measured
from time to time. The numbers obtained are given in the fol-
lowing table 3.

Fig. 8.

1 Berichte, 2, 156, 1869.

2 Compare with D in fig. 7, page 34.

3 The total pressure, reduced to 0°, is corrected for the initial pressure of the air
in the apparatus (2.01 mm.).

POLYMERISATION OF CYANIC ACID.

Time.

Pressure of the
formaldehyde.

23.6 mm.

.3 hours.

22.1 „

.5 „

20.6 „

days.

18.8 „

16.8 „

»i

15.0 „

11.8 „

months.

9.5 „

4.9 „

2.9 „

The course of this change does not correspond in any way
with that required
by the equations
which we have pro-
posed.

The same result
was always obtained
when the experiment
was repeated. l

2. Polymerisation of
cyanic acid.

The change of cy-
anic acid into cyame-
lide, which occurs in
the liquid acid with
explosive violence,
takes place in the gaseous acid so slowly that it is specially well
suited for a dynamical study.

1 The reaction does not take place so smoothly as might be desired, for simultane-
ously with the formation of the polymer, its decomposition takes place, and a final
maximum pressure is therefore obtained. This is in agreement with the fact that the
polymer sublimes (TOLLENS, Berichte, XV, 1629, 1882). The deviations observed
are however too large to be ascribed wholly to this cause.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The apparatus used in this investigation consisted of a cylin-
drical vessel A (fig. 9) to which a small manometer B was
attached. The liquid cyanic acid which was employed in filling
it was prepared by heating anhydrous cyanuric acid in the

retort H, and condensing it in
the cooled receiver J, (fig. 10).
The liquid acid is poured into the
small, well cooled bottle C, which
is then connected with the tap F,
by means of which its contents
may be put in communication
with the air pump. The air still
remaining in the bottle having been pumped out, it is put in
communication with the apparatus A B which has previously
been fused to E by means of the side tube D, and is vacuous.
After filling, the apparatus is disconnected by means of the
blowpipe and is then ready for the measurements of pressure.
The following table contains the results which were obtained.

Fig. 10.

Time.

Pressure of
the cyanic acid.

Time.

Pressure of
the cyanic acid.

139 mm.

23 days

89.1 mm.

1 day

136.8 „

26 „

85.5 „

2 days

131.8 „

27 „

84.1 „

3 „

128.4 „

29 „

82.3 „

4 „

125.4 „

45 „

68.4 „

5 „

121.4 „

50 „

65.9 .,

7 .,

116.7 „

2 months

56.5 „

9 „

112.2 „

4 „

44.1 „

12 „

106.1 „

5 „

39.7 „

13 „

104.1 „

6 „

33.3 „

16 „

99.2 „

8 „

30.3 „

19 „

94.7 ,,

10 „

27.6 „

21 „

91.5 „

20 „

13.0 „

Here, also, the measurements do not agree at all with any of

FOKMATION OF WATER.

the equations proposed. The experiment, repeated several times,
always yielded the same result.

3. The transformation of moist electrolytic gas into water.

The transformation of electrolytic gas into water was found
to take place at 440° sufficiently slowly to admit of its course
being followed; this change, especially attractive on account of
its simplicity, was therefore carefully studied.

The apparatus which was employed with moist electrolytic
gas resembled a large thermometer ; it was filled by means of

the

Fig. 11.

gas burette * A (fig. 11) which contained the electrolytic
gas. By means of the tap B the part of the apparatus to
be filled (shown in the figure in a horizontal position; may be
connected either with the air pump through D, or with A; in
this way it is first evacuated and then filled with the gaseous
mixture, after which, the tap C being closed, it is sealed off be-
tween C and B. Some mercury is now introduced into the part
of the tube to the left of the tap, which is then opened so as

Fig. 12.

to obtain a short index of mercury shutting off a column of air
of suitable length in the capillary tube of the apparatus (L in
fig. 12). The tube is finally sealed up before the blowpipe.

The bath in which the apparatus was heated (fig. 13) consists
of an iron cylinder A, containing boiling sulphur. Two windows
of mica, one of which is visible at C, permit the height of the
sulphur vapour to be observed.

1 This was constructed in the way described by BUNSEN, Gasometrische Methoden,
1877, p. 76.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The bath was heated in a PERROT'S gas furnace provided with
a gas regulator D l.

The quantity of the gaseous mixture remaining after the heat-
ing had been continued for a known interval of time, was deter-

Fig. 13.

mined by placing the apparatus in a horizontal position in the
water M, (fig. 12), so as to equalise the temperature in all its
parts. The length of the column of air, L, was then measured
on the scale which is shown in the figure. This length is in-
versely proportional to the pressure, and thus to the quantity
of the residual gas 2.

The results obtained are as follows: —

Time in hours.

Quantity of
electrolytic gas.

Time in hours.

Quantity of
electrolytic gas.

0.871

0.974

0.863

0.951

0.853

0.931

0.846

0.915

0.839

0.902

0.831

0.893

116.5

0.808

0.881

1 Constructed by HeiT CLAESSEN.

2 Both the electrolytic gas and the column of air are saturated with aqueous vapour.

FORMATION OF WATER.

The results of this experiment, which was repeated several
times, also do not agree with our equations.

4. The transformation of dry electrolytic gas into water.

For these experiments the following alterations were made in
the apparatus just described ; the reservoir A \ in figure 14, is

filled in the same way as formerly
through E, but it is now made to
communicate with the parts C, D
and F, which are united by means
of a flexible tube containing mer-
cury.

This arrangement allows a por-
tion of the gaseous mixture to be
transferred from A to C, (by
lowering F), in order to dry it by
contact with sulphuric acid con-
tained in C over the mercury.

While the apparatus is being-
heated in the sulphur bath (not in
the apparatus B shown in the figure,
which will be mentioned later) the
whole of the gaseous mixture is
contained in A, and the tap D is
closed.

When the mixture has been heated for the time desired, the
tap is opened and the tube F raised and lowered about a hundred
times so that the gas is dried while it is cooling.

The quantity of the gaseous mixture remaining is then deter-
mined by means of its pressure at constant temperature and
volume 2.

The results are the following: -

1 The lower part with the three side pieces serves to prevent A from coining in
contact with the iron cylinder in which the sulplur in boiled.

2 The reservoir A is placed in water from the water supply, and the temperature, the
height of the barometer, and the difference in level between the mercury in C aud F
when the gas occupies a given volume, read off by means of the cathetometer.

Fig. U

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

Time in hours.

Pressure of the electrolytic gas.

997.7 mm.

980

965.6 „

953.2 „

29.5

938.4 „

38.5

926.4 „

47.75

914.9 „

905.2 „

67.5

894.9 „

78.5

885.3 „

99.5

871.1 „

126.66

860

Here also the equations which we have deduced are entirely
at fault.

The researches carried out by KRAUSE and V. MEYER l in the
year 1891, and by ASKENASY and MEYER 2 in 1892 on the trans-
formation of electrolytic gas, which will be more fully considered
later, and which were made with electrolytic gas which had
been prepared in a state of purity with the utmost care, gave
the same results; disturbances occur in this case which com-
pletely mask the normal course of the reaction.

The experiments described justify the conclusion that while
the course of a reaction in a liquid medium is normal, even
when no special precautions are adopted, that is, it agrees with
the equations which we have deduced, this is, in general, by no
means the case with gases.

1 LIES. Ann. 264, 85, 1891. Naturwissenschaftliche Rundschau, VI, 349.

2 LIEB. Ann. 269, 49, 1892.

II. THE NATURE OF THE DISTURBING ACTIONS IN

GASEOUS SYSTEMS. ACTION OF THE WALLS

OF THE VESSEL.

Formation of cyamelide and of water ; decomposition
of phosphine.

Since the deviations from the normal course of change in
gaseous systems appeared be of a secondary nature, the question
as to their cause presented itself.

It was found possible to prove by experiment the existence
of disturbing actions in the cases which have been described.

Turning in the first place to the disturbing actions in liquid
systems, the volume occupied by the reacting substances must
be taken into account ; this volume must be a vanishing quantity
when compared with the whole volume of the system. This
condition is satisfied when we are dealing with gases under
atmospheric pressure; the other condition, that the nature of the
medium shall remain unchanged during the reaction is, however,
not satisfied in gaseous systems.

It is clear that in a reaction taking place between gaseous
substances, as for example the formation of water from electro-
lytic gas, the medium undergoes a profound change. In the
example mentioned, the medium at the beginning of the process
is electrolytic gas, at the end, it is the aqueous vapour which
has been formed.

In addition to the two disturbing actions which are found in
liquid systems, there are two other causes of irregularity which
exert their influence more especially in gaseous systems, viz : -

1. The area of the surface of the walls of the vessel.

2. The nature of the surface of the walls of the vessel.

1. Influence of the area of the surface of the walls of the vessel.
Polymerisation of cyanic acid.

The apparatus shown in figure 15 was used to investigate the
effects of the walls of the vessel on the rate of formation of
cyamelide *.

l On this ac-tio.i, see NAUMANN, LIEB. Ann. 160, 16, 1871.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The divisions A and B have the same volume, but the areas
of their walls are in the ratio 6:1.

A little anhydrous cyanuric acid having been
brought into D the apparatus is placed in
a burette containing mercury and evacuated
by means of the air pump which is attached
to it at D. The tube D is then closed
before the blowpipe.

By heating D both compartments are filled
with gaseous cyanic acid. On lowering the
apparatus communication between A and B
is cut off, after which the pressure of the
unaltered cyanic acid is measured from time
to time.

These measurements of the pressure show
that the reaction takes place at entirely
different rates in the two divisions.

. 188.4 mm.

f 146. 8 „ in A.
"157 B.

Initial pressure . .
After one day . .

Fig. 15.

Ratio of the velocities in A and B, -

1.33 : 1.

The velocity in the division with the greater surface is there-
fore much the greater.

2. Influence of the nature of the surface of the ivalls of the vessel.

Since the superficial area of the walls of the vessel influences
the rate of the reaction, it may be surmised that the nature of
these walls will also have some action.

This is a matter which is worthy of special attention in dy-
namical studies in which the reaction itself produces some change
in the walls, as for example when a solid product of the reaction
is deposited on them.

Although observations of this kind had previously been made \

NAUMANN, LIEU. Ann. 160, 16, 1871.

NATURE OF THE WALLS OF THE VESSEL. 45

it was still thought to be of special importance to study the
phenomena more completely, in order that their effects might
be eliminated.

Investigations were made on,

a-. The polymerisation of cyanic acid.

b. The transformation of electrolytic gas into water.

6'. The decomposition of phosphine.

a. Influence of the nature of the ivalls of the vessel on the
polymerisation of cyanic acid.

The influence of cyamelide, which is deposited on the walls
of the vessel during the polymerisation of cyanic acid, was stu-
died by means of the apparatus represented in figure 7.

The division B was filled with gaseous cyanic acid, in the
way which has already been described (p. 35). As soon as the
walls had, in consequence of the polymerisation, become coated
with cyamelide, the unaltered cyanic acid was divided between A
and B by raising the apparatus; the communication between the
two vessels was then interrupted by lowering it again, and the
measurements of the pressure proceeded with.

The following results were obtained ;

Initial pressure 49.5 mm.

(44.5 mm. in A.
Pressure alter one day . . . . {

\ 32.4 „ „ B.

Ratio of the velocities in A and B, —

1 : 3.42.

The rate of the reaction is therefore rather more than trebled
in the division the walls of which are coated with cyamelide.

b. Influence of the nature of the surface of the ivalls on the
transformation of electrolytic gas into water.

1. Older experiments.

The results obtained in the study of this reaction (p. 40) ap-
peared to point to a disturbance, arising during the progress of
the reaction, and retarding it more and more as it proceeded.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The apparatus shown in figure 14, when filled with electro-
lytic gas, gave the following results,

Initial pressure ......... 997.7 mm.

Pressure after heating to 448° for

5 hours ........... 980

Diminution of pressure per hour . 3.5 ,,

After having been used for 130 hours, the same apparatus,
when filled afresh, gave: —

Initial pressure . . . 801.1 mm.
Pressure after heating

to 448° for 20 hours 788.8 „
Decrease of pressure

per hour .... 0.6 .,

The change in the nature of
the walls, produced by heating
the vessel for 130 hours, has thus
reduced the velocity of the reac-
tion to one sixth of its original
value.

This result was confirmed by
means of the apparatus repre-
sented in figure 16.

The vessel A, which had been
used in the experiments just men-
tioned, and which had therefore
been heated for 150 hours, was
used along with a second, new vessel B of the same shape.
The two were connected by means of a capillary tube C D.
After evacuation, through E, both vessels were filled with elec-
trolytic gas, and a column of mercury was introduced into C D
in order to interrupt the communication between the vessels, and
to measure the pressure in them-; E was finally closed before
the blowpipe.

The two vessels were heated in the same way, in two PERROT'S
gas furnaces provided with therm o-regulators (see p. 40). They

Fig. 16.

NATURE OF THE WALLS OF THE VESSEL.

were immersed in the vapour of boiling sulphur contained in
cylinders of the form described on page 39.

The heating was discontinued from time to time, the vessels
allowed to cool, and immersed in water from the water supply
to bring them to the same temperature.

The height of the mercury column was then read off on the
millimetre scale.

Time in
hours.

Height of mercury column.

Difference in
velocity per hour.

Old apparatus.

New apparatus.

0
37.5

111.75
100.0

111.0
123.0

0.63

The result is clear; the formation of water takes place consid-
erably more slowly in the apparatus which has already been
used, than in the new one.

The change which occurs in the walls of the vessels in these
experiments, may probably be accounted for by a superficial de-
vitrification owing to the action of the hot aqueous vapour on
the glass ; although this is scarcely visible to the naked eye,
it exerts, as we have seen, an enormous influence on the velocity
with which the reaction proceeds.

It is, however, to be noticed that devitrification of the walls
of the vessel does not always retard the reaction ; the experiments
of KRAUSE, ASKENASY and V. MEYER, which will be considered
below, show that the very opposite may occur in the trans-
formation of electrolytic gas into water.

2. More recent experiments.

The laborious experiments of V. MEYER, KRAUSE and ASKENASY \
which were briefly mentioned on page 42, are to be consi-
dered here.

Sec literature mentioned on p. 42.

48 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

Since BUNSEN and ROSCOE had observed that exceedingly small
quantities of impurity, have a very great influence on the normal
course of the reaction between chlorine and hydrogen l, MEYER,
KRAUSE, and ASKENASY took pains to prepare absolutely pure
electrolytic gas for use in their experiments. With electrolytic
gas containing traces of other gases, they had previously ob-
tained entirely irregular results.

Their experiments were performed as follows : - - Small glass
bulbs, containing about 20 cc., after being filled with the
explosive gas, were heated for a certain time, either in a liquid
bath, or in the vapour of a boiling liquid.

The final experiments were made with an extremely pure
mixture of oxygen and hydrogen prepared by electrolysis, which,
in order to avoid impurity, had been passed for 10 — 14 days
through the bulbs which were to be filled, (the bulbs being
united with each other by means of glass capillary tubes). It
was found that the normal course of the reaction could not be
realised.

For example, two very carefully cleaned glass bulbs were
heated simultaneously, for exactly two hours, in the same bath,
(phosphorus sulphide, boiling at 518°), after which the quantity
of electrolytic gas remaining was determined.

The results are as follows: —

Number of the experiment I II III IV V

% of the electro- ( Bulb 1. 26.41 27.83 28.2 53.71 63.29
ly tic gas combined \ „ 2. 19.34 100.00 100.0 57.29 100.00

From these results, the only conclusion possible is, that even
the most carefully cleaned glass surfaces possess irregularities
which exert a variable influence on the transformation of elec-
trolytic gas, and that the surfaces of two glass bulbs which have
been prepared with the greatest care in the same way, may be
sufficiently different, or may become so during the reaction, to
account for the entire irregularity in the results of the experiments.

The attempt to prepare identical smooth bulbs was abandon-

1 See page 33.

NATURE OF THE WALLS OF THE VESSEL. 49

ed, and the internal surfaces made completely rough, as it was
thought possible that in this way they might be more easily
obtained the same. This remedy was however a complete failure,
as the following numbers show: -

Etched bulbs l]

Percentage of electrolytic gas transformed ( 1 . 33.8
into water. I 2. 51.1

The exclusion of glass surfaces was also unsuccessful. Glass
bulbs coated internally with silver yielded results similar to those
obtained with the etched ones.

Silvered bulbs.

L II. III.

Percentage of electrolytic gas I Vessel 1. 19.8 7.5 15.6
transformed into water \ „ 2. 97.7 92.9 35.2

These bulbs were heated in aniline vapour, at 183°, for two
hours, it having been found that the change takes place at a
considerably lower temperature in contact with a surface of silver,
than in glass vessels.

It has already been noticed, that MEYER and ASKENASY found
that the devitrification, which probably occurs in consequence of
the action of the heated aqueous vapour on the walls of the
glass vessels, does not always retard the formation of water, as
the older experiments of VAN 'T HOFF (p. 47) appear to show,
but that the results are completely irregular in this respect also.

Bulb previously heated
to 518° for

Percentage of electrolytic gas New bulb 22 24 26 28 hours,
transformed into water at 518° 24 . 81 21.8 29.3 78.7 37.4

c. Effect of the nature of the ivalls of the vessel on the
decomposition of gaseous phosphine.

In the course of an investigation on the decomposition of
gaseous phosphine at higher temperatures, D. M. KOOY " has also

1 Totally irregular results were also obtained in bulbs which had been protected
from light. In one series of experiments the percentage of gas which was changed
into water varied from 11.3 to 82.3.

! Zeit. phys. Chem. 12, 155, 1893. Inaugural Dissertation, Amsterdam, 1892.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

recently observed the effects of the surface of the vessels on
the velocity of the reaction. The experiments were made with
the apparatus represented in figure 14.

The following table contains the experimental results. (Tem-
perature = 446°).

New vessel1.

Time in hours.

Pressure in mm.

Velocity constant.

715.21

—

28.17

765.88

0.00236

33.42

773.89

232

38.50

781.59

232

45.33

793.93

238

Old vessel2.

Time in hours.

Pressure in mm.

Velocity constant.

706.02

—

29.58

830.35

0.00637

33.58

843.76

637

39.58

861.38

636

44.58

876.18

641

It must, however, be regarded as being doubtful, whether the
velocity of this reaction is always greater in vessels which
have already been heated.

III. THE NATURE OF THE DISTURBING ACTIONS
IN GASEOUS SYSTEMS.

a. The rate of oxidation of phosphine.

According to the equations which represent the relation between
the concentration of the reacting substances and the velocity of

1 The values of the velocity constant k have heeh calculated by the equation on
p. 3, common logarithms being substituted for those to the base e.

2 This vessel had already been used for a considerable time in similar experiments.

INFLUENCE OF PRESSURE ON OXIDATION. 51

the reaction, the latter increases when the former increases.

There are, however, a number of facts which seem to show
that the opposite to this is true.

FOURCROY l found that at the ordinary temperature and normal
pressure, pure oxygen does not act upon phosphorus, whilst air
oxidises it vigorously.

In 1798, VAN MARUM 2 observed that a piece of phosphorus
glows much more brightly in diluted air than in air under the
normal pressure, and that the phosphorus even takes fire at low
pressures if it be wrapped in a little cotton wool.

In 1817, HOUTON DE LABILLARDIERE 3 observed, in the course of
an investigation on phosphine, a very remarkable phenomenon,
which be described in the following words: —

"Le gaz hydrogene protophosphore se distingue du perphos-
phore en ce qu'il n'a pas la propriete de s'enflammer par le con-
tact de Pair. II est cependant a remarquer qu'on peut enflammer
ce gaz dans Fair, a la temperature ordinaire en le rarefiant.
On s'assure de ce fait en introduisant dans une eprouvette tres-
forte et longue, entouree d'un grillage de fil de fer pour eviter
les morceaux si le vase venait a casser, de 1'air ou de 1'oxigene
et de Fhydrogene protophosphore, en maintenant le mercure dans
1'eprouvette au niveau du mercure exterieur; alors, en elevant
1'eprouvette de maniere que le mercure de 1'eprouvette soit a
deux decimetres environ au-dessus du mercure du bain lorsqu'on
opere a 20° C , il se produit tout-a-coup une detonnation dans
1'eprouvette."

This experiment appears to have received no special attention.
DUMAS 4 repeated it and showed that the presence of an excess of
phosphine is necessary for the success of the experiment. (2 vols.
PH3 to 1 vol. 02.) DAVY 5 appears also to have noticed something
similar.

He says: - - "I found that phosphuretted hydrogen produced

1 Meaioires de 1'acad. des Sciences, 1788.

Verhandelingen uitgegeven door Teylers Gcnootschap. 10, 1798.
" Ann. Chim. Phys. (2) 6, 304, 1817.

4 Ann. Chini. Phys. (2), 31, 119, 124, 1829. See also ROSE, POGG. Ann. 24,
127. 1832.

1 Phil. Trans. 1817, 49.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

a flash of light when admitted into the best vacuum, that could
be made by an excellent pump of Nairn's construction."
To these facts the following similar ones may be added.
Arsenic, and sulphur begin to oxidise, according to JOUBERT \
only when the oxygen is sufficiently dilute.

FRIEDEL and LADENBURG 2 found that silicon hydride behaves in
a similar way, and according to BERTHELOT, nickel
carbonyl does so also.

REICHER and JORISSEN 8, however, found that the
last named substance is still spontaneously inflamm-
able in oxygen under a pressure of 13 atmospheres.

Further, according to ENGELMANN 4, oxygen appears
to have a more stimulating action on certain low
organisms when its pressure is decreased.

LABILLARDIERE'S experiment was repeated with the
apparatus shown in the accompanying diagram (fig. 17).
The tap C being closed, the tube is filled with
mercury, the mixture of phosphine and oxygen intro-
p duced, and the opening, F, closed with a cork. D
is then put in communication with the air pump,
and the tap, C, opened. The volume of the mixture
of gases increases, and an explosion takes place.

Fig. 17.

The observation of LABILLARDIERE having been con-
firmed in this way, the conditions under which the
phenomenon occurs were more carefully investigated.
The investigation could not however be begun,
until a special cause of the inflammation of the mixture
of phosphine and oxygen, had been discovered and eliminated.
It was found that this inflammation may be caused by move-
ments of the mercury which is in contact with the gaseous
mixture.

The following experiment shows that the mixture is so sensitive

1 These sur la Phosphorescence du Phosphore, 1874, Paris.

2 Ann. Chim. Phys. (4), 23, 430, 1871.

3 Maandblad voor Natuurwetenschappen, 1894, No. 1.

4 Botanische Zeitung, 1882, p. 320.

KATE OF OXIDATION OF PHOSPHINE.

to such movements, that the use of mercury is attended with
great difficulties.

The apparatus shown in figure 18 being initially full of
mercury, a mixture of 2 vols. of phosphine and 5
vols. of air is brought into it through A, which is
then closed; mercury is then pumped out through
C and E, as in the previous experiment, so that the
mixed gases are expanded until they fill the whole
apparatus. (75 vols.)

The taps C and B are now closed, the dilute gas
filling the two separate divisions B and D, in one of
which a globule of mercury has been left Combustion
is now produced by the slightest shock in the division
containing the globule of mercury. The
reason of this may possibly be found in
local dilutions of the gas, produced by
the mobile mercury. (See the explanation
given below.)

In order to avoid this cause of com-
bustion, the mercury was replaced by a
viscid solution of calcium chloride in
most of the experiments which follow.

Using the apparatus in figure 17,
it was proved that the explosion is not
produced by expansion alone. No change
is produced by a sudden, and much more considerable
expansion than that which gave rise to the ex-
plosion in the former experiments; the gaseous mix-
ture may be preserved in this dilute condition without
undergoing any change whatever ; the explosion
is produced, however, by the diminution of volume
which takes place when the tap is opened, after D Fig. 19.
has been brought below the surface of the calcium chloride solution.

Investigation of the rate of oxidation of phosphine near the
explosive limit.

Having cleared up the nature of the reactions which occur in the

Fig. 18.

ijr

DISTURBING ACTIONS- IN GASEOUS SYSTEMS.

slow oxidation of phosphine, J. D. VAN DE STADT l made a careful
study of the rate of oxidation.

For this purpose he used the apparatus represented in figure 19.
M serves as a manometer ; the apparatus having been completely
filled with mercury, with the help of an air pump, the gases
are admitted through g, mercury flowing out through h; the
volume of the gas is obtained by weighing the latter. The
pressure was read with a cathetometer, and the gas was in
contact with calcium chloride solution.

First series of experiments. After filling the apparatus, it was
heated to 50° in a water bath, for periods of one hour; at the
end of each period the pressure was diminished by about 100 mm.
by running mercury out through h.

No. 1. 2.64 cc. PH., and 1.55 cc. 09.

Initial pressure.

Final pressure.

Diminution
per hour.

n/0-age of the
initial pressure.

649 mm.

640 mm.

9 mm.

1.4

553 „

546 „

7 „

1.2

463 „

459 „

4 „

0.9

On further dilution the explosion occurs.

No. 2. 2.46 cc. PH3 and 2.54 cc. 02

589.4 mm.

588.0 mm.

1.4

0.24

524.7 „

521. 92 „

1.4

0.26

419.6 „

418.4 „

1.2

0.28

No. 3. 2.65 cc. PH3 and 1.58 cc 0,

623 mm.

612 mm.

1 1 mm.

1.8

521 „

510 „

H „

2.1

446 „

439 „

7 „

1.6

364 „

Bxplosionat50°.

1 Zeit. Phys. Chem. 12, 322, 1893. See also p. 20.

2 Duration of this experiment — 2 hours.

RATE OF OXIDATION OF PHOSPH1NE.

It follows from these data,

1 . That temperature, pressure, and quantity remaining approxi-
mately the same, the velocity of change varies considerably ; viz.
from 0.2 in No. 2 to 2.0 in No. 3.

2. That the explosion is not preceded by any well marked
acceleration of the reaction, but that large velocities may occur
without any explosion (No. 3), while small ones may be followed
by an explosion. (No. 1).

Second series of experiments. In the experiments No. 1 and
No. 3, the explosion took place during an operation, - - in No.
1 on diluting, and in No. 3 while bringing the apparatus into
the water bath ; in order to avoid these external influences com-
pletely, the artificial decrease of the pressure at the end of each
hour was abandoned, and the apparatus simply left to itself at
50°, so as to bring about spontaneous inflammation if possible.

Some calcium chloride solution was again added, as in the
first series. All the pressures given relate to the temperature
50°, at which they were measured.

No. 4. 1.99 cc. PH3, and 1.03 cc. 02.

Time in hours.

Pressure at 50 °.

Decrease of
pressure p. hour.

°/0-age of the
initial pressure.

0
1

2
3
4
5

763 mm.
739
716.5
694.5
671
643.5

24
22.5
22
23
27.5

3.2
3.0
3.1
3.3
4.1

The explosion took place some minutes later.

No. 5. 2.14 cc. PHo and 1.12 cc. 02.

765 mm.

—

757

0.5

737

3.3

0.5

724

3.2

0.5

696.5

0.4

685.5

2.8

0.4

665

3.4

0.5

655

3.3

0.5

The explosion occurred.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

No. 6. 1.44 cc. PH., and 1.48 cc. 02.

Time in hours.

Pressure at 50°.

Decrease of
pressure of hour.

°/0-age of the
initial pressure.

708.5

—

705

1.8

0.2

696

2.3

0.3

675

2.3

0.3

664 . 5

2.6

0.4

648

2.8

0.4

633

2.5

0.4

621

2.4

606

2.5

0.4

The explosion took place after several hours.

The result is the same as in the first series ; unexpectedly
large variations in the velocity are found, - - on the one hand
4.0 in No. 4, on the other, 0.4 in No. 6. The explosion is not
preceded by any noticeable acceleration ; it may occur when the
velocity is small (for example, 0.4 in No. 6) or it may not occur
when the velocity is large, (for example, 3.0 in No. 4).

It may therefore be regarded as proved, that although dilution
causes the explosion, yet the latter is not the culmination of an
acceleration of the reaction produced by the dilution. The
dilution seems rather to act in such a way that suddenly
something new comes into play ; this conclusion is in accordance
with the results obtained by IKEDA l in the oxidation of phophorus,
which have been confirmed by EWAN. 2 Both found that within
certain limits of pressure the process is quite normal, its velo-
city being proportional to the pressure of the oxygen.

Regarding the limiting pressure at which explosion occurs,
two cases must be distinguished according as we are dealing
with dry, or with moist mixtures of gases.

1. The explosive limit for dried mixtures.

There is, in this case, an upper limiting pressure of oxygen
above which the explosion does not occur.

1 Journ. Coll. Science. Imp. Univ. Japan, VI, 43. 1893.

2 Zeit. phys. Chem., 16, 315, ^1895.

EATE OF OXIDATION OF PHOSPHINE. 57

The determination of this limit is, as VAN DE STADT found,
extremely difficult, if the gases be completely dried.

The phosphine usually burns when it conies in contact with
the oxygen, with a visible flame, or formation of a dense cloud,
complete combustion taking place.

At the ordinary temperature, a definite result could only be
obtained in a few experiments.

The observations were made in a thick walled tube closed at
both ends by taps. This was first filled with mercury, after
which the gases were introduced through the upper tap, the
mercury displaced through the lower one being weighed in order
to measure the volume of the gases. After closing the upper*
tap and mixing the gases, they were caused to expand by allow-
ing mercury to flow from the lower tap into a vacuous space;
this was done very slowly and without shaking, (compare page 53),
for which purpose the lower tube was drawn out to a capillary.

Only one of the many experiments in which the gases were
dried over phosphorus pentoxide was successful.

2.09 cc. 02; 0.51 cc. PH3 ; Volume at the explosion 21.9 cc.

2 09
Pressure of oxygen 9^ Q =0.1 atmosphere. (10°)

After drying over soda-lime the following experiment was
successfully carried out without any cloud being formed.

0.54 cc. 02; 0.95 cc. PH3; Volume at the explosion 5 cc.

Pressure of the oxygen - - = 0.11 atmosphere.

The upper limit of pressure was also found to be 0.1 atmo.
after drying over crystallised glycerine.

A lower limit of pressure does not exist in the case of dry
gases. The explosion always occurs when working with dry
gases, even at the greatest dilution.

2. The explosive limit with moist gases.

VAN 'T HOFF determined the volume at which a mixture of 1
cc. of phosphine, and 0.5 cc. of oxygen explodes, by means of

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

the apparatus shown in figure 18. The mercury was covered by
a layer of calcium chloride solution.

The explosion was produced sometimes by expansion, some-
times by compression following on a sudden expansion, (com-
pare p 53.) The volume of the gas at the moment at which the
explosion took place, was measured on the scale on the tube A;
the reddish-brown deposit which covers the walls of the tube
after the explosion, facilitates the reading considerably.

The following table contains the values of the volumes, (in cc.)
occupied by 1 — 5 cc. of the mixture at the time of the explosion;
the corresponding pressures of the oxygen are also given.

Expansion.

Compression.

Volume of the
mixture.

Pressure of
oxygen in atmos.

Volume of the
mixture.

Pressure of
oxygen in atmos.

3.5 cc.

0.14

9.5 cc.

0.05

5.1 ,,

0.1

6.8 „

0.07

7.35 „

0.068

3.9 „

0.13

11.7 „

0.04

8.9 „

0.06

—

9.9 „

0.05

—

5.5 „

0.09

—

3.3 „

0.15

— '

—

5.6 „

0.09

Wibh moist gases, there are therefore, two limits to the oxygen
pressures at which the explosion takes place; an upper one,
which as the table shows, lies between 0.04 and 0.14 atm. in
these experiments, and a lower one, which varies between 0 . 05
and 0.15 atm. To what is this lower limit, which as we have
already seen does not exist when the gases are dry, to be ascribed?

Special experiments were made by VAN DE STADT on this point,
which showed that moisture retards the reaction. Since the gas-
eous mixture was preserved over an aqueous solution of calcium
chloride, the proportion of aqueous vapour in it must obviously
increase when it is expanded, and its retarding influence, therefore
become more pronounced, thus giving rise to a lower limit.

RATE OF OXIDATION OF PHOSPHINE. 59

The fact that traces of aqueous vapour completely stop the
change at great dilutions, is of some interest, since the expe-
riments of DIXON, BAKER, and others have shown that the presence
of water is absolutely necessary in many reactions. l

If the PH3 had been dried over phosphorus pentoxide, soda-
lime, or crystallised glycerine, it frequently took fire spontaneously
in the air, as if it were P2H4. This fact explains the curious
behaviour of mixtures of phosphine and oxygen, which, as ROSE 2
and VAN 'T HOFF observed, often explode only after standing for
some days.

VAN 'T HOFF brought together 130 cc. of phosphine and 8 cc.
of oxygen and noticed, that as the diffusion progressed, a cloud
was formed, this being followed, on one occasion after two
hours, on another after 20 hours, by an explosion.

If the oxygen be replaced by air the same phenomenon occurs
as soon as the oxygen has reached the necessary pressure.
15.5 cc. of air and 49 cc. of phosphine being mixed, for example,
the explosion did not occur until 30 hours had elapsed.

As soon as the hygroscopic substances H P02 and H3P03 3,
which are formed at first by the slow oxidation, have taken up the
moisture present, and thus dried the gases, the explosion takes place.

The table on the preceding page shows that when two limits
of pressure exist, they lie close together.

The upper limit of pressure has been accurately determined by
VAN 'T HOFF at the ordinary temperature,
and by VAN DE STADT at 50°.

VAN 'T HOFF used the apparatus shown
in figure 17. By means of the pipette,
(fig. 20), the gases were brought into the
apparatus in measured quantities.

The pipette was filled with mercury and
connected to the oxygen gasholder, the
tubes by which the connection was made
having first been freed from air by filling Fig. 20.

1 See p. 33.

-' POGG. Ann. 24, 158, 1832.

3 See p. 20.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

them with mercury. The taps F and H were then opened so
as to fill the pipette with gas up to a mark near Gr, which is
not shown in the figure. The taps were then closed, and the
pipette, containing 0.5 cc. oxygen between F and Gr, disconnected.
The tube between E and F was then filled with mercury, and F
brought into the lateral opening of the explosion apparatus A,
which had previously been filled with a viscid solution of calcium
chloride.

The phosphine was introduced in the same way, after which the
expansion was brought about in the manner described previously,
(page 52).

In this way, mixtures containing 0.5 cc. oxygen and varying
quantities of phosphine were examined. The following table
contains the results obtained.

PH3

CC.

02
cc.

Volume at
which
the mixture
exploded.

Explosion pressure in atmo-
spheres of the

PH3.

02.

0.5

0.1

0.5

3.3—11.7

0.19

0.096

1.5

0.5

4 - 8.5

0.28

0.092

0.5-

4.3— 7

0.38

0.095

2.5

0.5

5 - 9.8

0.38

0.075

0.5

9.5—14

0.27

0.045

3.5

0.5

6.2—14

0.41

0.059

0.5

9.6

0.62

0.052

While, therefore, the ratio of the quantity of phosphine to
that of oxygen increases from 1 to 12, and the pressure of the
phosphine at the moment of the explosion increases with the
quantity of it, the pressure of the oxygen remains approximately
YIO atmosphere l.

VAN DE STADT found, that also at 50° the upper explosive
limit corresponds to a definite pressure of the oxygen, which

1 It is to be noticed tliat the same limit was obtained with dry mixtures at tht
ordinary temperature (p. 57).

RATE OF OXIDATION OF PHOSPHINE.

however, is at this temperature considerably higher, viz. 180 mm.
approximately. This result is analogous to that obtained by
JOUBERT, who found that the pressure above which phosphorus
ceases to be luminous in oxygen gas, rises with rising temperature.
If the gases are saturated with moisture, and at the ordinary
temperature, the limiting pressure is depressed somewhat, owing
to the presence of the water vapour, (as it is also by increasing
the Quantity of the phosphine, see the foregoing table). The
following table shows the effect of moisture.

Final

cc 02.

cc. PH3.

volume.

Pressure of oxygen.

Temp.

1.16

3 17.9

0.065

14°

0.9

2.05 13.1

0.069

11°

1.02

2.1

12.6

0.071

14°

1.01

1.9

13.9

0.088

11°

b. The rate of oxidation of Phosphorus, Sulphur, and Aldehyde.

I. PHOSPHORUS.

The slow oxidation of phosphine having been found to be
unsuitable for the study of the connexion between the velocity
of the change and the concentration of the oxygen, owing to
the explosion which occurs preventing further measurements,
phosphorus, sulphur, and aldehyde were studied from this point
of view by T. EWAN. l

1. Phosphorus in moist oxygen,
a. Sate of oxidation in air.

This had already been studied by IKEDA 2. EWAN first repeated
some of the experiments described by IKEDA. The apparatus used
consisted of a bottle of 1 1/2 to 2 liters capacity with two necks,
into one of which a test-tube was fitted by means of a cork,
while the other communicated with a manometer. The test tube
reached to about the middle of the bottle, and its lower, closed
end was surrounded by a cylinder of phosphorus, which was kept

1 Zeit. phys. Cheni. 16, 315, 1895. Phil. Mag. (5). 38, 505, 1894.
'2 See p. 56.

62 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

cool by a current of water of the same temperature as the
water bath in which the apparatus stood. The experiments were
made as follows: - The bottle, containing air, and a little
water, was placed in the thermostat, connected with the mano-
meter, and allowed to stand until it had assumed the tempera-
ture of the bath.

The phosphorus was then quickly placed in position in the
apparatus, and the pressure noted. The readings of the pressure
were then repeated at suitable intervals of time. Since the
phosphorus is very little acted on during an experiment, the
area of its surface may be regarded as remaining unchanged.

The numbers which were obtained are given in the following
table. In it, kx is the velocity constant of the oxidation, cal-
culated from the expression

which on integration becomes,

where pL is the partial pressure of the oxygen initially,

Pt „ „ „ „ „ „ „ after partial oxi-

dation of the phosphorus,
and t is the time.

The values of kj which were obtained increase slightly, show-
ing that the rate of oxidation of phosphorus in moist air
decreases somewhat more slowly than the partial pressure of the
oxygen. IKEDA had also drawn this conclusion from his experi-
ments.

Phosphorus in moist air.

Temperature ........ = 20°. 2 -- 20°. 4

Pressure of the aqueous vapour = 17.8 mm.
., ,, phosphorus ,, = 0.113 mm1.

l JOUBERT, These, 1874. (cf. p. 52).

OXIDATION OF PHOSPHORUS IN AIR.

Time in
minutes t.

Pressure.
P.

Partial pressure
of the oxygen.

k,.

P-

773.1

157.8

—

750.6

135.3

0.00267

42.0

729.7

114.0

0.00282

43.1

714.3

99.0

0.00271

40.1

100

697.4

82.1

0.00284

42.3

130

682.2

66.9

0.00286

42.1

Since the values of k1 are calculated on the assumption that
the velocity of oxidation is proportional to the oxygen pressure,
the fact that they increase shows, that at smaller pressures, the
reaction takes place somewhat faster than this assumption leads
us to expect. The reason of this, is perhaps to be found in
the fact that bodies evaporate more quickly into a gas at a
lower pressure, than at a higher one.

The reaction, in the case under consideration, probably takes
place between the vapour of phosphorus and oxygen; it was
therefore natural to assume, that the rate of oxidation would be
proportional to the rate of evaporation of the phosphorus.

The rate at which a liquid of constant temperature and
constant surface area evaporates into a gas depends, according to
STEFAN l, on the pressure of the gas, the connexion being

v = c l°e p-=r^-

In this equation

V is the rate of evaporation,
P is the total pressure of gas and vapour,
Pi is the partial pressure of the vapour,
and c is a constant.

If now, in accordance with the assumption made above.
- in equation (1) be taken to be also proportional to V,

we obtain,

1 Sitzungsber. Wiener Akad. der Wissenschaften, 68, 385 1873.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

lo«

(2)

P -Pi •

This equation states, that the rate of oxidation of phosphorus
is not only proportional to the pressure of the oxygen, but also
to the rate of evaporation of the phosphorus.

In order to calculate the values of k, equation (2) must be
integrated.

If a be the sum of the partial pressures of the nitrogen and
aqueous vapour in the mixture of gases, and therefore a constant
quantity, we have p = P — a. Substituting this value in (2),
and developing the logarithm in a series, we obtain

P-a

- -

12 P "" 24 P

Integrating between the limits P! and Pt, and neglecting small
terms \ this gives,

t Pi

The values of k in the table on page 63 are calculated by
means of this equation; they are more nearly constant than the

values of ki ; we may there-
fore conclude, that the rate
of oxidation of phosphorus
in moist air is really pro-
portional to the pressure of
the oxygen.

This, however, can only
be true within certain lim-
its, for it is well known that
oxidation of phosphorus
does not take place in
Fig. 21. oxygen at higher pressures.

b. Rate of oxidation at higher pressures.
By means of the apparatus shown in the accompanying drawing,

1 With phosphorus px is small compared to a at the ordinary temperature.

OXIDATION OF PHOSPHORUS IN MOIST OXYZEN. 65

measurements were now made at all pressures at which the
oxidation occurs.

The glass vessel EPA, the volume of which was 50-— 70 cc.,
communicates, by means of capillary tubes of 0.5 mm. internal
diameter, with the tap B and with a manometer at D. The
junction at C was made, either by a ground glass joint luted
with mercury, or by a short length of thick-walled indiarubber
tubing.

The manometer was arranged so that the mercury always
stood at the same height in the tube D; the volume of the
apparatus therefore remained constant. A mercury manometer
was usually employed, though in a number of experiments a
brom-naphthalene manometer was substituted for it; the latter
could be read more accurately, and the vapour of the brom-
naphthalene had no efiect on the course of the reaction. The
phosphorus was purified by melting it under a weak solution of
potassium bichromate and sulphuric acid, and washing it.

A piece of this phosphorus was brought into the apparatus
through E, melted at P, (in an atmosphere of carbon dioxide,
or in vacuo,) and spread out over the upper surface of the bulb
in as thin a layer as possible, after which it was allowed to
solidify. A little water having been brought into the apparatus
at A, the opening E was sealed up before the blowpipe.

The apparatus, prepared in this way, was placed in a constant
temperature water bath, after which it was evacuated and oxygen
allowed to enter. The latter operations were repeated four or
five times. In doing this it is of importance to keep the phos-
phorus at a sufficiently low temperature, as otherwise it is very
apt to take fire when the oxygen is admitted to the vacuous
apparatus. The inflammation takes place particularly easily when
'the pressure is low and the phosphorus dry. With oxygen which
had been dried over phosphorus pentoxide, it occurred even at
0°, under a pressure of about 1 mm.

The greater part of the experiments were made at 20° *.
Two experiments, which were made at 20°, on the limiting

1 See the complete tables given in the Zeit. pliys. Chcm. 16 p. 321, 1895, or
Phil. Mag. (5), 38, 512, 1894.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

5/0

pressure above which no oxidation takes place, gave the following
results; the reaction just began in one case when the pressure
of the oxygen was 696 mm., in another case it began at 671 mm.,
but not at 723 mm. We may therefore conclude that phos-
phorus only oxidises in moist oxygen, at 20° — 21°, under pres-
sures which are less than about 700 mm.

It is of interest to notice, that JOUBERT, who has published

(375

two series of experiments on the pressures at which phosphorus
just becomes luminous in oxygen, finds, at 20°. 2, in the first
series 787 mm., in the second 666 mm., as the pressure at which
luminosity is first visible.

The pressure found here seems, therefore, to agree with those
obtained by JOUBERT, from which it follows that the pressure at
which the oxidation begins is the same as that at which the
phosphorus becomes luminous.

The curve, (fig. 22), illustrates the connexion between the

OXIDATION OF PHOSPHORUS IN DRIED OXYGEN 67

rate of oxidation of phosphorus in moist oxygen (at 20°), and

the pressure of the oxygen. In curve I, the values of -[- are

taken as ordinates, those of the mean partial pressures of the
oxygen as abscissae.

Curve I shows that the velocity of the reaction beginning
with the value 0 at 700 mm. increases at first very rapidly as
the pressure falls, then varies between narrow limits over a
considerable range of pressure (viz., from 500—100 mm.), and
finally decreases again rapidly.

Curve II represents graphically the connexion between the
pressure of the oxygen and the rate of oxidation, the rate of
volatilisation of the phosphorus being supposed constant, viz.,
dp P

The experimental numbers — represented in the figure by
circles — evidently lie on a straight line passing through the
origin. That is, the corrected velocity is proportional to the
pressure of the oxygen.

This is however only true up to a pressure of about 520 mm.;
at higher pressures the velocity rapidly decreases, reaching the
value 0 at 700 mm.

At the ordinary temperature, therefore, the following connexion
exists between the rate of oxidation of phosphorus in moist
oxygen and the pressure: —

dp .

-IT = tp log

dt - Pl '

Above a certain limiting pressure - - which probably varies
with the temperature this ceases to be true, the reaction

taking place very much more slowly.

2. Phosphorus in dried oxygen.

Quite a different result is obtained in this case. The experi-
ments were made in the same way as those with moist oxygen,

The data from wLich the curve is drawn are contained in the paper already
cited. Phil. Mag. Dec. 1894. p. 505.

68 DISTUKBING ACTIONS IN GASEOUS SYSTEMS.

except that phosphorus pentoxide was substituted for the water
in A (fig. 21).

Two experiments were made; in the first the oxygen was left
in contact with the phosphorus pentoxide for a week, in the se-
cond for two days.

The reaction now first began at a much lower pressure than
with moist oxygen. Under a pressure of oxygen of 377 mm.
no reaction occurred, at 202 mm. it went forward very slowly.

The connexion between the pressure of the oxygen, and the
rate of oxidation is represented graphically in curve I (fig. 23),

Setting out from the pressure of 200 mm., the velocity of the
reaction appears to increase continuously as the pressure falls,
without reaching a maximum value as is the case when the
gas is moist. (Compare the curve in fig. 22).

Curve II represents the rate of oxidation in dry oxygen when

Fig. 23.

the rate of evaporation of the phosphorus is constant. It is ob-
tained by dividing the values used in drawing curve I by the
corresponding values of the rates of evaporation of the phosphorus.
The numbers obtained in this way are very irregular ; it appears
however, that the rate of oxidation between 0 and 70 mm. is
proportional to the square root of the pressure of the oxygen.
We may therefore write: -

(3)

OXIDATION OF SULPHUR. 69

After expanding the logarithm in a series, and integrating,
we obtain — neglecting small terms — ,

1 2

The values of Iq calculated by means of this equation from
the experiments, remain approximately constant below 60 — 70
mm., at higher pressures they decrease.

The irregularity of the results obtained in these experiments
is probably due, in part at any rate, to the deposition of a
coating of oxide on the surface of the phosphorus. We may
therefore say, that, the rate of evaporation of the phosphorus
being supposed constant, the rate at which it is oxidised by dry
oxygen is proportional to the square root of the pressure of the
latter. This is only true (at 20°) up to a pressure of 60—70
mm., above this pressure the velocity is smaller.

It is of interest that the maximum velocity of oxidation — at
constant rate of evaporation of the phosphorus — occurs at a press-
ure of yio atmosphere; this pressure is also the most favourable
to the reaction between phosphine and oxygen (p. 60).

II. SULPHUR.

As we have seen, the deposition of phosphorus pentoxide on
the surface of the phosphorus introduces a difficulty into the
study of the rate of oxidation of this substance. The process
takes place more regularly when sulphur is used as the oxidis-
able substance, because the product of the reaction is volatile.

The apparatus shown in figure 24 was used in these experi-
ments ; by means of it the pressure may be kept constant during
the measurements, the volume being variable. It consists of a
glass tube S, on which two bulbs are blown, and having a capacity
of 60 — 70 cc. One bulb, S, contains 1 — 2 grams of sulphur,
the other 5 — 6 grams of soda-lime. A constant temperature of
about 160° is maintained by immersing the apparatus in the
vapour of boiling turpentine, which is contained in the flask.

The measuring tube A is graduated in Vm cc., and contains

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

mercury the level of which may be adjusted by means of the
reservoir B. C is a three way tap, D a small gauge contain-
ing bromnaphthalene which allows the pressure in the part of
the apparatus to the left of D to be made equal to that in the
bottle F.

By means of the tap E, these two parts of the apparatus may
be put in communication with each other.

Fig. 24.

The reservoir F, which serves to keep the pressure constant,
is in communication with the manometer Gr and with an air pump.

The part of the apparatus which is seen in the figure to the
left of D, was first filled with oxygen at a somewhat greater
pressure than that existing in F, the tap E opened for a moment
to equalise the pressure on both sides of D, and the position of
the mercury in A read off. By raising B it is easy to maintain
the pressure constant, and equal to that in F.

The diminution of volume per minute, when reduced to some
standard pressure, is then proportional to the velocity of the
reaction.

When the velocity has become constant, the pressure in F is

RATE OF OXIDATION OF SULPHUR

reduced, the tap E opened to equalise the pressure again, and
further readings made at the new pressure.
The following table contains the results.

A v

is the diminution of the volume per minute, the

In it

volume being measured at pressure P.

is the rate of change of the volume, calculated for a
dt

pressure of 819.7 mm.; and is proportional to the quantity
of oxygen which is converted into sulphur dioxide per minute,
that is to the rate of the reaction.

Pressure
P.

Av
At'

dv
df

Temp-
erature.

kx.

809.8

0.0176

0.0174

158°

0.0985

0.0035

587

0.0244

0.0175

158

0.0841

0.0035

380.6

0.0459

0.0213

158

0.0820

0.0042

198.5

0.147

0.0356

159

0.0975

0.0069

105.6

0.456

0.0588

159

0.118

0.0056

43.8

1.77

0.0946

159

0.108

0.0163

819.7

0.0149

158

0.085

0.0030

578.7

0.0243

0.0172

159

0.082

0.0034

422.2

0.0349

0.0180

159

0.088

0.0043

306

0.0653

0.0244

159.5

0.084

0 . 0048

194

0.133

0.0315

159.2

0.085

0.0061

147.3

0.222

'0.0399

0.093

0.0077

95.9

0.455

0.0532

159.4

0.098

0.0100

41.8

1.84

0.0938

0.104

0.0161

The constant ki is calculated from the following equation,
which is essentially identical with equation 3 : — l

dv '/2 p

_ kl ] log ____,

1 In the calculation px has been taken as 11.5 mm. (at 158°— 159°). This value,
which does not pretend to any great accuracy, was determined by a special experiment.
It is also to be noticed that an error in px has very little influence on the value of
k or of k.

72 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

while k is calculated by the formula

As the table shows, the experimental results are in much
better agreement with the first of these equations, in which the
rate of oxidation is put proportional to the square root of the
pressure, than with the second, in which it is supposed to be
proportional to the pressure itself.

200

Pressure.
Fig. 25.

C)OO

8OO

The curves in fig. 25 represent the connexion between the
rate of oxidation and the pressure.

Curve I is drawn with the values of -=~ as ordinates, and those

of the pressure as abscissae It has a strong general resem-
blance to that which was obtained with phosphorus and dried
oxygen, (fig. 23); in both cases, the velocity increases contin-
uously as the pressure falls.

Curve II is drawn with ordinates proportional to the square
roots of the corresponding pressures. The experimental values
of the velocity of oxidation corrected for the rate of evaporation

OXIDATION OF ALDEHYDE. 73

dv P

of the sulphur, viz. - - : log — , are represented in the

at Jr — pi

figure by circles.

The theoretical curve represents these points with fair approxi-
mation.

It is of interest that the whole curve here, up to 800 mm.,
corresponds to the part of the curve for phosphorus and dried
oxygen between 0 and 70 mm. l Whether a maximum velocity
such as was observed with phosphorus and oxygen, occurs also
with sulphur and oxygen at higher pressures, must be decided by
further experiments.

III. ALDEHYDE.

In experiments with solid or liquid bodies, such as phosphorus
or melted sulphur, the rate of evaporation has such a great
influence on the velocity of the oxidation, that it is not easy
to determine with perfect certainty what influence the concen-
tration of the oxygen has upon it.

It appears, however, from the foregoing experiments, very
probable that the rate of oxidation in dried oxygen is proportional
to the square root of its pressure. In order to further test the
truth of this result, experiments were made with oxygen and
aldehyde-vapour.

The reaction was found to take place with convenient speed
at 20°. It was assumed that aldehyde-vapour at 20°, and under
pressures which do not exceed about 550 mm., may be considered,
with sufficient approximation, as a perfect gas.

Numerous attempts were made to absorb the acetic acid
formed, by means of some solid substance without action on
aldehyde; Pb 0, ZnO, BaC03, anhydrous KC2H302, were tried,
but all produced a more or less rapid diminution in the quantity
of aldehyde-vapour. The experiments were therefore made
without any such absorbent, and by means of apparatus similar
to that represented in fig. 14, p. 41.

1 Compare fig. 23 on page 68.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The oxidation takes place in the bulb A (fig. 26), which is
kept at a constant temperature in a thermostat; its volume is
60 — 70 cc. The pressure of the gas is determined by means of
the manometer BCD. By raising or lowering the tube C, the

level of the mercury is
always brought to the mark
B before a reading is made.
The pressure, BD, may then
be measured on a vertical
millimeter scale or by means
of a cathetometer. CD is a
barometer dipping below the
mercury at C ; the air-trap
E serves to retain any air
bubbles which may leak
through between the glass
and rubber tubes.

By means of the three-way
tap H the apparatus may be
connected either with an air-
pump through F, or with a
little vessel containing liquid
aldehyde, G, which is ground to fit the lower limb of the tap.

The aldehyde-vapour is admitted by putting the apparatus -
evacuated as far as possible - - in communication with the liquid
aldehyde in G ; by repeating these operations the air is completely
replaced by aldehyde-vapour. The tap H is then closed, the
apparatus placed in the thermostat, and the pressure observed.

G is then removed, F connected up to the oxygen gas holder,
and a current of oxygen, dried over CaCl2, led for some time
through F H. The tap H is then quickly opened to admit the
oxygen to the apparatus, closed again, and the pressure observed.
Further readings are then made from time to time until the
reaction is ended.

Since the gases do not mix immediately, the velocity is fre-
quently rather small at the beginning of the reaction.

The calculation of the rate of oxidation from the experiments,

Fig. 26.

OXIDATION OF ALDEHYDE.

requires a knowledge of the composition of the gas remaining
in the apparatus at the end of an experiment.

As soon as the last reading of the pressure had been made,
therefore, a very dilute solution of caustic potash — used in
order to be polymerise the aldehyde - - was allowed to flow into
the apparatus from a weighed flask. The difference between the
volume of the apparatus - determined by weighing it full of
water - - and the volume of the caustic potash solution drawn
into it, gave the volume of the oxygen and nitrogen contained
in the residue. The oxygen was absorbed by alkaline pyrogallol *.

The experiments were made in the dark, special experiments
having shown that light has some influence on the velocity of
the reaction.

The following table contains the results, -

Time in

Pressure of

Total

minutes.

oxygen.

aldehyde.

pressure.

k X 105

225.8

536.0

785.0

210.3

499.1

744.5

2.91

117

200.5

466.9

702.5

2.94

190

188.1

427.3

651.5

2.81

259

177.1

395.8

608.0

2.84

270

174.6

388.8

598.5

2.93

296

167.2

368.7

571.0

3.16

332

161.4

353.5

550.0

3.19

386

150.7

324.7

510.5

3.43

476

136.6

292.3

464.0

3.57

673

118.3

251.6

405.0

3.40

1303

83.8

183.1

302.0

3.29

Tempers
Partial pressure of oxyg
„ „ ,, nitro
Total pressure at the en
Vapour-pressure of aceti
k

iture 20°. 1 — 20° .32.
en at end of experiment,
c^en

83.4 mm.
23.7 „
301.0 „
11.4 „'

d of the exp<
c acid at 20°

! = 0.00287

^riment . .
.2

1 It was found necessary to cover the surface of the mercury with a layer of
brom -naphthalene, in order to avoid the action of the mixture of oxygen and aldehyde
on the mercury of the manometer.

KAHLBAUM, Zeit. phys. Chem. 13, 35. 1894.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

Time in

Pressure of

Total

minutes.

oxygen.

aldehyde.

pressure.

k X 105

489.6

291.2

79X9.0

485.3

281.7 790.5

0.96

480.6

273.2

781.0

1.52

132

475.5

251.2

766.5

1.81

163

470.0

249.2

749.0

2.05

229

457.2

220.5

707.5

2.87

325

441.6

186.1

657.5

2.94

464

424.2

159.5

603.5

3.11

617

409.1

119.1

558.0

3.18

1330

376.5

57.2

463.5

3.00

Temperature 20°.5 — 20°.7.

Total pressure of resi

dual £*as 47

3.5 mm.

Partial pressure of residual oxygen. . . . 376.5 ,,

„ „ „ nitrogen. ... 18.2 ,,

Vapour pressure of acetic acid at 20°. 6. . 11.6 ,,

kj = 0.00103.

Time in

Pressure of

Total

minutes.

oxygen.

aldehyde.

pressure.

k X 105

595.7

270.0

878.0

146

—

878.0

—

533.2

241.6

785.7

136

532.3

239.9

783.1

—

1163

532.3

239.7

782.9

—

373.0

178.5

559.3

353

346.8

122.8

488.8

2.82

421

344.6

118.2

481.8

2.59

501

342.7

114.2

476.1

2.34

Te
Total pressure of resi
Partial ,, ,, oxy
„ „ „ niti

mperature 20°. 8.
dual o'as 44

2.6 mm.
1.9 „

7.8 „

gen . 33

ogen
= 0.001767.

OXIDATION OF ALDEHYDE. 77

In order to calculate, from the decrease of pressure, the
quantities of oxygen and aldehyde which have undergone the
change, it is necessary to take account of the solvent action of
the liquid acetic acid which is formed on the aldehyde.

Let the initial pressure of the aldehyde be a mm., that of
the oxygen b mm., and of the nitrogen N mm. Further, call
the total pressure of the gaseous mixture after t minutes have
elapsed, Pt , and suppose that x mm. of oxygen have combined
with 2x mm. of aldehyde. At first the acetic acid formed
remains in the condition of vapour, and since its density at 20°
is double the normal value, we shall have 2 volumes of aldehyde-
vapour and 1 volume of oxygen combining to form 1 volume of
acetic acid vapour.

The pressure and volume of the acetic acid are, therefore, the
same as those of the oxygen from which it is formed.

The pressure of the mixture is therefore

POV\_|_/"U v\ 4- v 4- XT o-^-K O v _L XT

t — \cL — £ JL) \ \\j — XJ i X r IN — a i D ^i X i iM

The pressure at the beginning of the experiment was PI = a + b + N,
so that

2 x = P, - - Pt.

After a time the acetic-acid vapour will attain its maximum
pressure, m mms., after which liquid acetic acid will be deposited,
and its quantity will be proportional to x — m.

If we assume that the quantity of aldehyde dissolved in the
acetic acid follows Henry's law, it will be proportional to the
pressure of the aldehyde, p2, and also to the quantity of liquid
acetic acid.

The pressure of the aldehyde is therefore

p2 -- a - - 2x - - kt (x - - m) p2,
or

a_j - 2 x

" 1 + kj (x - - m)'

Here, 2 x is the diminution of pressure due to the trans-
formation of aldehyde into acetic acid, kx (x — m) p2, that

78 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

which is produced by the solution of aldehyde in the liquid acid,
and ki some constant.

If the assumption that aldehyde-vapour dissolves in acetic
acid according to Henry's law is not strictly accurate, no great
error will arise, since the quantity dissolved is small.

Putting the total pressure equal to the sum of the partial
pressures of the different gases, we obtain, -

Pt = (b - - x) + p2 -f m + N.
Substituting in this the value of p2 found above, it becomes

pt = (b - x) -h 1 ,a~ 2X r + m + N.

1 + kx (x - -' m)

From this equation x — the diminution in the oxygen
pressure — may be obtained when ki is known. The analysis
of the gas at the end of an experiment gives an independent
determination of x, from which k: may be found.

The connexion between the rate of oxidation of aldehyde
vapour by oxygen, and the concentrations of the gases - - or
their partial pressures, which are proportional to the concen-
trations — is expressed by the equation

— - -j£ = kpi 2 p2 (A)

P! is the partial pressure of the oxygen, p2 that of the aldehyde.
In order to integrate this equation, substitute (see p. 77)

a — 2 x dpi dx

P2 '- i + kl (x -r^); Pl z dT IT

This gives

dx V, / a — 2 x \

IT x) d + kl (x . nffl

from which we obtain, after performing the integration,

UNT

OXIDATION OF ALDEHYDE. 79

'/2_/2b-

2 kj m — ki a — 2

l°g -TT-

1 Vs

-4- - kj (b — x) 4- const. . . (B)
L

The value of the constant is obtained from the condition that
x = 0, when t - 0.

This form of the equation can only be used when (2 b — a)
is positive.

When excess of aldehyde is used, and (2 b - - a) is therefore
negative, the integrated equation may be transformed into

1 2 kirn — 2 — kia -1. (b — xY/2 1

k = T ' /o_9K\V, ' tan /o— 9MV. + t" X (b " X) + C°nSt (C)

The values of k in the tables on pp.. 75 — 6 are calculated by
means of equations B and C. They show that, up to an oxygen
pressure of 450 mm., these equations are in harmony with the
experimental results.

When the partial pressure of the oxygen is higher than about
450 mm., however, the values of k decrease. This appears to point
to the existence of an upper limit of pressure, above which the reac-
tion either stops altogether, or goes forward with a velocity very
much smaller than that which would be deduced from equation A.

As a matter of fact, no oxidation took place when the
pressure of the oxygen exceeded 530 mm., as may be seen from
the numbers tabulated.

The experiments show, therefore, that the oxidation of aldehyde
vapour by oxygen takes place with a velocity which is proportional
to the pressure of the aldehyde-vapour and to the square root
of the pressure of the oxygen, and further that there is probably
a certain pressure of the oxygen above which the reaction takes
place more slowly, - - about 450 mm. of mercury at 20°.

As we have already seen on page 19, the velocity of a poly-
molecular reaction may be expressed as follows, —

_^l = kClV (D)

80 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

where m and n are the numbers of the different kinds of
molecules taking part in the reaction. It will be shown later,
p. 99, that the values of m and n may be calculated from
measurements of the velocity of the reaction in cases in which
they are unknown.

Applying this to the reaction between aldehyde and oxygen,

we have — -r— - proportional to - -~ (page 78). GI is propor-
(it dt

tional to the pressure of the aldehyde, C2 to that of the oxygen.
Making these substitutions in equation D, we obtain

dpi ! m n
It = kp2 Pl '

Comparing this with equation A we find
m = 1, and n = 1/2,

that is the reaction takes place between aldehyde molecules and
oxygen atoms, and is, to be written in the following way : -

C2 EU 0 + 0 = C2 H4 02.

The supposition that a certain small number of oxygen atoms
exists normally in oxygen gas, is in accordance with our present
knowledge of the subject.

The mathematical theory of reactions between gases, which
was published in 1884 by J. J. THOMSON !, is also in agreement
with the results obtained with aldehyde and oxygen.

It is probable, on other grounds, that oxygen gas contains
free atoms; there can be little doubt that the oxygen molecule
would, at a sufficiently high temperature, be dissociated into its
atoms. Equilibrium between the dissociated and undissociated
molecules will be established when the concentration of the atoms
has reached a value determined by the equation

C(02) — k C<o),

where C(02) is the concentration of the oxygen molecules, C(0)
that of the atoms, and k a constant the value of which depends
on the temperature 2.

1 Phil. Mag. (5), 18, 233, 1884.

2 This is treated fully further on.

EXISTENCE OF FREE ATOMS IN OXYGEN GAS. 81

Since the heat of formation of the oxygen molecule from its
atoms is probably positive, the equilibrium well be displaced, in
such a way that at lower temperatures the concentration of the
oxygen atoms will be smaller than at higher temperatures. It
will, however, probably never become zero, and we shall have
therefore at the ordinary temperature

(02).

We may take the concentration of the oxygen molecules as
being proportional to the pressure of the gas; the concentration
of the oxygen atoms is therefore proportional to the square root
of the pressure.

If we assume that the oxygen atoms alone take part in the
oxidation of the aldehyde, the rate of oxidation must also be
proportional to the square root of the oxygen pressure.

Although the results obtained with aldehyde may be explained
in this way, it is doubtful whether this is also the case with
phosphorus and sulphur.

It is possible that the reaction between oxygen and phosphorus
or sulphur takes place in different stages, for example,

P4 + 0 = P4 0 '.

The velocity of each of these partial processes would then be
proportional to the concentration of the oxygen atoms. This
view is also in agreement with the fact that when phosphorus
is burnt with a limited supply of oxygen, the lower oxides,
such as PA, are formed.

The fact that the presence of moisture accelerates the oxidation
of phosphorus and sulphur 2 is also in accordance with the view
that the oxidation is due to the action of oxygen atoms, for
J. J. THOMSON 3 has found that the electric discharge (without
electrodes) passes much more easily through the moist, than
through the dry gas; the moisture apparently favours the
formation of the atoms which carry the electricity.

1 The existence of this oxide, discovered by LE VERRIER, is rendered probable by
the work of REINIZER and GOLDSCHMIDT (Berichte 13. p. 845. 1880).

2 Compare the experiments of BAKER and of DEWAR. See also page 33.

3 British Association, Oxford, 1894.

82 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

It must, however, be pointed out that the above hypothesis
does not explain the formation of ozone which accompanies the
oxidation of phosphorus, not only in moist oxygen but also,
according to MARCHAND, in the dry gas.

We have, so far, always spoken of oxygen atoms as taking
part in the oxidation of aldehyde, etc. The question, however,
arises whether we are dealing here with atoms, or with ions,
that is with positively or negatively charged atoms. VAN 'T HOFF l
has investigated this question.

According to the commonly received view on the subject,
one half of the oxygen molecule may be regarded as employed
in the slow oxidation, while the other half brings about the
formation of ozone.

From E WAN'S experiments, which show that the rate of
oxidation is proportional to the square root of the pressure of
the oxygen, it would follow that the dissociation -of the oxygen
molecule is not a consequence of the oxidation, but that it exists
previous to it.

If we are really dealing with the equilibrium 2

02 ^ 2 0,

and if the atoms are oppositely charged, it is conceivable that
the oxidisable substance should show preference for those with
one kind of charge, the remainder giving an electrical charge
to the oxygen which is finally removed by some secondary
reaction such as the formation of ozone, or the decolonisation
of indigo.

Some indications that this may be the case are to be found in
the literature of the subject. The white fumes formed during
the oxidation of phosphorus, for example, are due chiefly to the
condensation of steam, and persist in air which, after being in
contact with phosphorus, has been freed from ozone by means of
potassium iodide. 3 They therefore, resemble the cloudiness which
was observed by R. v. HELMHOLTZ in electrified steam. 4

1 Zeit. phys. Chem. 16, 411. 1895.

2 The meaning of equations written in this way is explained later.

3 MEISSNER, Untevsuchungen iiber den Sauerstoff. 1863, 20, 218.

4 Wied Ann. 32, 1, 1887; also MEISSNER, loc. cit.

We shall also see that in oxygen made active by contact with
phosphorus the primary product is not ozone, because it stops
the luminosity of phosphorus, while ozone favours it; l it might
be electrically charged oxygen.

The maximum quantity of oxygen taking part in the secondary
actions which accompany a slow oxidation was first determined,
in order to compare it with the quantity of oxygen employed
in the oxidation itself.

The determinations of SCHONBEIN 2, and LEEDS 3 give very different
results.

SCHONBEIN'S method was modified, so as to allow of quantitative
determinations, in the following way: A small stick of

phosphorus was placed in a large flask together with a very
dilute solution of indigo, either as indigo sulphate, or as com-
mercial sodium sulphindigotate, the oxidation value of which
had been determined by means of a standard permanganate
solution by SKALWEIT'S 4 method.

It was found in some preliminary experiments that it is
necessary to use small quantities of phosphorus, and that it is
absolutely essential to keep the temperature low during the
oxidation (40°), and to shake the flask vigorously.

21.3 mgrs. of phosphorus were used; to obtain such quantities
easily, the phosphorus was cast in thin sticks about 1 mm. in
diameter by drawing it up while melted into a thick walled
glass tube.

These sticks were easily removed from the tube, after which
they were cut into pieces of known length by bringing them into
a short piece of the same tube, which had been ground flat at
both ends, and cutting off the projecting parts with a knife.

First experiment. 60 cc. of indigo solution, to which 10 cc.
of sulphuric acid had been added, were shaken with 21.3 mgrs.
of phosphorus and excess of air, until the phosphorus had
disappeared. It was then found that an equal volume of the

1 CHAPPUIS, Bull. Soc Chim. 35, 419, 1881.

2 Journ. prakt. Chem. 53, 501, 1851.

3 LIEB., Ann. 200, 295, 1880.

4 Eepertorium der analyt. Chemie. 4, 247.

84 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

indigo solution was brought to the same greenish tint as that
acquired in the experiment by treatment with 79.5 cc. perman-
ganate solution, (0.00987 N).

During the oxidation of 21.3 mgrs. of phosphorus, therefore,
79.5 X 0.00987 X 8 — 6.28 mgrs. of oxygen had taken part
in the secondary reaction. The atomic ratio is thus P : 00.57.

Second experiment. This was carried out in a similar way,
except that the phosphorus was introduced gradually in four
parts. The 60 cc. ! of indigo solution were now almost com-
pletely decolourised, loosing the green tinge. 6 X 1-H =6.66
mgrs. of oxygen were therefore used in the secondary reaction,
or P : Oo.6.

In some further experiments without sulphuric acid it was
noticed that the acid accelerates the reaction considerably, the
ratio between the phosphorus and the oxygen, however, remained
unchanged. A final series of experiments was now made in the
dark so as to avoid the possible oxidation of indigo by the
action of the light. Sodium sulphindigotate was used, and the
slow combustion of the phosphorus conducted in a special way.
The phosphorus was brought into a condition of fine division
in the same way as in the earlier experiments, by warming the
flask until the phosphorus melted, and then shaking it thoroughly.

From this point the experiment was conducted in a somewhat
different way, because it was seen in the dark that the oxidation
took place in two different stages. The well known phosphor-
escence is first seen; phosphoric acid is practically the only
product formed in this stage when such small quantities of
phosphorus are employed. Secondly, if the particles of phosphorus
are completely covered by the liquid, luminosity is seen through-
out the whole flask, and phosphorous acid is also formed.

To give an example, the flask was placed in water at 50°,
taken out and shaken well about thirty times, and replaced in
the water, after this the luminosity was seen. On repeating
these operations the same results were obtained.

9.18 mgrs. of phosphorus were used, and after 277 repetitions

1 10 cc. of this indigo solution required 14.1 cc. permanganate, or 14.1 X 8 X
0;009S7 = 1.11 mgrs. oxygen.

FORMATION OF OZONE BY SLOW OXIDATION. 85

of the shaking and luminosity, 40 cc. of indigo solution had been
decolourised; on standing in the cold an additional 4 cc. of
indigo were gradually decolourised, and the phosphorus totally
disappeared.

50 cc. of the indigo solution were equivalent to 40.73 cc. of
0.00987 N permanganate solution, so that the quantity of

oxygen used in decolourising 44 cc. of indigo is 44 X — ^7—

[ 0.00987 = 2.83 mgrs. The ratio between phosphorus
and oxygen is thus P : O0.e-

It is therefore probable that when an atom of phosphorus is
oxidised, it converts approximately half an atom of oxygen into
the active condition, independently of whether phosphorous or
phosphoric acid is formed.

The difference between the quantity of oxygen actually found
and 0.5 appears to be real, and may be due to the fact that
the oxidation of phosphorus appears to take place in two
directions, - - first and chiefly, with formation of phosphorous
and phosphoric acids, and secondly, to the extent of about 15
per cent according to SALZER, with formation of hypophosphoric
acid; it is perhaps possible that the latter process produces a
larger amount of active oxygen.

It may also be pointed out here that in the oxidation of
phosphorus, ozone does not appear to be formed at first. The
luminous phenomena just described show that something was
present in the atmosphere of the flask which prevented the
oxidation of the phosphorus; oxygen was obviously present in
sufficient quantity, and there was no lack of phosphorus vapour
since on opening the flask phosphorescence was seen in contact
with the air. The experiments of CHAPPUIS show that ozone
promotes the phosphorescence.

This inhibitory action, which may be due to the electric
charge, or to the excess of positive or of negative oxygen ions,
is removed by shaking with indigo solution, in which process
sulphuric acid has a marked accelerative effect, possibly on
account of its conductivity.

That the effect of the shaking, viz., rendering possible a renewed

8b DISTURBING ACTIONS IN GASEOUS SYSTEMS.

appearance of the phosphorescence, is not due merely to a
renewed saturation of the air with phosphorus vapour , is
proved by the fact that the characteristic phosphorescence is
not seen when phosphorus, air, and water alone are used,
without indigo.

It is also to be noticed that the substance exercising the
inhibitory action disappears very gradually when the flask
is not shaken, so that a spontaneous outburst of luminosity
appears, which is repeated at intervals of a few hours. In this
way the intermittent phosphorescence which was noticed by
JOUBERT l may be explained.

Chapter III.
Elimination of the disturbing actions.

I. METHODS OF ELIMINATING THE DISTURBING ACTIONS.

FORM AND DIMENSIONS OF THE APPARATUS. USE OF A SOLVENT.

MOISTENING THE WALLS OF THE VESSEL.

The object of the preceding studies was not only the discovery
of the disturbing actions but also their elimination.

The secondary actions which have been examined may now
be enumerated together with the methods which may be adopted
in order to avoid them. These methods will then be more
fully explained.

Disturbing actions.

1. The influence of the volume of the bodies undergoing change.

2. The effect of a change in the nature of the medium during
the reaction.

3. The influence of the walls of the apparatus.

4. The influence of changes in the walls of the apparatus
occurring during the reaction.

1 See note p. 52.

[Also BAKER, Phil. Trans. 1888, p. 583; THORPE and TUTTON, Chem. Soc. Journ.
p. 569, 1890. T. E.]

THEIR ELIMINATION. 87

Methods of eliminating the disturbing actions.

1. Form and dimensions of the apparatus.

2. Use of a solvent.

3. Moistening the walls of the vessel.

1. Form and dimensions of the apparatus.

Any action which is connected with the walls of the vessel
will evidently be diminished in intensity by diminishing the
internal surface of the apparatus, and therefore, also by increasing
its volume.

By using spherical flasks of considerable diameter, both the
influence of the walls on the reaction, and the effect which the
reaction frequently exerts on the walls, will be diminished.

2. Use of a solvent.

One of the most important conditions for obtaining the normal
course of change, is that the reacting substances be distributed
through a large excess of some substance which does not itself
take part in the change. We will call a substance of this kind
a "solvent", although it may be a gas when a reaction in a
gaseous system is under consideration.

A solvent of this kind serves several different ends.

First, by its use we obtain the dilution which is often
necessary in order to reduce the influence of the volume of the
reacting substances to a negligible quantity, secondly, the change
in the nature of the medium which is caused by the accumulation
of the products of the reaction is diminished by the presence
of the solvent.

Further, special experiments have shown that the influence
of the three other disturbing actions which have been mentioned
is reduced to a great extent by the use of a solvent, although
it is not totally eliminated.

Since the disturbing actions are most prominent in gaseous
systems, the effect of a solvent on them was studied in such
systems.

In order to prove that the effect of the walls of the vessel

88 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

is diminished by the addition of a solvent gas, the apparatus
represented on p. 44 was used ; by means of it the ratio between
the rates of polymerisation of cyanic acid in the two divisions
A and B can be determined

1, when the acid is alone present,

2, when it is mixed with excess of dry air.

1 . Cyanic acid alone.

Initial pressure .... 209.9 in A, 210.3 in B.

Pressure after 19 hours 190.0 in A, 198.0 in B.

Ratio between the velocities in A and B: -- 1.6 : 1.

2. Cyanic acid ivitli an excess of dry air.

Initial pressure . . . . 677.2 in A and B.
Pressure after 41 hours 661.5 in A, 662.9 in B.
Ratio of the velocities in A and B: — 1.1 : 1.

From these numbers it will be seen that the velocities tend
towards the same value; that is, the influence of the walls, to
which the difference in the velocities is due, is diminished by
the addition of air.

In order to show that the effect of the changes which the ivalls
of the vessel undergo is diminished by the presence of a solvent
gas, a similar series of experiments was made with the apparatus
shown in fig. 7, page 34.

After depositing a coating of cyamelide on the wall of B,
the ratio of the rates of polymerisation of cyanic acid in A and B,
was determined,

1, when the acid alone was present,

2, when it was mixed with an excess of dry air.

1. Cyanic acid alone.

Initial pressure 89.8 in A and B.

Pressure after 3 days . . 88 in A, 85.3 in B.
Ratio between the velocities in A and in B : - - 1 : 2.5.

2. Cyanic acid after addition of dry air.

Initial pressure 542.3 in A and B.

Pressure after 15 days. . 532.4 in A, 529.3 in B.
Ratio of the velocities in A and in B : — 1 : 1.3.

MOISTENING THE WALLS. 89

3. Cyanic acid alone.

Initial pressure 77.4 in A, 79.4 in B.

Pressure after three days 74.5 in A, 71.6 in B.

Ratio of the velocities in A and in B : - - 1 : 2.7.

Here, also, the velocities tend towards the same value; that
is, the influence of the deposit of cyamelide, which accelerates
the change, is diminished by the addition of air. The explanation
of the action of the solvent gas is to be found in the formation
of a protecting layer of it near the walls. The change, which
occurs most rapidly in the neighbourhood of the walls, removes
the cyanic acid from the gaseous mixture existing there, so that
the influence of the walls cannot be exerted until the cyanic
acid has been replaced by diffusion in the layer of gas in contact
with them.

3. Moistening the walls.

This artifice diminishes the influence of the deposits which
are formed in certain changes in a very remarkable way; by
using it we shall become acquainted with the surprising magnitude
of the disturbing actions which come into play in these reactions.

The apparatus shown in fig. 7, p. 34, was also used in this
case. The walls of one of the two divisions, A for example,
were covered internally with a coating of valvolin. The effect
of this coating on the rate of formation of ammonium carbamate
and of trioxymethylene was then investigated.

The manipulation of the experiment is the same as that
already described, so that it is only necessary to say that there
is an enormous difference between the rates of the reaction in
the two divisions, owing to the influence of the liquid coating.
The velocity in B, the walls of which were not moistened, was
greater than that in A, both with the carbamate and with
trioxymethylene, the ratios of the velocities being 6:1, and
16 : 1. This difference shows, therefore, that moistening the
walls diminishes the accelerative influence of the deposits of
carbamate and of trioxymethylene. The reason of this is probably
that the pores of the substances deposited are filled up by the
liquid.

90 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

It must also be pointed out that special care is required in
the choice of the liquid with which the walls are covered ; it
must be viscid, have a very small vapour pressure, and dissolve
the reacting gases as sparingly as possible.

The question now arises, whether it is possible to realise the
normal course of the reaction in the different cases which have
been considered, by making use of the methods which have been
described for eliminating the disturbing actions.

In answering this question, it is necessary to differentiate
between reactions taking place in liquids, and those taking place
in gaseous systems.

In liquid systems, the use of a solvent in large excess does
certainly suffice to practically eliminate the disturbing actions.
But in the case of gases, a gaseous solvent cannot be used to
the same extent, because great difficulties are introduced by the
large volume needed.

As we shall see, however, it has proved possible to realise the
normal course of the reaction in several cases.

The greatest difficulty is found in those cases in which the
gases undergo a change which produces a deposit on the walls
of the vessel which increases in quantity as the reaction pro-
gresses.

How this difficulty is to be avoided will be shown in a
subsequent chapter; here, we may remark that it is very conside-
rable even in liquid systems where, as we have already seen,
the conditions are much more favourable to a normal course
than with gases. The following experiments may be mentioned
as yielding additional evidence in support of this.

URECH *, while studying the action of FEHLING'S solution on
invert sugar, found that the velocity of the change increased in
a curious way when vessels with a larger internal surface were
used, he also noticed that the rate of change increased during
the first period of the reaction reaching a maximum value, he
observed, in short, although in a lesser degree, all the irregu-
larities which have been described in the polymerisation of
cyanic acid, and which are due to the accelerative action of the

1 Berichte, 15, 2687, 1882.

CHEMICAL INDUCTION OR INITIAL ACCELERATION. 91

deposit of cyamelide. This indicates that the phenomena observed
by URECH had a similar cause, namely, the formation of cuprous
oxide.

This experiment should serve as a warning to investigators
who are engaged with the study of reactions in gaseous systems ;
whenever a deposit of a solid substance which accelerates the
reaction is formed, the difficulties to be expected are such that
even under the favourable conditions existing in liquids, conside-
rable irregularities may be found.

II. THE FIRST PERIOD OF CHEMICAL CHANGE.

Chemical induction.

The first period of a chemical change is of special interest in
chemical dynamics. An exceedingly curious phenomenon is
frequently encountered in it, viz. the velocity of the reaction
increases during this period, finally attaining a maximum value.

The names "chemical induction1', and "initial acceleration"
have been given to this phenomenon.

Since an acceleration of this kind is incompatible with the
views which have been put forward in this book, it was submitted
to experimental examination. This showed that the cause of the
phenomenon is to be found in the disturbing actions which have
already been mentioned. It showed also what importance must
be attached to the occurrence of an initial acceleration in studies
of this kind.

The existence of an initial acceleration is established by the
following observations.

1. BUNSEN and ROSCOE, to whom the term " chemical induction"
is due, observed the acceleration in question on exposing a
mixture of chlorine and hydrogen to light. In one of their

92 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

experiments the quantity of change in the eighth minute was
ten times that which occurred in the first. 1

They observed a similar acceleration of the action of bromine
on tartaric acid, light being excluded, and expressed themselves
with regard to the phenomenon in general in the follow-
ing way: -

"The occurrence of such a maximum appears, therefore, to
depend, not on some special peculiarity in the action of light,
but on the mode of action of the force of affinity itself."

2. BAEYEE 3, working in BUNSEN'S laboratory, found another
instance of chemical induction in the action of bromine on lactic
acid in presence of hydrobromic acid.

3. WEIGHT, LUFF, and RENNIE 4, again, found the same pheno-
menon while studying the reduction of certain metallic oxides
by hydrogen and carbon monoxide; they say: —

"In all cases for a length of time the action is so slight as
to be almost or quite imperceptible; after which it goes on at
an accelerating rate until a maximum rate is attained, when
it again diminishes .... it is evidently a case of the chemical
induction studied by BUNSEN and ROSCOE."

4. The expression "initial acceleration1' is due to BEETHELOT
and PEAN DE SAINT GILLES ; 5 they noticed it in the process of
etherification and considered it to be of a specific character.
They say: -

"Pour concevoir 1'acceleration initiale il faut admettre une
sorte d'inertie, de resistance a vaincre qui retard la combinaison
dans les premiers instants."

1 POGG. Ann. 100, 488, 1857. OSTW AID'S Klassiker der exacten Wissenschaften,
34, p. 93.

2 POGG. Ann. 100, 513, 1855. OSTWALD'S Klassiker. 34, p. 93.

3 LIEB. Ann. 103, 178, 1857.

4 Journ. Chem. Soc. 1879, 495.

5 Ann. Chim. Phys. (3) 66, 26, 1862.

INITIAL ACCELERATION. 93

More recently MENSCHUTKIN 1 made similar observations on the
formation of acetanilide, and says: -

" We find here a phenomenon similar to the acceleration of the
etherification which BERTHELOT and PEAN DE SAINT GILLES have
observed."

In the course of his researches on tertiary amylacetate he met
with the same phenomenon again. "2

The examples cited have caused the phenomenon of initial
acceleration to be regarded as a characteristic feature of chemical
change.

Another interpretation of these phenomena may; however, be
given ; they may be regarded as due to secondary actions.

BUNSEN and ROSCOE found a sufficient explanation of the acceler-
ation observed in the action of light on mixtures of chlorine and
hydrogen, in the fact that the light, when it is absorbed by the
mixture of chlorine and hydrogen, brings about what might be
called a "dislocation" of the molecules, which does not produce
chemical change until it has reached a certain magnitude.

In consequence, however, of their observation that a similar
phenomenon occurs with tartaric acid when light is excluded,
they expressed the view which has already been quoted.

HARCOURT and ESSON 3 appear to incline to the opposite opinion ;
having observed an initial acceleration of the reaction between
potassium permanganate and oxalic acid in the presence of sulphuric
acid and manganese sulphate, they considered it to be due to a
secondary action, and found that this was really the case, the
reaction taking place in the two stages

2 KMn04 + 3 MnS04 + 2 H20 = K2S04 + 2 H2S04 + 5 Mn02,
and Mn02 + H2 S04 + H2 C2 04 = MnS04 + 2 H2 0 + 2 C02.

It is the second reaction which is actually observed and which
exhibits the acceleration ; this is hardly surprising, since the
Mn02 which enters into the second reaction is a product of
the first.

1 Berichte, 15, 1616, 1882.

2 Berichte, 15, 2512, 1882. KONOWALOW, Zeit. phys. Chem. 1, 63, 1887. See
also SPRING on this subject. Zeit. phys. Chem. 1, 217, 1887; 1, 468, 1887.

3 Phil. Trans. 1866, 201.

94 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

NAUMANN l also appears to regard the initial acceleration as
secondary ; having observed an acceleration in the conversion of
a mixture of ammonia and carbon dioxide into ammonium carba-
mate he did not hesitate to ascribe it to the accelerative action
of the solid ammonium carbamate formed.

URECH 2, finally, having observed the phenomenon in the case
of the action of bromine on fatty acids, says : —

"These results would be incomprehensible from a theoretical
point of view, if the action of the bromine consisted of a simple
substitution, for then the maximum velocity must occur at the
beginning of the reaction.1'

SPRING 3 also found an example of chemical induction in the
solution of marble in dilute mineral acids, and SPRING and VAN
AUBEL 4 another, in the action of dilute acids upon zinc (con-
taining 0.6 per cent, of lead).

The following experiments were made in order to dis-
cover whether the initial acceleration is something essential
to a chemical change, or whether it is merely a result of
secondary actions.

The experiments were made on

1. The change of rhombic, into monosymmetric sulphur.

2. The formation of water.

3. The polymerisation of cyanic acid.

1. The initial acceleration of the change of rhombic
sulphur into monosymmetric sulphur.

The experiments were made by T. L. REICHER 5, the
expansion which occurs during the change being measured.
The apparatus used - - a dilatometer - - has the form of
a large thermometer (fig. 27) ; the bulb A contains a
quantity of rhombic sulphur together with sufficient sul-
phuric acid (sp. gr. 1.77) to fill the bulb and part of the
rig. 27. capillary tube, the whole was heated in boiling water.

1 LIBB. Ann. 160, 21. 1876.

2 Berichte, 8, 539, 1875.

3 Zeit. phys. Chem. 1, 217, 1887.

4 „ „ „ 1, 465, 1887.

5 QUOTE'S Zeitschrift fur Krystallographie, 8, 593, 1884. Inaugural Dissertation,
Amsterdam 1883, 45.

INITIAL ACCELERATION. 95

The expansion produced by the rise of temperature being at an
end, a further slow expansion indicates the progress of the change.
The expansions, which were read off every five minutes, were
as follows : —

1, 2, 4, 5, 8, 11, 13, 15, 18, 17, 17, 16, 14, 12, 9, 7, 5, 4, 3, 2, 1.

The velocity of the change therefore increases at first, reaching
its maximum value when approximately one half of the rhombic
sulphur has been converted into the monosymmetric modification. l

It has been found that this acceleration is simply due to the
well known influence which the presence of monosymmetric
sulphur exerts on the change.

2. Initial acceleration in the formation of water.

While studying the course of the transformation of electrolytic
gas into water at 440° in presence of nitrogen, 13.8 cc. of
electrolytic hydrogen, and 32.7 cc. of purified air were intro-
duced into the reservoir K of the apparatus represented in
figure 12, page 39; the mixture of gases was separated by an
index of mercury I, from the column of air L, the length of
which, Lt, measured in the way already described, gives the
pressure of the gas which is being examined. Calling the quan-
tity of the mixture of oxygen and hydrogen present at the
beginning of the experiment unity, and the quantity which has
undergone change at the time t, n, we obtain "

46.5 (Lt-L0) = 20.34 n Lt,

L0 and Lt being the lengths of the column of air, L, at the
beginning of the experiment, and at the time t.
Therefore

1 — n = 2.28 ^ — 1.28.
-Lit

There is a remarkable similarity in this respect to the change of tertiary amyl
acetate studied by MENSCIIUTKIN. Berichte, 15, 2512, 1882.
2 See appendix, note 2.

DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The results are given in the following table.

Time in hours.

Quantity of 2H2 + 02
unchanged.

Diminution in the
quantity of
2H2 + 02 per hour.

—

0.956

0.006

0.899

0.008

0.826

0.010

0.749

0.011

0.669

0.011

0.525

0.010

0.399

0.009

0.317

0.006

111

0.173

0.005

139

0.102

0.003

181

0.060

0.001

The initial acceleration is very noticeable, but it is easy to see
that it is of a secondary character. The experiments on page
40 show that the acceleration disappears when the nitrogen is
omitted. It is well known that oxides of nitrogen are formed
when electrolytic gas explodes in the presence of nitrogen \ the
acceleration observed in this experiment is, therefore, evidently
to be referred to the formation of these substances.

3. Initial acceleration in the polymerisation of cyanic acid.

An initial acceleration of the change of cyanic acid into cyam-
elide occurs, as may be seen from the experiments on page
38, and also from the following table.

Time in hours.

Pressure in mm.

Decrease of pressure
per hour.

201.6

0.31

186.7

0.52

173.7

0.42

164

1 Chem. News 49, 237, 1884, in which LEEDS states that NH4N02 is formed.

INITIAL ACCELERATION.

The cause of the acceleration in this case was found in the
fact that the cyamelide which is formed promotes the change of
the cyanic acid in a very marked way, as we have already seen.

The following experiment gives a further proof that the acceler-
ation is conditioned by the change in the walls of the vessel,
since it may be produced at any period of the change, and
is not by any means confined to the initial period. The appar-
atus shown in fig. 7 was used in the experiment, the reservoir
B was filled with cyanic acid vapour, A with mercury, and the
pressure of the acid (at constant volume) measured from time
to time.

Time in hours.

Pressure in mm.

Decrease of pressure
per hour.

282.9

1.44

271.4

1.55

245

1.07

220.4

As may be seen the initial acceleration has taken place. The
remaining part of the cyanic acid was now divided between the
two vessels A and B by raising the apparatus, after which they
were separated from each other by lowering it again.

The acceleration was again observed, but this time only in
the reservoir A, the walls of which were not coated with
cyamelide.

Time in

Pressure and decrease of pressure.

hours.

Reservoir B

Reservoir A

108.8

110.6

0.14

0.044

105.3

109.5

0.136

0.094

48.5

102.1

107.3

0.104

0.076

120.5

94.6

101.8

98 DISTURBING ACTIONS IN GASEOUS SYSTEMS.

The experiments which have been described show that chem-
ical induction, or initial acceleration, may be referred to second-
ary actions, and therefore the phenomenon may be of service
in investigations relating to chemical dynamics, since it indicates,
in a way which is not to be undervalued, that some necessary
precaution has been omitted.

THE COURSE OF CHEMICAL CHANGE.

THIRD PART.
APPLICATIONS.

I. DETERMINATION OF THE NUMBER OF MOLECULES
WHICH TAKE PART IN A CHEMICAL REACTION.

A. METHOD IN WHICH THE VOLUME KEMAINS CONSTANT.
Decomposition of arsine and phosphine.

The difference which is found in the course of chemical reactions
in which different numbers of molecules take part may be employed
in the solution of an interesting problem. In the first part of
this book the course of a reaction was deduced from the number
of molecules taking part in it ; in this part, inversely, the number
will be determined from the observed course of the reaction.

The principle on which the determination depends is very simple,
for the course of a polymolecular reaction is represented by
the equation

^ -kC°

where n is the number of molecules taking part in the reaction,
and we have to determine this quantity experimentally.

Since this can be done in different ways, we shall first develop
those methods which depend on the investigation of the course
of the reaction at constant volume.

The integrals of the differential equation which has just been
given will be used, viz : —

l°g ~7T or rta-i = kt + constant, !

1 The value of k is (n — 1) times that which it has in the differential equation.
Cf. p. 19.

100

NUMBEK OF MOLECULES TAKING PART IN A REACTION.

and we shall have to find which of these equations represents
the experimental results.

The decomposition of phosphine has been investigated with
this object. We have to decide, by experiment, whether this
decomposition really takes place in accordance with the equation
which is usually assumed to represent it, viz. -

4 PH3 = P* t GH2,

that is whether four molecules of phosphine really produce, by
their mutual action, one molecule of phosphorus and six molecules
of hydrogen.

The experiment was made by measuring the pressure, at con-
stant volume, of a quantity of phosphine at different stages of
its decomposition.

We have then

= Co (3 -

where C0 and P0 are pressure and concentration initially, Ct
and Pt the same quantities after partial decomposition. l The
apparatus used was that which is described on page 41, only
in place of the boiling diphenylamine which was used in a
copper bath for maintaining a constant temperature of 310°
in the very similar experiments with arsenic hydride described
on p. 2, sulphur boiling at 440° was employed here. 2

The following table contains the results of the experiment.

Time in
hours.

Pressure
in mm.
P

hoc P°

i r/ P \3 ~
° i

tlog3 P0 - 2 Pt

tL\3 Po - - 2 Pt/ J

758.01

—

769.34

0.00759

0.055

781.46

0.00709

0.055

795.57

0.00746

0.060

819.16

0.00732

0.066

35.9

843.71

0.00713

0.073

46.3

865.22

0.00718

0.085

1 Cf. p. 2.

2 The heating apparatus is described on p. 40.

METHOD AT CONSTANT VOLUME. 101

The steady increase of the numbers given in the last column
shows that the course of the reaction does not correspond to the
quadri-molecular equation

^r- = kfc -f- const.
UJ

and that the decomposition, therefore, is not represented by the
equation

4 P H3 = P4 + 6 H2.
On the other hand the values of
1 po

t" log 3~p^~- ^ pT

are strikingly constant.

From this result we are justified in concluding that the change
is monomolecular, that is, that each molecule of phosphine decom-
poses independently of the others, according to the equation

PH3 = P + 3H,

and that the molecules P4 and H2 are formed subsequently by
the combination of the atoms of phosphorus and hydrogen.

II. DETERMINATION OF THE NUMBER OF MOLECULES
WHICH TAKE PART IN A CHEMICAL REACTION.

B. METHOD IN WHICH THE VOLUME VARIES.

While the method of determining the number of molecules
taking part in a reaction which has just been described depends
on the investigation of the course of the reaction at constant
volume, that which is about to be considered depends on the
influence of a change of volume on the velocity of a reaction.

This influence depends on the number of molecules taking part

102 NUMBER OF MOLECULES TAKING PART IN A

REACTION.

in the reaction. This is shown by the equations,

therefore,

a ct . * d °2

IT : k Cl' and ' IT : k

d d d C2 a *

dt dt

n = ^1r_^f

log I

The calculation of n from this differential equation cannot,
however, lay claim to any great degree of accuracy.

For if we substitute for the differentials dCi anddC2, the very
small changes of concentration which take place at the very
beginning of the reactions, for example, the result will be in-
accurate on account of the magnitude of the experimental error
due, partly, to the smallness of the changes of concentration
measured, and partly, to the initial disturbances to which the
reactions are subject.

If, again, we substitute a large change of concentration the
result is still inaccurate, since we assume implicitly that the rate

of the reaction, -Y-, remains constant while the concentration
at

undergoes a considerable diminution. This error is partially eli-
minated owing to the fact that the same assumption is made
with respect to both the differentials dC^ and dC2; it is, how-
ever, difficult to say to what extent this occurs. It is much better
to deduce the strictly accurate integrated equation, from which,
under certain circumstances, it is possible to calculate n exactly. l
According to what is said on page 19 we have for an n-
molecular reaction,

d C i />,„

1 I am indebted to Mr. A. A. No YES of Boston for this calculation in a somewhat
different form. [E. COHEN].

METHOD AT VARIABLE VOLUME. 103

or, after integration,

—1— = kt H- const. ' .... (1)

By making two independent experiments, in which we will call
iCa and iCe the concentrations in the first experiment at the times
ita and ite, and similarly, 2Ca and 2Ce the concentrations in the
second experiment at the times 2ta and 2te, we obtain, introducing
these values into equation (1), and eliminating the integration
constant,

n-l\ n— 1 n — 1

2^a 2Ce ti

n — 1 \ n — 1 n — 1

r1 P

where ti — ]ta — jt^ and t2 — 2ta — 2te<

If now the change of concentration is, in both experiments,
the same fraction of the initial concentration, that is

_ _

p p — m»

l^a 2^a

and therefore,

n — 1 n — 1

l^e 2^6 , / 2Ce\ /2^a\

— _ -^-, and -^- = -^- ,

l^a 2^a \lW \l^a/

equation (2) assumes the following simple form : -

and therefore

(n - 1) log &. = iog *!.,

l^a *2

log (tt / t,)

Under the conditions specified, n may be calculated from
this equation with complete accuracy.

1 k in this equation is (n — 1) times greater than it is in the differential equation.

104 NUMBER OF MOLECULES TAKING PART IN A REACTION.

We have here a method which is not merely similar to that
described in the preceding section, but one which is considerably
more simple, and in which the measurements can be made with
greater certainty.

The method described in the preceding section becomes valueless
in cases in which disturbing actions occur ; for example, in those
cases, so frequently observed, in which the products of the
reaction accelerate or retard the change. If the change be re-
tarded by the products of the reaction, the value obtained for
n will be too great, if it be accelerated, the value found will
be too small.

These influences may be avoided by means of the method in
which the volume is variable.

This advantage of the method is due to the fact that the same
change of volume produces very different changes in the velocities
of different reactions, according to the number of molecules taking
part in them ; for example, if the volume be doubled, the velocity
of a mono-molecular reaction is reduced to one half, that of a
bimolecular reaction to one fourth that of a trimolecular reaction
to one eighth. Where such great differences exist the disturbing
actions become less noticeable.

The value of this method is clearly seen in the researches of
No YES and SCOTT l. They show that the method at constant
volume leads to completely inaccurate results, in many cases,
owing to the occurrence of disturbing actions, while the true
nature of the reactions is brought to light by the application of
the method with variable volume. No YES and SCOTT found, for
example, that while the reaction between hydriodic acid and
hydrogen peroxide appears to be trimolecular when examined
by the first method, a more careful investigation by means of
the second shows it to be bimolecular. A similar result was
obtained with the action of bromic acid on hydriodic acid ;
the reaction, which according to the results of the first method
is to be regarded as trimolecular, is really bimolecular.

Finally, the decomposition of potassium hypoiodite in presence of
/

1 Zeit. phys. Chem. 18, 118, 1895.

METHOD AT VARIABLE VOLUME.

105

a small quantity of iodine, which was studied by SCHWICKER l, by
means of the first method, and which he considered to be tri-
molecular, turns out on examination by the second method to be
really monomolecular under certain conditions.

The method with variable volume was also used in the
investigation of: —

1. The action of bromine on fumaric acid.

2. The polymerisation of cyanic acid.

3. The action of stannous chloride on ferric chloride. (NOYES.)

1. Action of bromine on fumaric acid.

The formation of dibromsuccinic acid by the addition of bromine
to fumaric acid in aqueous solution exhibits certain irregularities
which make it impossible to apply the method at
constant volume. These irregularities are due to
the partial conversion of the dibromsuccinic acid
formed into brommaleic and tartaric acids.

The method at variable volume, however, at
once yields satisfactory results.

The experiments were made by REICHER by means
of the apparatus shown in fig. 28, the advantage
of which is that the solution of bromine and fumaric
acid, contained in A, cannot lose bromine by
evaporation.

The apparatus is completely filled with the solu-
tion, which contains 2 . 3 grains of fumaric acid,
and an equivalent quantity of bromine, per litre ;
this can be caused to flow out through the tap by
depressing the cylinder B into A, after which a
known volume, measured by means of the small
burette E, can be brought into a solution of pot-
rig. 28. assium iodide. The iodine liberated is titrated
by means of sodium thiosulphate, the concentration of the
system, which is to be determined, being proportional to the

1 Zeit. phys. Chem. 16, 303, 1895.

106

NUMBER OF MOLECULES TAKING PART IN A REACTION.

quantity of thiosulphate employed. The result of the experi-
ments is contained in the following table.

Time in minutes,
t.

Concentration. l

d(V

0
95

8.88

7.87

0.0106

The volume is then changed by introducing water into the
apparatus by means of the tap and mixing it with the solution,
after which further determinations of the titre are made.

Time in minutes.

Concentration.

dC2
- dt

0
132

3.81
3.51

0.00227

The value of n calculated from the equation

n m

log (d : C2)

is found to be 1.87 3.

If the reaction were mono-, bi-, or tri-molecular, and if no
disturbing action were at work, the value of n found would be
1, 2, or 3; since, however, a disturbing action does exist in

1 Since the choice of the units has no influence upon the result, the concentration
has been taken as equal to the numher of cc. thiosulphate required.

2 The value of -r£ has been replaced in the calculation by the ratio of the finite

g gg_'7 C7

differences, viz. - — . (cf. p. 102).

y o

3 The mean values have been taken for the concentrations, for example Cj —
8.88 4- 7.87

METHOD AT VARIABLE VOLUME. 107

this case we must expect to find a number differing more or
less from an integer. The result obtained, 1 . 87, thereforer
makes it permissible to regard the reaction under consideration
as bimolecular.

2. Polymerisation of cyanic acid.

The course of this change, also, exhibits irregularities which
make it impossible to employ the method at constant volume.
The irregularities in this case originate in the accelerative action
of the cyamelide which is formed.

We are thus opposed here by the greatest difficulties which
are to be met with in the study of the course of a reaction;
the experiments of UKECH, to which reference has already been
made, have shown that the formation of a deposit having an
accelerative action on the change may be very troublesome even
in liquid systems; in a gaseous system, with which we have to
deal in the case of cyanic acid, this difficulty becomes very
much more serious.

It is for this reason that the question as to the number of
molecules of cyanic acid which take part in the formation of
cyamelide formed the subject of a very protracted research,
extending, with intervals, over several years and in the course
of which more than five hundred experiments were made. The
method with variable volume, the advantages of which have
been pointed out, has to be improved, in this case, by the real-
isation of a special condition.

This consists in comparing the velocities of the reaction,
at very different concentrations, and in vessels the walls of which
are as far as possible identical.

The experiments may be arranged in three groups, according asr

a. The initial velocities were compared in clean vessels.

b. The velocities were compared in different parts of the
same apparatus, the walls of which were covered by a layer of
cyamelide.

108

NUMBER OF MOLECULES TAKING PART IN A REACTION.

c. The velocities were compared in the same vessel, the con-
dition of the walls being the same as in b.

A synopsis of the results is first given, after which the appa-
ratus used is described.

No.

Time in hours,
t

Concentration. l

/d Ct .d Ca\

n = g\ dt ' dt )

log (d : C2)

23
20

f 188.84
i 153.46
n , 79.07
{ 76.04

2.9

72
48

T I 126.44
* 117.66
n , 221.2
{ 189.15

3.3

24
48
24

T f 356.72
ia \ 320.68
TT r 160.34
t 152.33
n{ 304.66
0 1 280.56

2.9

23
47

j 244.97
1 220.37
TT r 111.03
t 105.3

2.8

24
73

; 533.77
t 514.23
TT f 261.31
^253.96

2.9

48
353

1 568.7
1555.56
TT f 283.36
11 1271.47

23 K

T t 271,43
1 244.97
TT f 109.48
« 107.28

3.2

Mean value

1 Since the choice of units docs not influence the result, the pressure of the cyanic
acid, reduced to 0°, is taken in place of the concentration to which it is proportional.

METHOD AT VARIABLE VOLUME.

109

a. Comparison of the initial velocities in perfectly clean vessels.

The object of this part of the investigation being to compare
the initial velocities at different concentrations in vessels of the
same form, the apparatus represented in fig. 29 was employed.
The lower extremity of the apparatus having been
placed under mercury, the compartments A and B
were evacuated, and the tap separating them closed.
The division B was then filled with cyanic acid in
the way described on page 38, and the initial velo-
city of polymerisation determined. (Experiment 1, I.
in the table.) When at least half of the cyanic acid
had disappeared, the tap was opened, the apparatus
depressed in the burette so as to transfer the cyanic
acid to A, and the initial velocity again determined
at the smaller concentration which obtained in the
apparatus. (Experiment, 1, II). Result, n = 2.9.

b. Comparison of the velocities in different parts

of the same apparatus, the walls being covered by a

layer of cyamelide.

For this purpose a globe (fig. 8) was used which
was evacuated, and filled with cyanic acid. (Experi-
ment 2, I.)

Fig. 29. The globe was then depressed so that the mercury

entered it and doubled the concentration of the cyanic
acid, after which the rate of polymerisation was again determined
(Experiment 2, II.) This experiment gave n = 3.3.

In another experiment of this kind the apparatus shown in
fig. 29 (with omission of the tap) was used. The cyanic acid
was first contained entirely in the compartment A, the mercury
filling B; then by raising the apparatus the acid was distributed
equally through A and B ; finally the original condition was
restored. The results are given under experiment 3 in the table,
and lead to the value n := 2.9. 1

and -r-i are the mean values of the first and third observations.

110 NUMBER OF MOLECULES TAKING PART IN A REACTION.

c. Comparison of the velocities in the same apparatus, the
condition of the walls being the same as in b.

The apparatus shown in fig. 7 was used in this case. Both
compartments were completely evacuated, and one of them, A,
filled with cyanic acid, the rate of polymerisation of which was
then determined. (Experiment 4, I.) By raising the apparatus
half of the cyanic acid was transferred from A to B, and the
velocity in A again measured. (Experiment 4, II.) The value of
n obtained was 2.8.

The experiment was repeated, dry air being added to the
cyanic acid in one case, in order to diminish the influence of
the walls of the vessel (Experiment 5), in another the further
precaution was taken of keeping the temperature constant by
means of a current of cold water from the water supply which
circulated round the vessel A. (Experiment 6.) The results are,
n = 2.9 and n = 3.

This apparatus is also suitable for comparisons of the veloci-
ties in clean vessels, at different concentrations. The initial velo-
city was measured in this way in A, (Experiment 7, I.) and
then in B after transferring the half of the residual acid into
it. (Experiment 7, II.) Result, n = 3.2.

From the results obtained, — the mean value of n found is
3 — it appears very probable that the polymerisation of cyanic
acid is a tri-molecular reaction which takes place according to
the equation

3CNOH = CsNaOgHg.

All doubt on the subject would be removed, if it were not
that the experiments on the effect of moistening the walls des-
cribed on page 89 have shown how very large the disturbing action
of the deposit of cyamelide formed during the reaction may be.

3. The action of stannous chloride on ferric chloride.

The reaction which occurs between stannous chloride and
ferric chloride has been carefully investigated recently by

METHOD AT VARIABLE VOLUME. Ill

A. A. NOTES \ in order to determine the number of molecules
taking part in it. According to the equation

2 FeCl3 + SnCl2 = 2 FeCl2 + SnCl4

it should be trimolecular. 2

The data which are contained in the memoir referred to will
be used in order to show how the method which was explained
on p. 103 may be applied in solving the problem which we are
considering.

A solution of ferric chloride, as neutral as possible, was placed
in flasks of 500 — 800 cc. capacity, which stood in a water bath
the temperature of which was maintained constant at 25°. The
air in the flasks was first expelled by carbon dioxide. The neutral
solution of stannous chloride 3 was then quickly added from a
pipette with a wide opening, the time was noted, and the flasks
thorougly shaken. From time to time portions of the liquid
were removed by means of a pipette and mixed with excess of
mercuric chloride solution, by which means the reaction was
at once stopped; 4 the time at which the mixture took place
was noted.

The ferrous salt formed was then titrated by means of N/10
potassium bichromate solution, potassium ferricyanide serving as
indicator.

The initial volume of the liquid in which the reaction occurred
was usually 300, sometimes 600 cc., the portion titrated varied,
according to the concentration, from 25 to 100 cc.

The following table contains the experimental results obtained
by XOYES. Ca is the initial concentration of the ferric chloride
solution employed, hi gram equivalents per litre, Ca — Ce gives
the number of equivalents of ferric chloride reduced at the time
t. The times are given in minutes.

1 Zeit phys. Chem. 16, 546, 1895.

Further proofs that this is really a trimolecular reaction are to be found in the
original memoir.

The concentration of this solution and also that of the solution of ferric chloride
were determined with N/10 potassium bichromate solution.

4 The mercuric chloride oxidises the remaining stannous chloride.

112

NUMBER OF MOLECULES TAKING PART IN A REACTION.

I. Ca -± 0.1

II. Ca =0.0625

III. Ca= 0.05

IV. Ca =0.025

Time.t

Ca-Ce

Time.t

Ca-Ce

Time.t

Ca-Ce

Time.t

Ca-Ce

0.75

0.0359

0.01434

0.00944

0.00450

0.0419

1.75

0.01998

1.5

0.01191

0.00637

1.5

0.0510

0.02586

0.01365

0.00692

2.5

0.0618

4.5

0. 03076 j 3

0.01681

0.00755

0.0700

0.03612

0.01882

0.00929

6.5

0.0770

0.04102

0.02073

12.5

0.00991

0.0866

0.04502

0.02366

0.01084

—

0.04792

0.02693

0.01210

—

0.05058

0.03091

0.01272

—

0.03402

0.01338

—

0.03708

0.01483

—

0.03915

0.01538

—

• —

0.01627

—

0.01732

—

0.01788

The following table gives the values of n which have been
calculated in different ways from the above data.

The values of n, calculated by means of equation (3) on p. 103
for m = 1/s, are to be found under nt ; the values calculated by
the same formula for m — !/2 are tabulated under n,. The values
of the time, tt and t., are obtained by graphical interpolation.

HI
(m = Vs)

n2
(m = Va)

From I

and II . .

3 22

3 54

Ill

3 20

3.51

2 56

2.79

III

2 37

2 58

Mean ....

2.84

2.90

The reaction is therefore trimolecular.

113

III. RECOGNITION OF MIXTURES.

Decomposition of dibromsuccinic and isodibromsuccinic acids.

A further application of the study of the course of a reaction
is to be found in the possibility of determining by it whether a
given substance is a single compound or a mixture of isomers.
Suppose, for example, that a -monomolecular reaction takes place
in a mixture of two isomeric substances, the course of the reac-
tion will not correspond to the equation

d-°--kC

because, owing to the fact that the substance is a mixture, two
changes will take place simultaneously, in accordance with the
equations

and _ L? = k C.

Supposing we were unaware that we were dealing with a
mixture, it would only be possible to take account of the variation
of the total concentration C = C^ + C2, and it would be found
that it did not follow the equation

dc--kc
W

but rather an equation of the form

In order to test this experimentally the course of the change
was investigated in the following three cases : —

1. The decomposition of dibromsuccinic acid.

2. The decomposition of isodibromsuccinic acid.

3. The decomposition of a mixture of the two.

Since both the iso-acid and its isomer split off a molecule

1 The two equations give the same result only when k1rrk2, that is when both
isomers decompose at the same rate. No account is taken, in these considerations, of
any catalytic action of the one isomer on the rate of change of the other.

114

NUMBER OF MOLECULES TAKING PART IN A REACTION.

of hydrobromic acid, the course of the decomposition was easily
followed by titrating the aqueous solution of the acid after heating
it in sealed tubes at 50°.

The following table contains the results.

Time

Titre.

Velocity constant.

minutes.

1 i T0

1. Dibrom-
succinic acid

0
214

10.095 (T0)
10.37

-tlog3T0 — 2TD
0.000114

380

10.57

0.000113

1 3 T 2 Ti

lr — Inrr

- t10g3T0-2Tn

2. Iso-dibrom-

9.94 (TO

—

succinic acid.

10.45

0.00081

150

11.11

0.00081

300

11.93

0.00077

*i T°

k — , log Q nn o T*
t o 10 — z in

3. Mixture of

9.87 (T0)

—

both acids.

10.31

0.00068

155

10.76

0.00056

300

11.23

0.00047

The tabulated numbers show plainly that the values of k remain
constant with the pure acids, while with the mixture of acids
they decrease.

With regard to the iso-dibromsuccinic acid, it is to be noticed
that the decomposition which it undergoes in aqueous solution at
the ordinary temperature must be taken into account in calculat-
ing k. The titre of the solution of the acid, immediately after
it was made up, was T0 = 9.83.

The constant k was obtained by eliminating x from the equations

= x log 3"T _°

and k -

2 T,

COMPARISON OF THE VELOCITIES OF REACTIONS. 115

where x is the unknown time which would be needed for the
titre to increase from T0 to T! and t the time during which the
reaction had proceeded, reckoned from the time at which the
titre was Tj.

After eliminating x we find,

1 . 3 T0 — 2 T!

k =

IV. COMPARISON OF THE VELOCITIES OF DIFFERENT

REACTIONS.

a. Hydrolysis of esters by bases.

If the velocities of different reactions are to be compared
together it is essential that their normal courses, free from
any disturbances, should be realised. If this condition be not
fulfilled the results obtained will not be comparable, on the
other hand, when it is fulfilled, perfectly definite values of the
velocity constant k may be obtained.

In order to determine the hydrolysing power of different bases
the rate at which they bring about hydrolysis has been deter-
mined by REICHER, l and more recently, and very comprehensively,
by OSTWALD. 2

REICHER'S work was carried out by the method and with the
apparatus which have been fully described on page 6. It will,
therefore, be sufficient to give here the rates of hydrolysis of
ethyl acetate which were found when different bases were used.

Hydrolysis of ethyl acetate at 9°. 4.

Base. k

Sodium hydroxide 2.370

Potassium „ 2.298

Calcium „ 2.285

Strontium „ 2.204

Barium „ 2.144

l LIEB. Ann. 228, 275, 1885.

i Journ. prakt. Chem. (2), 35, 112, 1887.

116 COMPARISON OF THE VELOCITIES OF REACTIONS.

The influence of the nature of the alcohol and acid forming
the ester was also investigated by REICHER in a similar way. The
base used was sodium hydroxide.

Influence of the nature of the alcohol. Temp. = 9°. 4.

Ester. k.

Methyl acetate 3.493

Ethyl „ 2.307

Propyl „ ........ 1.920

Isobutyl „ 1.618

Isoamyl ,, 1.645

Influence of the nature of the acid. Temp. = 14°. 4.

Ester. k

Ethyl acetate 3.2041

,, propionate 2.816

butyrate 1.702

,, isobutyrate 1.731

,, isovalerate ....... 0.614

„ benzoate . 0.830

It appears, therefore, that the greater the number of atoms
in the molecule of an ester the smaller is the velocity with which
it is hydrolysed.

b. Hydrolysis of esters by acids.

The catalytic action of the hydrogen ion having been estab-
lished by OSTWALD'S classical researches on the hydrolysis of
methyl acetate, it appeared to be of interest to investigate the
action of acids on the esters mentioned in the preceding section.

This investigation was carried out by A. DE HEMPTINNE 2 in the
following way: -

Flasks, capable of containing about 1/2 litre, were filled with
N/io hydrochloric acid and placed in a water bath the temper-
ature of which was maintained constant at 25°. In order to
diminish, as far as possible, the error arising from the solubility

1 WARDER found 3.240.

2 Zeit. phys. Chem. 13, 561, 1894.

HYDROLYSIS OF ESTERS BY ACIDS. 117

of the glass, the flasks were previously filled with strong* hydro-
chloric acid and allowed to stand for several days. That the
error was thus reduced to negligible dimensions was proved by
titrations.

A quantity of ester, such that when it was dissolved in the
acid, a 1/20 to 1/M normal, or if necessary still more dilute
solution would result, was then weighed out in a small tube.

This tube, with the ester, was placed in one of the flasks,
which was then corked up and well shaken, whereupon 50 cc.
of the contents were at once titrated with an approximately
N/10 baryta solution; in this way the exact quantity of base
required to neutralise the hydrochloric acid was obtained.

Since 50 cc. of the solution were removed for each titration,
the empty space in the flask increased rapidly ; in order to avoid
this the contents of the flask were distributed among a number
of smaller flasks of about 60 cc. capacity, which were then se-
curely corked up. Errors arising from evaporation were avoided
in this way.

At suitable intervals 50 cc. of the liquid contained in the
flasks were removed and titrated. Two burettes were used for
this purpose; from the first a quantity of N/io baryta solution,
exactly equivalent to the hydrochloric acid present, is run in, by
means of the second the excess of acid is titrated with N/20
baryta solution.

The velocity constant is calculated from the equation l

- Tt = -

After integration and elimination of the integration constant
we obtain

1 C0

k = T log £

where C0 is the concentration of the ester at the beginning of

the experiment, and Ct its concentration after partial decomposition.

The degree of purity of the ester having been determined

beforehand by decomposing a weighed quantity of it with baryta,

1 Compare pp. 2 and 3.

118

COMPARISON OF THE VELOCITIES OF EEACTIONS.

the concentration C0 is known, and, therefore, k can be cal-
culated from the titrations without awaiting the completion of
the hydrolysis which in this case requires a rather prolonged
time.

Some preliminary experiments with acetic acid showed that
it does not possess a catalysing power which is at all compar-
able with that of hydrochloric acid. Using a N/20 solution
of ester, the acceleration produced by the acetic acid set free
during the hydrolysis may be neglected during a considerable
part of the change. A small acceleration becomes perceptible
only when 60 to 70 per cent of the ester has been decomposed.
The following results were obtained with methyl acetate.

Time. l

Percentage of the
ester decomposed.

p 2

"4:

17.96

0.0860

0.001433

280

60.18

0.3990

0.001428

350

68.29

0.4987

0.001425

Mean =:

0.001428

18.88

0.0908

0.00144

290

61.68

0.4164

0.001436

350

68.59

0.5030

0.001437

Mean =

0.001437

The mean of the two experiments is 0.001432.

In order to determine the influence of the nature of the alcohol
and acid forming the ester on the velocity with which it under-
goes hydrolysis, R. LOWENHERZ 3 has extended HEMPTINNE'S work
to other esters.

The following table contains the whole of the experimental

1 The unit of time used here is 5 minutes.

2 If we make C0 = 100, then Ct = (100— 17 .!

3 Zeit. phys. Chem. 15, 389, 1894.

— 82.04, and so on.

HYDROLYSIS OF ESTERS BY ACIDS.

119

results obtained by DE HEMPTINNE and LOWENHERZ expressed in
the same units l as the numbers obtained by REICHER for the rate
of hydrolysis by caustic soda, which are also included in the
table to facilitate comparison.

1. Influence of the nature of the alcohol.

Hydrolysis of different esters of the same acid at 25°.

Table A.

Ester.

for hydrolysis
with hydro-
chloric acid.

k
for hydrolysis
with caustic
soda.

Methyl acetate
Ethyl

0.00662)
0.0068

9.66
6.38

ProDvl

0.0067

5.31

Phenvl

0.0040

(rlvoervl

0.0031

IVIethvl propionate

0.0071

Ethyl

0.0073

5.61

ProDvl

0.0072

Methyl butyrate . ....

0.0039

Ethyl

0.0042

3.39

Propyl

0 0041

v.r j

Methyl monochloracetate . .
Ethyl „ . .

0.0043
0.0040

—

1 The numbers obtained by REICHER (at 9°.4 and 14°.4) and by LOWENHERZ (at
40°) have been calculated for 25° by means of the equation ^ — — — -f B,

which will be explained later. REICHER used the minute as unit of time; the unit of
concentration of the ester, as explained on p. 13, does not affect the value of k, the
reaction being monomolecnlar ; REICHER also calculated the values of k for normal
caustic soda solutions, and used natural logarithms, so that the numbers in table

] n V" 9 S025
A are obtained by multiplying HEMPTINNE'S numbers by -

2 OSTWALD found 0.00689. Thai; k is here found somewhat smaller is doubtless
due to the greater dilution.

120 COMPARISON OF THE VELOCITIES OF REACTIONS.

2. The influence of the nature of the acid.
Hydrolysis of different esters of the same alcohol at 25°.

Table B.

Ester.

k
for hydrolysis
by hydrochloric
acid.

for hydrolysis
by caustic
soda.

Ethyl formate

0 13 l

acetate . . .

0 0068

6 38

,, monochloracetate . . .
,, dichloracetate
, propionate

0 . 0040
0.0064
0 0073

5 61

,, butyrate . . .

0 0042

3 39

,, isobutyrate ....

0 0041

,, valerate

0.0014

Methyl benzoate * . .

0. 00004 l

The differences between the rates at which the, esters formed
from the same acid and different alcohols are hydrolysed (table A)
are very small compared with the differences which are found
between the rates of hydrolysis of the esters of the same alcohol
with different acids, (table B).

While the differences between the velocity constants for the
esters of methyl and ethyl alcohols with the same acid scarcely
exceed the experimental error, the constants for the ethyl
esters of two similar acids, such as formic and acetic, are
approximately in the ratio 20 : 1.

The extreme values of the constants obtained when the alcohol
is varied are nearly in the ratio 2:1, (methyl alcohol and
glycerin), while when the acid is varied the ratio is approximately
3300 : 1 (Formic and Benzoic acids).

The following table, which is taken from table A, shows that
if the velocities of hydrolysis of the esters of acetic acid be

1 This number makes no pretension to exactitude, it merely gives the order of
magnitude correctly.

2 This ester was used in place of the ethyl ester because it is more readily soluble.

HYDROLYSIS OF ESTERS BY ACIDS.

121

known, the corresponding values for the esters of any other acid
may be approximately calculated from them, when the value for
one of the series has been determined. l

Ester.

io of rates
lydrolysis.

Ester.

| .3

"g |'

f§ **

tf *S

Methyl acetate j
Ethyl

Propyl „ 1

0.971
1.015

Methyl propionate \
Ethyl
Propyl „ 1

0.972
1.014

Methyl butyratei
Ethyl „ 1
Propyl „ I

0.928
1.024

It is also to be seen from the table that the hydrolysing
power of the hydroxyl ion is very much greater than that of the
hydrogen ion, (about 1000 times). The activities of the two
ions do not appear to be proportional to each other, for while
the velocity of hydrolysis by caustic soda decreases with increas-
ing molecular weight of the ester hydrolysed, this is not the
case with hydrolysis by acids.

1 There are two errors in HEMPTINNE'S table I, p. 565 loc. cit. The ratio of
the velocities of methyl and ethyl butyrate should be 0.944 instead of 0.9736, and of
ethyl and propyl butyrate should be 1.024 instead of 1.004.

THE INFLUENCE OF TEMPERATURE ON
CHEMICAL CHANGE.

FIRST PART.

THE RELATION BETWEEN THE VELOCITY-
CONSTANT K AND THE TEMPERATURE.

a. Application of thermodynamics.

We shall employ here a formula the strict proof of which
will be given later in the chapter dealing with chemical
equilibrium.

Taking the chemical equilibrium which occurs with nitrogen
peroxide as a concrete example, we may represent it in the
following way,

N204 ^=± 2 N02.

We are dealing here with two changes taking place in opposite
directions, namely

N204 = 2 N02, and 2 N02 = N204.

At any given temperature the velocity constant of each of
these changes has a perfectly definite value, which we will call
ki for the first, and k2 for the second change.

It may be proved, by means of thermodynamics, l that the
values of kx and k2 must satisfy the following equation: -

d log ki d log k2 q m

dT dT " 2T2 '

T is the absolute temperature, and q the quantity of heat, in
calories, which would be evolved by the transformation of unit

1 The proof of this equation is given on p. 148 et seq.

APPLICATION OF THERMODYNAMICS. 123

quantity (in this case 92 kgrms.) of the first system into the
second at constant volume.

Although this equation does not directly give the relationship
between the constants k and the temperature, which we are
seeking, it shows that this relationship must be of the form

= ± + B. . . . (2)(VAN'THOFF)

where A and B are constants.
If we put A = 0, we obtain

-jjTjT^ : : B ...... (3) (BEETHELOT).

This equation corresponds to the expression k =: ab*, which
was proposed by BERTHELOT in connexion with his experiments
on etherification.

As will be shown later, the results of experiment are often
in good agreement with the formula when we put B = 0, and
consequently

d log k A

By integration of (4) we obtain

log k =: - - FfT ~f~ constant.

So far, we have assumed that q is independent of the temp-
erature. This is, however, certainly not allowable when the
equation is applied to considerable intervals of temperature. The
quantity of heat evolved by a reaction changes with the temp-
erature to some extent.

Taking this into account, and writing qT = q0 + bT, where
b is the difference between the specific heats of the two systems, 2
we obtain, in place of equation (4),

d log k A + BT
— - --

1 Zeit. phys. Chem. 4, 226, 1889.

2 Appendix, note 3.

3 Inaugural Dissertation, Amsterdam 1893. Zeit. phys. Chem. 12, 155, 1893.

124 THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

From this equation, we obtain by integration,

j£

log k = — — -|- B log T + constant.

If we put A — 0 in equation (5), we obtain

— -— —- — ^-, .... (6) (HARCOURT and ESSON) !

or after integration

log k = B log T + constant.

Equation (4), p. 123, which in many cases is in good agree-
ment with the observations which have been made, makes it
possible to calculate the effect of a given change of temperature
on the velocity of a reaction. 2

BERTHELOT'S equation reproduces the chief characteristic of the
relation between velocity of reaction and temperature, which is
that if the temperatures form an arithmetical series the rates of
change at these temperatures will form a geometrical series.

By integration between the limits T! and T2, we obtain from
equation (4)

k! A T! - T2

log — = A ,

K2 J-l -^2

ki and k2 being here the velocity constants at the temperatures
T! and T2 respectively.

For a rise of temperature of 10 degrees, therefore,

ki 10

log k7 : : A TTT;

We see from this, and on this point all the functions which
have been proposed are in agreement, that at higher temperatures
the increase in the ratio of the velocity constants produced by
a rise of temperature of 10 degrees will be smaller than at lower
temperatures.

1 Proc. Roy. Soc. 58, 112, 1895. HARCOURT and ESSON express, in this paper,
the connexion between the rates of reaction «i and a..2 at the temperatures Tj and T.2,
as follows

2 D. M. KOOY, loc. cit.

APPLICATION OF THERMODYNAMICS.

12S

The great majority of cases which have as yet been investi-
gated in this direction have been studied in the interval of temp-
erature lying between 0° and 184°, and it is very striking that
the ratio of the velocity constants for two temperatures differing
by 10 degrees has a value between 2 and 3 approximately. In
other words, a rise of temperature of 10° doubles or trebles the
velocity of a reaction.

The following table will serve to illustrate this. 1

Reaction.

Interval of
temperature.

Mean ratio
of velocities
at T and
(T + 10).

Sodium ethylate -4- methyl iodide 2 . .
HPOs + H>O — H3PO4 3

0°— 30°
0°_61°

3.34

300

Hydrolysis of ethvl acetate4

30 6—30° 4

2.03

9° 4—44° 94

1.89

KClOs + FeSO4 -f H? SCh 6

10° 32°

244

C4H4O4Br2 = HBr f C^CUBr 7 . . .

Decomposition ofethylene hydrochloride
into hydrochloric acid and ethyleiie 8
Decomposition of methylethylene hy-
drochloride

15°— 101°
24°. 5— 43°. 6
24° 5—43° 6

2.65

2.87
268

Decomposition of dimethylethylene hy-
drochloride 8

24° 5—43° 6

266

Decomposition of trimethylethylene hy-
drochloride 8

040 5_43<> Q

270

Decomposition of #-dichlorhydrine 8 . .
Inversion of cane sugar 9

24°.5— 43°.6
25°_55°

2.79
363

Hydrolysis of acetamide by acids 10 . .
Action of caustic soda on sodium chlor-
acetate n .

65°— 100°
70°— 130°

2.12
2.54

C-2H3C1O2 + H>O =: aH403 + HC112.
Hydrolysis of tertiary amylacetate 13 . .

80°— 130°
156°— 184°

2.55
2.19

It is also of interest that similar phenomena are, according

KOOY, Zeit. phys. Chem. 12, 155, 1893.

2 HECHT and CONRAD, Zeit. phys. Chem, 3, 473, 1889. • also p. 133.

3 SABATIER, Corapt. Rend. 106, 63, 1888.
* WARDER, Berichte, 14, 1365, 1881.

5 REICHER. LIEB. Ann., 232, 111, 1885. also p. 130.

6 HOOD, Phil. Mag. (5) 20, 185, 1885. also p. 132.

7 Page 127.

8 EVANS, Zeit. phys. Chem. 7, 356, 1891.

9 SPOHR, Zeit phys. Chem. 2, 195, 1888.
OSTWALD. Journ. prakt. Chem. (2), 27, 1, 1883.

11 Page 129.

12 Page 130.

13 KONOWALOW, Zeit, phys. Chem. 1, 64, 1887.

126

THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

to the researches of CLAUSEN *, to be observed in the respiration
of plants. The quantities of carbon dioxide expired in equal inter-
vals of time increase rapidly when the temperature rises between
0° and 25°. A rise of temperature of 10° increases the quantity
2.46 times (on the average) with wheat, 2.45 times with lupins,
and 2.47 times with syringa (lilac).

Above 25° the increase in the rate of the metabolic changes
is smaller, and above 50° it approximates to that which is
found at lower temperatures.

With regard to the ratio of the velocity constants at high
temperatures, KooyV experiments on the decomposition of phosphine
at temperatures between 310° and 512° confirm the result which
was obtained from the equation

kt 10

log r- = A =-=-.

K2 J-l i2

The following table contains the velocity constants determined
experimentally at different temperatures.

If the ratio of the velocity constants be calculated approxim-
ately, for differences of temperature of 10°, in the intervals
310°_367°, 367°— 446°, 446°— 512°, the value obtained is 1.2,
while for the interval of temperature 0° — 10° the number 2.92
is obtained, so that at lower temperatures it is of the same order
of magnitude as the ratio found already for other reactions at
the ordinary temperature.

Decomposition of phosphine.

Temperatures.

Velocity constant. 3

310°
367°
446°
512°

0.00048
0.0015
0.0057
0.0186

1) Landw. Jahrbucher. 19, 894, 1890.

2) loc. cit.

3) That the velocity constant found here does not agree with the number found on
page 100, is due to the influence of the walls of the vessel. Any change in the vessel
produces a change in the constant. The two series of experiments in question were
separated from each other by an interval of about ten years, so that they were made
with quite different pieces of apparatus.

DECOMPOSITION OF DIBROMSOCCINIC ACID.

127

b. Experimental treatment of the subject.

The influence of the temperature on the velocity of a reaction
has been studied in a number of cases which are described in
what follows. •>

1. Influence of the temperature on the rate of decomposition of
dibromsuccinic acid.

Since it was found that dibromsuccinic
acid decomposes at 100° in aqueous
solution in only approximate accordance
with the equation

C, H4 04 Br2 = C4 H3 04 Br + H Br,

it became necessary to investigate the secondary
reactions which occur at different temperatures.
With this object the increase which the titre
of a solution of the acid undergoes on heating
to 75°, 100°, 125°, and 150° was determined.
The solution was heated in sealed tubes and
the carbon dioxide, formed by the secondary
decomposition of the acid, removed before making
the determinations of the titre. The tubes A
(fig. 30) were opened after being heated, and
brought, by means of the hook E, into a
kind of exsiccator containing a pice of caustic
potash at B. This was connected, at D, to the
air pump and partially evacuated, the tubes
being then allowed to remain in the partial

vacuum for 24 hours. !

The following table contains the augmentations of the titre

produced by heating for different periods of time and at different

temperatures.

Special experiments had shown that the carbonic acid may be removed in this
way without loss of hvdrobromic acid.

128

THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

75°

100°

125°

150°

Duration

Ratio of

Duration

Ratio of

Duration

Ratio of

Duration

Ratio of

of heating
in hours.

increase to
initial litre.

of heating
in hours.

increase to
initial titre.

of heating
in hours.

increase to
initial titre.

of heating
in hours.

increase to
initial titre.

0.507

3.3

0.501

0.5

0.464

0.1

0.396

0.5191

4.3

0.504

0.8

0.462

0.2

0.356

It is evident that below 100° the increase of the titre cor-
responds to the decomposition of the dibromsuccinic acid into
hydrobromic acid and brom-malei'c acid, the increase being about
50 per cent, while above 100° the smaller increase is due to the
secondary decomposition of the acids with formation of carbon
dioxide.

The following table contains the values of the velocity con-
stants.

Temperature.

Observed. 2

Calculated.

101

0.0138

89.4

0.00454

0.00458

0.002

0.00183

70.1

0.000734

60.2

0.000284

0.000287

0.000108

0.000109

0.0000375

0.0000422

0 . 0000042

0.0000039

The values given in the third column are calculated by means
of the equation

d log k _ _ A

1 This number is somewhat to high owing to an error in the determination of the titre.

2 Each number is the mean of two observations.

EXPERIMENTAL TREATMENT.

129

Puttmj

we obtain

A = 0, B = 0.0412, and T = t + 273,

log k = 0.0412 t — 6.02219.

2. Influence of the temperature on the rate of the reaction
between sodium chloracetate and caustic soda.

The experiments on this point were made by SCHWAB in the
way which has already been described on page 17.

The following table contains the experimental results, together
with those calculated.

Temperature.

Observed. *

Calculated.

130°

.0.217

0.217

120

0.0857

0.0856

110

0.0305

0.0338

100

0.0128

0.0133

0.00499

0.0525

0.00198

0.00207

0.000822

0.000818

The numbers in the third column are calculated by means of
the equation

log k = 0.0404 t — 5.91554,
which is obtained from the equation

dT T2

by putting A = 0; B = 0.0404; T = t + 273.

1 Each number is the mean of from three to six observations.

130

THE INFLUENCE OF TEMPERATUEE ON CHEMICAL CHANGE.

3. Influence of the temperature on the rate of change of
chloracetic acid in aqueous solution.

This series of experiments also was carried out by SCHWAB.

Temperature.

Observed !.

Calculated.

130°

0.00237

120

0.00105

0.00102

110

0.000436

0.000424

100

0.000173

0.000167

0.0000603

0.0000627

0.0000222

If we put

we obtain

B = 0,

log k = — =- + 11.695, where log A = 3. 76 125.

4. Influence of the temperature on the rate of hydrolysis of
ethyl acetate by caustic soda.

Two series of experiments have been made on this subject,
one by WARDER, 2 the other by REICHER, 3 the values of k obtained
agreeing together satisfactorily.

REICHER employed in his experiments the apparatus represented
in figure 1, and described fully on page 6, except that the
temperature was maintained constant at any desired point by
means of a thermostat.

1 Each number is the mean of six observations.

2 Amer. chem. Journ. 3, 203, 1881. Berichte, 14, 1365/1881.

3 LIEB. Ann. 232, 103, 1885.

EXPERIMENTAL TREATMENT.

The results obtained were as follows.

131

Temperature.

Observed. l

Calculated.

9.4

2.307

14.4

3.204

3.2

24.22

6.151

35.14

12.096

11.97

44.94

21.648

The numbers in the third column have been calculated, in this
case also, by means of the equation

d_log_k
dT

Putting

A = 1780, B = 0.00754, T = t + 273,

we obtain

1780

log k = — ^~ + 0.00754 T + 4.53.

ARRHENIUS 2 has shown that many of the observations which
have been recorded by different authors may be represented by
the formula

d log k A

This formula is also applicable to the experiments of series
5 — 9 which follow.

1 The first, third, and fifth numbers have been used in calculating the constants of
the equation.

2 See page 123.

132

THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

5. Influence of the temperature on the velocity of the reaction
between potassium chlorate and ferrous sulphate in presence of

sulphuric acid.

This reaction has been very carefully investigated by HOOD; l
0.5637 grams of ferrous sulphate, 0.2057 grams of potassium
chlorate, and 3.099 grams of sulphuric acid were brought into
a flask, which was kept at the desired temperature by means
of a thermostat, and diluted to 260 cc.

The progress of the oxidation was followed by titrating 10 cc.
of the liquid with permanganate from time to time. The results
are contained in the following table.

Temper-
ature.

Observed.

Calculated.

Observed.

Calculated.

1.00

2.51

2.54

1.21

2.96

3.02

1.46

1.462

3.59

3.62

1.73

1.76

5.08

5. OS3

2.11

6.04

—

7.15

7.11

The values of k are calculated by means of the formula

log k = -

+ 27.189.

1 Phil. Mag. (5), 20, 323, 1885.

2 The value of k at 10° is taken as unity.

3 These values were used in calculating the constants in the equation.

EXPERIMENTAL TREATMENT.

133

6. Influence of the temperature on the rate of hydrolysis of
ethyl acetate by caustic soda.

We shall consider here the experiments of WARDER to which
reference has already been made. The results are contained in
the following table.

Temper-

ature.

Observed.

Calculated.

ature.

Observed.

Calculated.

3.6

1.42

1.48

27.0

7.24

7.16

5.5

1.68

1.70

28.4

8.03

7.81

7.2

1.92

(1.92)

304

8.88

8.82

11.0

2.56

2.51

32.9

9.87

10.24

12.7

2.87

2.82

34.0

10.92

(10.92)

19.3

4.57

4.38

35.0

11.69

11.60

20.9

4.99

4.86

37.7

13.41

13.59

23.6

6.01

5.78

—

The values of k are calculated by means of the equation

log k = -

+ 20.562.

7. The influence of the temperature on the inversion of cane
sugar was investigated by URECH, ' and more recently by SPOHR. *
The values of k obtained, in this case also, are well represented
by the formula of ARRHENIUS.

The same remark is true with reference to (8) the influence
of the temperature on the action of sodium ethylate on methyl iodide,
which was studied by HECHT and CONRAD, 3 and to (.9) the influence
of temperature on the formation of nitrites from syn-aldoxime
acetates and on the change of the latter into the antwnodifi cations,
which were studied by H. LEY. 4

1 Berichte, 16, 765, 1883; 17, 2175, 1884.

2 Zeit. phys. Chem. 2, 196, 1888.
;; „ „ „ 3, 450, 1889.
4 » ,,18, 376, 1895.

134 THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

10. Influence of the temperature on the rate of decomposition of
the hydrides of arsenic and phosphorus.

While the reactions which we have so far considered have
been investigated only within rather narrow limits of temperature,
we have here a case in which determinations of the velocity
have been made over a fairly wide range.

KOOY has determined the velocity constants for the decom-
position of arsenic and phosphorus hydrides at temperatures as
much as 200° apart.

a. Arsenic hydride.

The apparatus used, and the way in which the experiments
were made, are described on page 41. The velocity constants
were determined at the boiling points of amyl benzoate (256 °)r
diphenylamine (310°), and anthraquinone (373°).

We have already seen (p. 43) that changes in the nature of
the walls of the vessel may have a considerable influence on
the velocity of a reaction, so that to obtain results at different
temperatures which would be comparable with each other it was
necessary to avoid disturbances arising from this cause.

This was achieved by making all the determinations of the
velocity in the same new vessel and by avoiding prolonged
heating. By taking these precautions the nature of the walls
changed very little, and the values of k obtained are comparable.

The following table contains the results.

Temperature.

Velocity constant. l

256

0 0209

311

0.0506

367

0.202

See also p. 2, and note 3 on p. 126.

EXPERIMENTAL TREATMENT.

135

b. Phosphine.

The experiments were made in the same way as those with
arsenic hydride, the rate of decomposition being determined at
310° (diphenylamine), 367° (anthraquinone), 446° (sulphur); and
512° (sulphide of phosphorus).

The results have already been given in the table on page 126,
moisture had no influence on the value of k.

The agreement between the observed values of k and those
calculated by means of the formula of ARRHENIUS,

d log k A
dT " T2'

is not satisfactory.

In this case the intervals of temperature are large, and the
variation of q with the temperature cannot therefore be neglected,
so that it is better to employ the formula

d log k A + BT
dT T2 '

or, after integration,

log k = - - ~ + B log T + const. (See page 124.)

The values of k calculated by means of this equation agree
better with the observed numbers. The formula of HARCOURT and
ESSON likewise gives fairly correct results, as the following
table shows.

Temper-

k
calculated

calculated

k
calculated

ature.

observed.

from (4)
p. 123.

from (5)
p. 123.

from (6)
p. 124.

310

0.00048

(0. 00048) l

(0.00048)

367

0.0015

0.0017

0.0014

0.0015

446

0.0057

0.0071

(0.0057)

0.0063

512

0.0186

(0.0186)

1 The numbers enclosed in brackets have been used in calculating the constants in
the equations.

THE INFLUENCE OF TEMPERATURE ON
CHEMICAL CHANGE.

SECOND PART.
THE TEMPERATURE OF IGNITION.

One of the conclusions arrived at in the preceding section
requires further consideration, since it appears to be out of
harmony with the phenomena of inflammation.

The investigations on the influence of temperature on chemical
change, to which attention has so far been directed, led to
the conclusion that this influence was a continuous one; the
experiments which have been described, and the theoretical
considerations which have been advanced agree in this respect.
The phenomenon of ignition appears to indicate, however,
by its sudden occurrence at a definite temperature, that there
are exceptions to this continuity. L. MEYER l expresses himself
on the subject in the following way: —

" The lowest temperature at which a given chemical reaction
occurs, which in the case of combustible substances is known
as the temperature of ignition, might be called, in general,
the temperature of reaction. "

There is here a distinct contradiction of the views which
have been advanced as to the influence of temperature on the
velocity of reactions. These views do not admit the possibility
of any sudden acceleration of the reaction, and require us to
suppose that if a reaction occur at any given temperature
it will also go forward at any other temperature, although with
a different velocity.

1 Dynamik der Atome, 1883, p. 417. Also BUNSEN, Gasom. Methode, 1877, p. 336.

THE TEMPERATURE OF IGNITION. 137

A closer study of the subject will, however, show that
the phenomena of ignition do not in the least oblige us to
admit the existence of a temperature at which the reaction
begins ; the occurrence of inflammation then falls into line with
the ideas which have so far been acquired.

The proof of this statement depends on the fact that there are
three conditions fulfilled by every reaction which exibits the
phenomenon. By inflammation we shall understand here not
only the phenomena of combustion, but also any complete chemical
transformation which occurs in consequence of a local elevation
of the temperature to the so-called temperature of ignition.

In every change of this kind the following conditions are
fulfilled :-

1 . The reaction which produces the inflammation evolves heat.

2. The reaction occurs more or less rapidly below the temp-
erature of ignition.

3. The reaction is accelerated by an elevation of temperature.
The necessity of the first condition being sufficiently proved

by facts which are generally known, it will suffice to cite the
rather sparse observations which lead to the admission of the
truth of the second; the third condition appears to be fulfilled
equally by all chemical changes so that there is no reason for
considering it in more detail.

The following, then, are the observations which appear to
show that the reactions occur below the temperature of ignition :

The oxidation of phosphorus, phosphine, arsenic, sulphur, hy-
drogen *, hydriodic acid, carbon monoxide, ether, and paraffin, has

I A striking example of this is given in the most recent experiments of V. MEYER
and \V. RAUM (Bcrichte, 28, 2804, 1895) on the effects of prolonged exposure of
electrolytic gas to a moderate temperature. At the ordinary temperature the rate of
formation of water is so small that it practically cannot be observed. On heating
electrolytic gas continuously for 10 days to 300°, the formation of water could not be
proved, but on heating day and night for 65 days, to this temperature, a distinct
formation of water occurred. It is, therefore, natural to suppose that even at lower
temperatures it would be possible to demonstrate the formation of water, by healing
for a sufficiently prolonged period of time. In the experiments at 300°, which have
been referred to, the following percentages of the electrolytic gas contained in three
bulbs (see p. 4S) were transformed into water; —

9.5, 0.4, 1.3.

No change could be detected at 100°, after heating for 218 days and nights.

138 THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

been observed considerably below the temperature of ignition.

The same is true of the chemical transformations undergone
by ozone, chloride of nitrogen, cyanic acid, mixtures of chlorine
and hydrogen, and of chlorine and hydrocarbons, etc. l ; they take
place more or less slowly at temperatures below those which
determine ignition or explosion.

The three conditions mentioned being fulfilled, a phenomenon
of the nature of ignition may occur.

To prove this, suppose we have a substance which is not
susceptible of chemical change, for example, atmospheric air,
and suppose its temperature to be raised locally from 0° to TI° ,
(fig. 31). On removing the source of heat, the increased temp-

rig. 31.

erature will be communicated to the surrounding gas, and will,
therefore, give rise to a kind of hot wave which will be propagated
with a certain velocity, its temperature sinking continually
towards 0° .

l Bull. Soc. Chim. 13, 1, 1370. Compt. Rend. 78, p. 1853, 1874. Berichte, 15,
2155, 1832; 16, 139 and 478, 1883. VAN 'T HOFF observed that the slow oxidation
of heated paraffin is accompanied by a phosphorescence which is very similar in appear-
ance to a combustion.

THE TEMPERATURE OF IGNITION. 139

The curve T^Ai, which is obtained by measuring the temper-
atures along OT and the distances along OD, represents graphically
the relation between the temperature of the wave and the distance
which it has travelled from the starting point. For brevity we
will call /\ T the diminution in the temperature of the hot wave
during the first moments of its progress.

Suppose, now, that a chemical reaction which satisfies the
three above-mentioned conditions may occur in the gas ; suppose
for example, that we have electrolytic gas in place of atmospheric
air. A local elevation of temperature will then produce a wave
of the kind described, but with the difference that the temp-
erature, especially at first, will sink less rapidly during its
propagation, because the chemical change produced by the eleva-
tion of temperature evolves heat. The value of /\ T will thus
be diminished, and the graphical representation of the temperature
of the hot wave will be given by the curve TjAx (fig. 32).

Fig. 32.

We will now consider the effect of a greater initial elevation
of the temperature in the two cases. The matter is simple, so
far as the substance which does not undergo chemical change

140 THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

is concerned; the temperature of the hot wave will fall more
rapidly than before, owing to the greater difference of temp-
erature between it and the medium through which it is propag-
ated; this is represented by the curve T2A2 in fig. 31. When a
chemical change occurs, however, as with electrolytic gas, we
have in addition to this influence, which increases A T, another
which diminishes it; for the chemical change, accelerated by the
higher temperature, will now produce a greater quantity of heat.
If the action which tends to diminish /\ T exceed that which
tends to increase it, it is evident that the value of A T w^
diminish as the initial temperature rises.

This being the case, we perceive the possible existence of a
temperature, T2, at which the value of /\ T will be zero, in
other words, of a temperature at which the wave will preserve
its initial temperature unchanged; this is represented by the
line T2A2 (fig. 32).

A still higher initial temperature, T3. would give rise to a
hot wave the temperature of which, instead of falling, would
rise until it reached the temperature which the total transform-
ation of the substance is capable of producing. (T3A3, fig. 32.)

It is obvious that those waves the temperature of which falls
can only give rise to a very minute quantity of change, while
those of which the temperature rises lead to the transformation
of the whole of the substance. The temperature T2, therefore,
which gives rise to a wave of constant temperature, corresponds
in every particular to the ignition temperature.

It would not be difficult to translate the preceding into
mathematical symbols, but it is preferable to express it in words
as follows: -

The ignition temperature is the temperature at which the initial
loss of heat, due to conduction etc., is equal to the heat evolved
in the same time by the chemical reaction.

It must, however, be remarked that certain facts are not
accounted for by the foregoing considerations. It is known
that, at a given temperature, phosphorus is no longer lum-
inous in oxygen gas the pressure of which exceeds a certain
limit; in other words there is a definite pressure at which

THE TEMPERATURE OF IGNITION.

141

the velocity of the reaction suddenly assumes a finite value.
JOUBERT l found that the luminosity first became visible at the
different temperatures given in the following table, when the
pressure of the oxygen was diminished to the corresponding
value which is given.

Temp.

Pressure of
oxygen.

Temp.

Pressure of
oxygen.

1.4°

355 mm.

9.3

538 mm.

3.0

387

11.5

580

4.4

408

1.4.2

650

5.0

428

18.0

730

6.0

460

19.2

760

8.9

519

Eepresenting these numbers by means of a curve, the abscissae
of which are the temperatures, and the ordinates the pressures,
we obtain the approximately straight line shown in fig. 33.

Suppose, now, that the pressure of the oxygen is maintained

Pressure,

JV0 oxidation.

Oxidation occurs.

-Temperature.

Fig. 33.

constant and the temperature raised, then, passing from left to
right across the figure, as soon as we cross the line oxidation

1 Tlu'se, p. p. 29, :i(). Sn- also p. .">:> ante.

142 THE INFLUENCE OF TEMPERATURE ON CHEMICAL CHANGE.

suddenly begins, in other words, we find, on raising the temp-
erature, a per saltum transition from conditions under which no
oxidation occurs to conditions under which it does occur.

Mathematically considered the phenomenon perhaps indicates
that the equation

d log k j\._
~~dT~ !?'

should have another term containing (T— t), where t would
represent the temperature at which the discontinuity occurs.

CHEMICAL EQUILIBRIUM.

FIRST PART.

THE THREE FORMS OF CHEMICAL
EQUILIBRIUM.

The study of chemical equilibrium yields results which form
a very important addition to our knowledge of chemical change.

This will be obvious if, with PFAUNDLER, we regard equilibrium
as the result of two changes taking place in opposite directions
with equal velocity.

Since, according to HORSTMANN, the principles of thermodyna-
mics may be applied to chemical equilibrium, and since the
experimental difficulties which are encountered in its study are
frequently much smaller than is the case in dynamical researches,
the experience gained in the domain of chemical equilibrium
may advantageously be applied in the study of chemical change.

Three kinds of equilibrium may be distinguished : -

1. Equilibrium in homogeneous systems.

2. „ ,, heterogeneous ,,

3. „ „ condensed ,,

I. HOMOGENEOUS SYSTEMS.

a. At constant temperature.

In cases of equilibrium in homogeneous systems the bodies
forming the system may be gaseous, liquid, or solid. l

An example of the first of these is found in the case, which

1 This latter form of equilibrium will not occupy us further; the so called "solid
solutions", and also many diffusion phenomena in solid bodies show, however, that it
is probably justifiable to speak of equilibrium in a homogeneous solid system.

144 CHEMICAL EQUILIBRIUM.

has already been mentioned, of the dissociation of nitrogen
peroxide ^

NA ^=± 2 N02.

The following is an example of a homogeneous equilibrium
in a liquid system,

CH3COOH + C2H5OH ^ CH3COOC2H5 + H20.

As we have already observed, the equilibrium is to be regarded
as the result of two changes taking place with the same velocity
in opposite directions, so that, in the case of a homogeneous
equilibrium, the study of the velocities of the opposing reactions
permits us to calculate the ratio between the concentrations of
the two systems when the state of equilibrium is attained.

In the example chosen \

N,0, ^ 2 NO,,
the velocities of the two reactions are given by the equations,

- = kjCj, and — -~ — k2C2.
at at

GI and C2 are the concentrations of the systems N204 and N02
respectively, in the units which have already 3 been employed
(92 kgrms, per cubic metre).

Equilibrium having been attained, the velocities of the reactions

rip I p \

and — • <•— I are equal, and therefore
at at /

d = k2C2,

or in general,

1 Henceforward the system written to the left of the ~>" sign will be called the "first
system", that to the right the "second system", the letters Cj and Iq will be used with
reference to the first, C2 and k2 to the second. This choice is of course purely arbitrary,
since the part taken by the two systems in producing equilibrium is the same.

2 Page 4.

ISOTHERMAL EQUILIBRIUM IN HOMOGENEOUS SYSTEMS. 145

where r\i and n2 are the numbers of molecules in each of the
systems which take part in the reaction.

An equation of this form has already been given by GULDBERG
and WAAGE, by PFAUNDLER, and also by HORSTMANN.

It is to be noticed, however, that we have deduced it from
the equation

dC _ n

~ dt

which is exactly true only for great dilution. The derived equation
also is therefore subject to the same restriction, and where this
restriction is observed the experimental results are found to be
in agreement with those obtained from the equation. l

Just as the determination of the velocity constants may be
used in order to calculate the ratio between the concentrations
of the opposing systems in the state of equilibrium, so this ratio
may be employed to obtain a knowledge of the velocity constants.

The investigation of the equilibrium gives the values of the
concentrations of the systems taking part in it, and, therefore,
that of the ratio between the velocity constants Iq and k2 which
henceforth will be denoted by the letter K and called the equili-
brium constant.

We have thus,

If, for example, Iq had been determined by the study of the
velocity of one of the two opposing changes, the value of the
velocity constant of the other change would be obtained from a
study of the equilibrium.

BERTHELOT and PEAN DE SAINT GILLES 2 have determined, under
conditions which were varied as much as possible, what part of
an acid is convertible into ester by treating it with a given
quantity of an alcohol.

1 Juurn. prakt. Chetn. (2), 19, 69 et seq. 1879.

-' Ann. Chim. Phys. (3), 05, 3S5, 1*02; (3), 60, 5, 1862; (3), 68, 225, 1863
Also VAN 'T MOIT, Bcrichte, 10, 069, |s?7.

146 CHEMICAL EQUILIBRIUM.

The reaction takes place as follows,

Acid + alcohol ^z± Ester -f water.

If we bring together 1 gram-molecule of acid, w gram-molecules
of water, and a gram-molecules of alcohol, we have in the con-
dition of equilibrium when e gram-molecules of ester have been
formed,

(1 - - e) (a — e) _ e (w + e)

1 V V '

where V is the volume of the mixture, and l&i and k2 are the velocity
constants.
Or,

kl (1 _ e) (a - e) = k2e (e + w) . . . . (I)

When ki and k2 are known, this equation allows the quantities
of the different substances which will exist side by side in
equilibrium (their "limiting values") to be calculated, and the
equation may therefore be called the limiting equation.

The experiments of BERTHELOT and PEAN DE SAINT GILLES show
that when acid and alcohol are mixed together in molecular
proportions, 2/3 of the mixture is converted into ester. That is,
experiment gives e = 2/3, for a = 1, and w = 0.

Putting these values into the limiting equation we get,

k, (l-2/3) (!-'/•) = k2 V/8,
or

Introducing this value into the limiting equation, and solving
it for e, we obtain

1 r

e = g- [4 (a + 1) + w — V 16 (a2 — a 4- 1) + 8 w (a + 1) + w2]

Since the experiments of BERTHELOT and PEAN DE SAINT GILLES
were made with mixtures of acid and alcohol without the addition
of water, we must put w = 0 in the last equation, and find

e = a/3 (a + 1 - V a* - a -f~T)

ISOTHERMAL EQUILIBRIUM IX HOMOGENEOUS SYSTEMS.

147

The following table contains, under a the number of molecules
of alcohol used to one molecule of acid, under e the number of
molecules of ester formed. l

e observed.

e calculated.

0.05

0.049

0.08

0.078

0.18

0.171

0.28

0.226

0.232

0.33

0.293

0.311

0.50

0.414

0.423

0.67

0.519

0.528

1.00

0.665

0.667

2.00

0.858

0.845

8 . 00

0.966

0.945

It may also to be pointed out that the further conclusions
Reducible from equation (I) on page 146, r being taken as

equal to 4, are in agreement with the results of experiment.
1. If we write the equation in the form

e (e -f w)

we find e — 1 when a =: cx>, that is if a given quantity of an
acid be mixed with a very large quantity of an alcohol, the
whole of the acid will be converted into ester.

From the form of the original equation (1) it is easily seen
that the same is true for the alcohol if it be mixed with a large
quantity of acid.

2. The transformed limiting equation gives e = o when a — o,
that is, no ester is formed from acid without addition of alcohol
and rice versa.

See also VAN 'T HOFF'S original memoir, Bent-hie, 10, 669, 1877.

148 CHEMICAL EQUILIBRIUM.

3. If the equation be written

4 (1 - e) (a — e)

w + e

we find for w = cx5 e = o, that is, formation of ester is pre-
vented by a very large addition of water. The same is true for
addition of a very large quantity of ester.

b. Tlie temperature is variable.
Application of Thermodynamics.

The influence of the temperature on the equilibrium constant
is expressed by the following equation *,

d log K q

dT ITr*1

where T is the absolute temperature, q the quantity of heat
evolved when unit quantity (in kgrm. molecules) of the second
system is transformed into the first at constant volume.

This equation, which is true both for homogeneous and for
heterogeneous equilibrium in gases and in dilute solutions, may
be obtained in the following way : -

Let us suppose that equilibrium exists between (1 — x) kgrm -
molecules of the first and x kgrm. -molecules of the second system,
that the volume of the whole is V, and the temperature T.
A reversible cycle of operations may be carried out with the
system for which we shall have, (from thermodynamics),

l_ /dPv 1 /dQ\

J IdT/v "" T VdVV

where P is the pressure acting on the system.

— - I is the quantity of heat which is absorbed when the

volume of an indefinitely large quantity of the system is increased
by unity at the temperature T. Call q the quantity of heat which

1 J. H. VAN 'T HOFF, Lois de i'equilibre chimique dans 1'etat dilue, gazeus on
dissous. Koflgl S VCD ska Vet. Akad. Handlingar, 21, 1885; Archiv. Xecrland. 20,
239, 1885.

INFLUENCE OF TEMPERATURE. 149

Is absorbed when unit quantity of the first system is converted
into the second without any external work being performed.
When the volume of the system changes at constant temperature

a certain quantity of the second system is formed (viz.

the quantity of heat absorbed by this, (viz. q I -^== I ) mav also

\dV/ T

be obtained by subtracting the quantity of heat equivalent to
the external work done by the system during the expansion,

viz. - cals, from the total amount of heat absorbed,

J \dv/T

so that we obtain

....(1)

dv/T-\dv/T j • j r VdiVv i " j i dr

If n! molecules of the first and n2 molecules of the second
system take part in the reaction, we have

PV = [>! (1 - - x) + n2 x] RT. . . . (2)

Therefore

P R

_ -; [ m + (n2 - - nO x ] ^

and

f**\

Substituting this in equation (1), we obtain
/dx\ T-'R /dx\

At constant temperature, we have the relationship

r"2 f^)"2

= K, or - - = K, .... (4)

and therefore,
log K + (n2 - - ni) log V = n2 log x - - nj log (1 — x).

150 CHEMICAL EQUILIBRIUM.

By partial differentiation with respect to V, this yields

n2 — nj

Similarly differentiating with respect to T, we obtain

/dx\
VdT/v "

d log K
dT

Introducing these values into equation (3), it becomes

d log K Jq _q_i

dT RT2 " 2 T2 *

This equation applies likewise to the case of heterogeneous
equilibrium, for equations (2) and (4) apply equally well in this
case when ^ and n2 are taken to mean the numbers of molec-
ules of the gaseous or dissolved substances which take part in.
the reaction. Since the values of i\i and n2 do not appear in.

the equation - ~Vrp " = ~o~rm"» t^is alteration in their signific-
ation makes no difference.

Applications.

In applying the equation to homogeneous chemical equilibrium
we have to distinguish two cases: —

a. The value of q is zero.

b. The value of q is 5 zero.

a. The value of q is zero.

In this case we have equilibrium between two systems which
may change into each other, at constant volume, without evolution
or absorption of heat, consequently

1 This formula has also been deduced from the principle of the increase of the
entropy by VAN DEVENTER, Zeit. Phys. Chem. 2, 92, 1888.

INFLUENCE OF TEMPERATURE. 151

d log K
dT

which indicates that K is independent of the temperature.

An equilibrium of this kind is therefore not displaced by
elevation or depression of the temperature at constant volume.
We therefore obtain the rule: If a displacement of the equil-
ibrium has no effect on the temperature, a change of temperature
trill not displace the equilibrium.

As examples of equilibria which are unaffected by changes of
temperature the following may be mentioned :

1. The equilibrium of ether ifi cat ion.
CH3COOH + C2H5OH :j=± C2H302C2H5 + H20.

The opposing changes are here accompanied by an insignificant
evolution of heat, J and the equilibrium is found to be practically
unaffected by a change of temperature. At 10° the limit of etherific-
ation is reached when 65.2 per cent has undergone change, at
220° the limit is found at 66.5 per cent. 2

2. Equilibrium between optical isomers. 3

The mutual transformation of optical isomers developes no heat,
and it is found that the equilibrium between them is unaffected
by the temperature ; a mixture of them which is inactive at
the ordinary temperature remains inactive when it is heated.

3. The following case is also of interest,

H20 -f- CO ^=±L H2 -f- C02.

At moderate temperatures this change is accompanied by an
evolution of heat, which diminishes as the temperature rises in
consequence of the difference between the specific heats of the
two systems; its value should be zero at 1700°. l HORSTMANN 5

1 Bull. Soc. Chiro. 31, 352, 1879.

2 BERTHELOT, Essai de Mecanique Chimique, II, 73.

:! VAN 'T HOFF, Die Lagerung der Atome im Raume, 1894, p. 33.
4 Compt. Rend. 93, 10*, 1881.

r> Ucber Verbvennnngsem-heinungeu bei Gasen. II. Vcrhandlungen des natiu-histor-
isc,heu med. Vereins zu Heidelberg.

152 CHEMICAL EQUILIBRIUM.

has found that the equilibrium ceases to be displaced at a temp-
erature which he estimates to be 2250°. The difference between
1700° and 2250° may well be due to the difficulty of determin-
ing such high temperatures.

b. The value of q is ^ zero.

In this case K will vary with the temperature, and by means
of the equation

d log K q

ciT " 2T2

it will be possible to calculate the value of q from observations
of the equilibrium, and to compare the value so obtained with
that directly determined by experiment.

As an example of this we shall consider the equilibrium

NA ^ 2N02.
The quantities which occur in the equations

d log K _ q , „ C2

~TT~ ~2T2al : ^T'

have the following signification in this special case: -

G! and C2 are the concentrations of the first and second
systems respectively, that is the quantities of N.204 and 2N02
per cubic metre, unit quantity being, in both cases, 92 kgrms;
ni and n2 are the numbers of molecules forming the first and
second systems, in this case, their respective values are 1 and 2;
q is the heat, in calories, which is evolved when 92 kgrms. of
the second system are converted into the first at constant volume.
The dissociation of nitrogen peroxide has been studied by
DEVILLE and TROOST, l whose observations will be used in order
to calculate q. They determined the vapour density of nitrogen
peroxide, at atmospheric pressure, at different temperatures. 3.

1 Compt. Rend. 64, 237, 1867.

2 See also A. J. SWART, Inaugural Dissertation, Amsterdam, 1890. Zeit. phys. Chcm.
7, 120, 1891.

INFLUENCE OF TEMPERATURE. 153

The fraction x of the peroxide which exists as 2N02 is ob-
tained from the expression

3.179
~~ *

where 3.179 is the vapour density of N204 compared with air,
and D is that of the dissociated mixture.
In order to calculate q, the equation

d log K q

~~df~ " 2T-

must be integrated, whence we obtain

KI and K2 are here the equilibrium constants at the absolute
temperatures TI and T2.
Further since

we obtain

T, (1 - x*) Tt (1 - x?)

where Xi and x2 are the fractions of the dissociated mixture
existing in the form 2 N02 at the temperatures Tt and T2.
Substituting this value of the ratio K2 : Kx in equation (1),
we obtain

, (1 - 5) T, (1 - xl

154

CHEMICAL EQUILIBRIUM.

The following table contains the experimental data, and the
results of the calculation.

I).

x. q.

273 + 26.7

2.65

0.1996

273 + 111.3

1.65

0.9267

12900

On the other hand the value of q may be calculated approx-
imately from the calorimetric researches of BERTHELOT and OGIER\
who determined the specific heat of nitrogen peroxide at atmo-
spheric pressure between 27° and 150°; in this interval 92 kgrms.
of the gas absorb 12620 cals. This heat has served to produce
three changes, corresponding to three quantities of heat a, b,
and c.

1. The temperature has been raised from ti to t2 at constant
pressure. The quantity of heat required for this purpose (a) may
be calculated from the heat capacity of nitrogen peroxide at
higher temperatures, where the change of dissociation may be
neglected, this is 16.86 cals. for 92 kgrms., so that

a = 16.86 (t2— y.

2. A certain amount of external work is performed when
N204 is converted into 2N02 at constant pressure, for 92 kgrms,
it is 2T cals., so that since the part of the gas existing as
2N02 increases from Xj at tj to x2 at t2 the heat equivalent to
this work will be

b = 2 T (x2 - x,).

3. A quantity of heat (c) is absorbed by the conversion of
N204 into N02, for 92 kgrms. this is q cals., so that

c = q (x2— xj).

The following table contains the results of the calculation.
1 Bull. Soc. Chim. 37, 435, 1882.

EQUILIBRIUM IN HETEROGENEOUS SYSTEMS.

155

a =

x =

b =

q =

a-hb-J-c

16.86(t2— tO

3.179

2T(x.2-xO

T-\ *

X2 Xi

27°

0.2015

12620

2074

577

12500

150°

The values of q obtained from the study of the equilibrium

(12900), and calculated from the calorhnetric determinations

(12500) are, therefore, in very satisfactory agreement with
each other.

II. EQUILIBRIUM IN HETEROGENEOUS SYSTEMS.

Heterogeneous equilibrium is characterised by the existence
in presence of each other of gaseous or dissolved bodies and
liquid or solid (undissolved) bodies. The following cases may
serve as examples : —

NH5S ^z± NH3 + H2S,

where the ammonia and sulphuretted hydrogen are in the gaesous,
the ammonium sulphide in the solid condition;

C204Ca + HC1 z=± C204H2 -4- CaCl2,

where all the substances, except the calcium oxalate, are in the
dissolved state.

An equilibrium of this kind may be regarded as a special
case of homogeneous equilibrium, for it may be produced from
the latter by diminishing the volume, or by removing solvent,
until the maximum vapour pressure, or the maximum solubility,
of one of the bodies taking part in the equilibrium has been
attained, after which this body will undergo partial condensation
or precipitation.

We must therefore assume that, in the examples chosen, a
certain, perhaps very small, quantity of the NH5S or CaC204r
exists in the gaseous and dissolved conditions respectively, and
that this gaseous or dissolved part is in equilibrium, on the

156

CHEMICAL EQUILIBRIUM.

one hand, with its products of decomposition, which likewise
exist in the gaseous or dissolved state, on the other hand with
the solid substances, so that the NH5S or CaC204 existing as
gas or in solution remain constantly in the condition of satur-
ated vapour, or of saturated solution, at the given temperature.

The equilibrium which exists here between the condensed, or
precipitated and the gaseous, or dissolved parts of the same
substance belongs to the class of physical equilibria.

The law by which this latter class of equilibria is governed
requires that the concentration of the gaseous or dissolved part,
which is proportional to the vapour pressure or solubility of the
substance, shall depend only on the temperature and not on the
volume of the system.

It has already been pointed out on page 150 that the formulae

cllogK q

hold good in the case of heterogeneous equilibrium, nx and n2
referring, however, only to those substances which exist in the
gaseous or dissolved condition.

We must, therefore, conclude that a heterogenous equilibrium
in not displaced by a change of temperature ivhen g — 0 ; and
that the value of q may be calculated, in the same way as
formerly, from determinations of the equilibrium, and compared
with the value obtained from calorimetric determinations.

Cases investigated.

As an example of a calculation of this kind, we will take the
dissociation of ammonium sulphide,

NH5S ^=± NH3 4- H2S,

which was investigated by ISAMBERT. 1

The value of q will first be calculated by means of the equation

K2 q /I 1\

log K7 : 2 IT, • fa>'

Compt. Rend. 92, 919, 1881.

EQUILIBRIUM IN HETEROGENEOUS SYSTEMS.

157

For this purpose, we put

rij = 0, and n2 = 2,

and, therefore, K = C2.

\\ e have, further, the following connexion between the
maximum vapour pressure p of the mixture of ammonia and
sulphuretted hydrogen, which was determined experimentally by
LSAMBERT, and its concentration C2: -

^ : (C2), = £ : &

where (C2)t and (C2)2 are the concentrations at the absolute
temperatures T! and T2, and px and p2 are the corresponding
pressures.

Substituting this for log ~, we obtain

P2 Pi q / 1 1 "\

log -^ . - log T- T (^ . . TJ-),

from which q may be calculated.

The experimental data are the following: —

P-

q (calculated.)

273 + 9.5
273 + 25.1

175 mm.
501 mm.

21550

Again, the heat evolved by the formation of 51 kgrms. of
NH5S at constant volume, according to the equation NH3 + H2S
= NH5S, which we have called q. may be obtained from thermo-
chemical data.

Calculated from the numbers given by different observers, the
amount of heat evolved by the change, under constant pressure,
varies from 22620 to 22990 cals !. Subtracting from this the
quantity of heat which is equivalent to the external work
performed during the change, viz. 4 T =z 1160 cals, we obtain
q == 21460 to 21830 cals.

, 1 I, 12*3, 1881.

158 CHEMICAL EQUILIBRIUM.

The value calculated (21550) is, therefore, in good agreement
with that found by direct experiment (21460—21830).

b. The dissociation of salts containing water of crystallisation,
which has been studied by FROWEIN l and others with special
reference to the thermodynamical equation, may suitably be consid-
ered here.

Taking, for example, the equilibrium

CuS04. 5H20 ^=±: CuS04. 4H20 + H20,
we may apply the equations

K - md

— , and

when nx and n2 refer only to the uncondensed substances, in
this case, therefore, to the aqueous vapour, so that ni ~ 0,
n2 •=. 1, and, therefore, K — C2.

That is, K is equal to the concentration of the aqueous vapour

which is in equilibrium with the salt. Call this concentration Cs.

q is here the quantity of heat which is evolved when 18

kgrms. of aqueous vapour combine with the salt CuS04.4H20

to form CuS04.5H20; calling this qs, our equation becomes

dT " 2T2

This expression may, however, be transformed so that qs is.
replaced by the quantity of heat determined calorimetrically,
that is, the quantity of heat which is evolved by the com-
bination of 18 kgrms. of liquid water with the dehydrated
salt.

~. d log K q

bince the general equation, — ~ — =. 7^7, applies to phys-

Cll u 1

ical as well as to chemical equilibrium 2> we may write

dlog_Cw qw ^

dT ' 2T2'

1 Zeit. phys. Chem. 1, 1, 1837.
^ See page 205.

EQUILIBRIUM IN HETEROGENEOUS SYSTEMS.

159

where Cw is the concentration of saturated steam, and qw the
heat which is evolved by the condensation of 18 kgrms. of
saturated steam at the temperature T.

The quantity of heat which is determined calorimetrically,
qK, is the difference between qs and qw.

By subtracting equation (2) from (1), we obtain

log 7^

^w qs — qw

2T2

~- is the ratio between the dissociation pressure of the salt

and the vapour pressure of water, both at T. Calling this F,
we obtain

d log F qK

~~dT~ " 2T*

where qK is the heat evolved by the combination of 18 kgrms.
<• of liquid water with the partially dehydrated salt.
Assuming that qK is constant for small inter-
vals of temperature, we obtain by integration
of the above equation

™

l 1

from which qK may be calculated when Fx and
F2 are known at the temperatures Tj. and T2.

The apparatus, a terisimeter, which was emp-
loyed in determining the vapour pressures of
salts containing water of crystallisation is shown
in fig. 34.

Two bulbs, A and B. l contain the finely
powdered and dry salt, and strong sulphuric
rig. u. acid respectively ; they are connected together

by means of a U-tube half filled with olive oil.

The openings at a and b having been closed before the

1 A similar tensimeter was used by BREMER for the determination of differenced
of pressure. Rec. trav. ohim. des Pays-Bas, 6, 121, 1887.

160

CHEMICAL EQUILIBRIUM.

blowpipe, the apparatus is placed in a horizontal position, the oil
collecting in the bulbs C and D, connected to the air-pump at c,
and evacuated, the last trace of air being removed by warming
the whole apparatus with the flame of a spirit-lamp ; it is
finally sealed at c. The apparatus having been left to itself for
24 hours in a vertical position, in order that the water of
crystallisation may be equally distributed throughout the salt,
the measurements of pressure are begun. These are made by
means of a cathetometer, the tensimeter being immersed in a
HERWIG'S water bath the temperature of which is maintained
constant by continual stirring. Two separate tensimeters were used
simultaneously in each experiment. After the completion of the
observations, the bulbs containing the salt were detached and
the water of crystallisation determined.

The following table contains the results of the experiments
with copper sulphate.

Temperature.

Maximum pressure
of the aqueous vapour
over the crystals
in mm. of Hg.

Ratio of the maximum
pressures of aqueous
vapour over crystals
and water. F.

13°. 95

2.993

0.2522

20 .46

5.056

0.2828

26 .30

8.074

0.3174

30 .20

10.897

0.3414

34 .75

15.307

0.3710

39 .55

21.452

0.3999

39 .70

21.726

0.4019

The heat of combination qK calculated from these numbers is
given in the next table.

Temperatures.

flK

13°. 95— 26°. 30

3220

20 .46—26 .30

3475

26 .30—30 .20

3390

26 .30-34 .75

3400

26 .30—39 .55

3250

26 .30—39 .70

3300

Mean .... 3340

EQUILIBRIUM IN HETEROGENEOUS SYSTEMS.

161

THOMSEN'S l direct determination gives qK = 3410 cals. The
agreement is thus satisfactory.

The whole of FROWEIN'S results are given in the following
table, from which it may be seen that there is a good agreement
between the values of qK obtained directly and indirectly.

Salt examined.

qK«

Determined by the
calorimeter.

Calculated from the
vapour pressures.

CuS04. 5H20

3410

3340

BaCla. 2H20

3830

3815

MgS04. 7H20
ZnS04. 7H20

3700
3417

3990
3440

ZnS04. 6H20

2178

2280

Na2HP04.12H20

2244 2

2242

c. The decomposition of copper bi-potassium chloride, which
takes place at 92° according to the equation

CuCl2. 2 KC1. 2 H20 ^=± CuCl2. KOI + KC1 + 2 H20,

has been investigated by J. G. C. VRIENS. 3

The heat evolved by the combination of the water of crystallis-
ation may be calculated, as before, from the pressure of dissoci-
ation by means of the formula on page 159, and, inversely,
when the value of the dissociation pressure is known at one
temperature its value at other temperatures may be calculated
from the known value of qK, and compared with the numbers
obtained by experiment.

The heat of combination for 18 kgrms. of the water of
crystallisation contained in the salt CuCl2 2KC1 2H20 was determ-
ined, by means of the calorimeter, as the difference between the

1 ThcTiuochemische Untersuchungeu III, p. 141.

- Tli is number is given by THOMSEN, Tliermochem. Untei's. Ill, while PFAUNDLKR.
JJcrichte, 4, 773, 1871, gives 2234.

:; Inauiriirstl Dissertation. Amsterdam, 1890; Zeit. phys. Chem. 7, 194, 1891.

162

CHEMICAL EQUILIBRIUM.

heats of solution of CuCl2 KC1 + KC1 and CuCl2 2KC1 2H20 ;
the mean of two experiments gave 3063 calories.

The apparatus used in measuring the pressures was the same
in principle as that employed by FROWEIN but somewhat different
in detail.

The pressure of the aqueous vapour evolved by a mixture of
CuCl2 2KC1. 2H20, CuCl2 KC1, and KC1 was: —

Temperature.

Pressure found.

Pressure calculated.

42°. 3

18.9 mm.

18 mm.

46 .6

51 .5

30.9 „

56 .1

44.1 „

59 .1

50.7 „

64 .5

73.2 „

73.4 „

74 6

131

129.5 „

89 .2

278.5 „

277.6 „

91 .1

308

305.1 „

319

318.9 „

92 .6

S27

O*J< ,,

328.4 „

The numbers in the column headed " calculated'' are the
pressures, in mm. of mercury, which have been calculated by
means of the equation given on page 159, qK being taken as
3063 cals., and the pressure observed at 46°. 6 being used as
starting point.

The agreement between the values calculated and observed l
shows that the loss of water of crystallisation is really accomp-
anied by a decomposition of the double salt, this being the
assumption made in determining qK.

d. The decomposition of Rochelle salt into its components,

1 With respect to the deviations which occur it is to be remembered that the
pressures are determined at temperatures ranging from 40° to 100°, while OK is de-
termined at 16°, and doubtless is only to be regarded as independent of the temperature
over a very small range.

EQUILIBRIUM IN CONDENSED SYSTEMS.

163

which occurs at temperatures higher than 55° according to the
equation

2(C4H406 NaK. 4H20) ^ C4H406K2. | H20 + C4H,06Na2. 2H20 -4- 5i/2 H20,

has been studied by J. DOCTERS VAN LEEUWEN. 1

At temperatures lower than 55° the double salt is reformed
from its components.

Here, again, qK may be calculated from the dissociation
pressure of the crystals.

The pressures were determined by means of a tensimeter (fig. 36)
containing finely powdered and partially dehydrated Rochelle salt
in the bulb d, and concentrated sulphuric acid in the bulb e.

Temperature.

Dissociation pressure.

18C

>.8

20 mm.

.95

.70 10.

.05

14.

From these figures qK is calculated as follows : —

Temperatures.

20°. 95— 25.70
25 .70—31.05
18 .80—31.05

2530
2505
2247

while BERTHELOT 2 found qK — 2370 cals.

III. CONDENSED SYSTEMS.

'A simple example of the class of phenomena referred to
in this section will first be given.

!• The experimental data, which will shortly be published, have been kindly placed
at my disposal by the author. (CoHEK).
2 Essai de mecanique chimique. I. 539.

164 CHEMICAL EQUILIBRIUM.

In the course of an investigation on ammonium nitrate LEHMANN*
made the following observations : —

" When fused ammonium nitrate is allowed to solidify, skeleton
crystals belonging to the regular system are formed. The behaviour
of these crystals in polarised light shows them to be completely
iso tropic. On further cooling a sudden change occurs at about
127°, the crystals becoming doubly-refractive. On still further
cooling needle shaped rhombic crystals are formed at about 87°,
these can also be obtained from a hot alcoholic solution. These
crystals generally change while still in contact with the solution,
and invariably on removing them from it, into a fourth modific-
ation which also belongs to the rhombic system and which may
be obtained in fairly good crystals from aqueous solutions at
the ordinary temperature. On heating this fourth modification
gradually, it passes through all the changes described, but in
inverse order, at about 36° the other rhombic modification is
formed, at about 87° the rhombohedric, and at 120 the regular".

We are therefore dealing here, not with an equilibrium such
as is found in homogeneous and in heterogeneous systems which
is continuously displaced by a continuous change of temperaturer
but rather with per mltum displacements of the equilibrium at
36°, 87°, and 120°.

At the latter temperature an equilibrium exists which may be
represented thus,

NH4N08 rhombohedric ^=± NH4N03 regular.

The characteristic part of the phenomenon is that, on cooling
the system below 120° the equilibrium is displaced totally to-
wards the left-hand side of the equation, on raising the temperature
above 120° it is displaced completely towards the right. A
temperature possessing properties of this kind will be called a
transition point, 2 for the system concerned.

The kind of equilibrium just described may be expected to

l GROTH'S Zeitschrift fur Krystallographie, 1, 106, 1877.

1 When the expression "transition point", or "transition temperature" is used,
the transition temperature under the pressure of one atmosphere is always meant. The
influence of pressure is considered later.

INCOMPATIBILITY OF CONDENSED SYSTEMS.

occur when none of the substances are in the gaseous or liquid
condition; viz. in so called condensed systems.

The necessity of the existence of a point of transition in such
cases may be proved, quite generally, from the known laws of
equilibrium. l

Consider an equilibrium between dissolved substances, for
example two salts which have undergone a partial double decomp-
osition, then in order to find what the condition of equilibrium
will be in the absence of the solvent we may remove it gradually,
at constant temperature, by evaporation.

During the evaporation all the dissolved substances will separate
out except one, in the special case considered three of the salts
separate ; the remaining substance (the fourth salt) cannot separate
out owing to the laws governing solubility and chemical equil-
ibrium. The laws of solubility require that each substance which
separates out shall have a certain concentration in the solution
corresponding to saturation, while those of chemical equilibrium
require that these shall be a certain definite relationship between
the concentrations of all the dissolved bodies.

Owing to these two conditions the concentration of the last
substance is, after all the others have partially separated out,
definitely fixed ; further evaporation cannot increase it, and it
must, therefore, remain equally far removed from the concentration
corresponding to saturation even when the solution is evaporated
to dryness. This last substance can thus never separate in the
solid state.

From this it follows, that in case the substances are present
in equivalent quantities, the whole system to which the last
body belongs must be absent in the condensed condition, while
if equivalent quantities are not used, only the excess of the
substances belonging to this system can separate out. Both
systems, therefore, cannot exist together in the solid condition. This
may be called the law of the incompatibility of condensed systems.

The coexistence of both systems in the condensed condition
is, however, possible under certain exceptional circumstances.

Consider again the condition of affairs described above; by

l VAN 'T HOFI- and VAN DEVENTER, Zeit. phys. Chem. I 164, 1887.

166 CHEMICAL EQUILIBRIUM.

evaporating a solution containing a number of substances in
chemical equilibrium with each other all of them had been caused
to separate out partially, except one, the concentration of which
remains constant, and less than the concentration corresponding
to saturation, so long as the temperature does not change.

Since the concentration of a saturated solution generally changes
with the temperature, and since this is also the case with the
condition of equilibrium of substances in solution, it will be
possible, by raising or lowering the temperature, to cause the
concentration of the substance which has not separated out to
approach the saturation point, and it is, therefore, conceivable
that there is a temperature at which this will be reached. At
this temperature, and at it only, is the separation of all the
substances, and, therefore, the coexistence of both systems in the

condensed condition, possible. It must now be shown that above
and below the temperature at which the two systems can coexist

either the one or the other of them is in stable equilibrium,

and that the name "transition temperature" is therefore justified.
In order to do this we may write the equation for a chemical

equilibrium in the form

F (C,

where F (C2. . • •) is the product of certain powers of the con-
centrations of the constituents of the second system, and F (Ci. . . .)
is the same for the first system.

Calling c2 and Cx the concentrations corresponding to saturation,
and substituting them in the above equation, we obtain a value
of K which we may call M.

In general K and M will vary in different ways with the
temperature, and may therefore be represented by curves which
will cut each other at some temperature T ; at this point K and
M are equal to each other, at temperature above or below it
they differ. The temperature T is thus the temperature at which

THE TKANSITION TEMPERATURE. 167

equation (1) is satisfied when the solution is just saturated for
all the substances which are in equilibrium, at this temperature
all the substances will separate out of the solution on evaporation,
and consequently the two systems can coexist.

When we have K > M, the second system only can separate
out ; for K < M, the first only A partial separation of all the
substances except one having occurred, we may replace the
values of C2. . . ., and CL. . . ., in equation (1), all except one, by
c-2 • . . • , and CJL . . . . ; for K ^> M this unreplaced concentration,
which must be smaller than the concentration corresponding to
saturation, must occur in the denominator, that is the first system
cannot separate out ; for K < M the second system must be
absent in the solid condition for similar reasons. There is thus,
as the name " transition temperature'' clearly indicates, a com-
plete transformation of the one system into the other on passing
through this point.

Cases investigated.

The examples of the phenomenon which have been investigated
may be grouped under the following headings : —

a. The transition temperature of polymorphous bodies.

b. The transition temperature of salts containing water of
crystallisation.

c. The transition temperature in the case of the formation
and decomposition of double salts.

d. The transition temperature in the case of double decomp-
osition.

e. The transition temperature of isomeric bodies.

The very close relationship which exists between these phen-
omena and that of ordinary fusion, or solidification, may be
pointed out here. !

a. The transition temperature of polymorphous bodies. 2
•An exceedingly simple case of this kind has been investig-

1 It is considered in more detail later

The literature of the subject is given pretty fully by W. SCHWARZ, Eeitrage zur
Kenntniss der umkehrbaren Umwandlungen polymorpher Korper, Gottingen 1892.
See also SILVIO LUSSANA, Nuovo Cimento, (4), vol 1, 97, 1895.

168 CHEMICAL EQUILIBRIUM.

ated by REICHER l by a method which will be described later.
The equilibrium referred to is that between rhombic and mono-
symmetric sulphur. The transition temperature was found to be
95°. 4, that is, under atmospheric pressure rhombic and mono-
symmetric sulphur can exist side by side at 95° .4, while above
this temperature only the monosymmetric modification is in stable
equilibrium, and below it only the rhombic modification ; on
passing through the point of transition a complete transformation
of the one into the other occurs.

LEHMANN'S observations on the changes of the different crystal-
line modifications of ammonium nitrate into each other have
already been mentioned.

b. The transition temperature of salts containing water
of crystallisation.

The apparent melting of salts containing water of crystallis-
ation is often due to a chemical change which occurs above a
certain temperature and which is reversed at lower temperatures,
as is shown by the fact that a salt containing less water than
the original substance oftenseparates out during the fusion.

Phenomena of this kind are observed not only in the case of
salts containing water of crystallisation, but also with many
other hydrates, such as those of carbon bisulphide 3, phosphorus
hydride3, sulphuretted and seleniuretted hydrogen, methyl chloride4,
chloroform 5, sulphur dioxide, bromine, chlorine, and hydrobromic
acid 6.

It is well known that Glauber's salt " melts" at a definite temp-
erature in its own water of crystallisation (LOEWEL 7, MULDER 8);
the apparent melting-point is however nothing but the transition
point in the equilibrium

1 GROTH'S Zeitschrift fiir Krystallographie 8, 593. 1884. Inaugural Dissertation,
Amsterdam, 1883.

2 DUCLAUX, Compt. Rend. 64, 1099, 1867.

3 CAILLETET and BORDET, Compt. Rend. 95, 58, 1882.

4 DE FORCRAND, Compt. Rend. 94, 967, 1882.

5 CHANCEL and PARMENTIER, Compt. Rend. 100, 27, 1885.

6 BAKHUIS ROOZEBOOM, Sec. des Trav. Chim. des Pays-Bas, 3 and 4, 1885-86.

7 Ann. Chim. Phys. (3), 29, 62, 1850; (3), 37, 157/1853; (3), 49, 32, 1857.

8 Geschiedenis van het scheikundig gebonden water, Rotterdam, 1864.

THE TRANSITION TEMPERATURE. DOIT.LE SALTS. 169

Na2S04. IGHoO ;*-± Na2S04 -f- 10H20,

which VAN 'T HOFF and VAN DE VENTER, COHEN and BREDIG, and
VEKSCHAFFELT have found, by different methods, to be about 33° .
Similar changes have been investigated in the cases of CdClo.
2H20 !, which loses a molecule of water of crystallisation at
about 34°, of ZnS04.7H20 2, where the same thing occurs at
about 40°, and of Na2HP04.12H20, 3 which is converted into
the salt containing seven molecules of water of crystallisation
at about 37°.

c. The transition temperature in the formation and decomposition

of double salts.

A few characteristic cases will be fully described.

1. The formation of astrakanite.

The equilibrium is represented by the following equation.
NaaS04. 10H20 + MgSO,. 7H20 ^i± Na2Mg(SO,)2. 4H20 + 13H20,

and the transition temperature is about 21°. 5. 4 The double
salt is known mineralogically as astrakanite, simonyite, or
bloedite.

If finely powdered astrakanite be mixed with water in the
proportion represented by the above equation, at temperatures
below 21°. 5, the thin paste which is at first formed solidifies
after a short time to a dry, solid mixture of the sulphates of
sodium and magnesium; at temperatures higher than 21°. 5 this
does not take place. A finely powdered mixture of the hydrated
sulphates of sodium and magnesium remains completely unchanged
at temperatures below 21°. 5, if it be preserved in closed flasks
in order to prevent loss of water; on warming the mixture,

l E. COHEN and D. M. Kooi.i, Zeit. phys. Chem. 14, 71, 1894.
- E. WIEDEMANN, WIED. Aun. 17. 561, 1882, investigated several sulphates. Cf.
E. COHEN loc. cit.

:! A. E. BATH, Xcit. phys. Cliem. 18, 180, 1895. See p. 203.

4 VAN 'T HOFF and VAN DEVKNTER, Zeit. phys. Clunu. 1, 170, 1887.

170 CHEMICAL EQUILIBRIUM.

however, above 21°. 5 astrakanite is formed sooner or later.
partial fusion being apparently produced by the water liberated.
The last-mentioned change is accelerated, and takes place more
readily, if astrakanite be added to begin with, but even without
this it occurs after some time.

2. The formation of sodium ammonium, and of
sodium potassium racemate.

In the case of astrakanite we were dealing with the combination
of two sulphates to form a double salt, while here we have to
do with the combination of sodium ammonium dextro- and
laevo-tartrates, NaNH4C4H40G.4H20, to form the racemate (Na
NH4C4H406.H20)2, which was first prepared by SCACCHI. l

2(NaNH4C4H406.4H20) ^=± (NaNHAH406. HaO)2 -f- 6H20.

The transition temperature is about 27°, according to VAN
'T HOFF and VAN DEVENTER, " who found that if finely powdered
sodium ammonium racemate be mixed with water in the proportion
given in the above equation, at temperatures below 27°, the
thin paste which is at first obtained solidifies after some time
to a completely dry, solid mixture of the two tartrates, and
that at temperatures above 27° this does not occur.

Further, the finely powdered mixture of equal quantities of the
two tartrates may be preserved without change in closed vessels
at temperatures below 27°, whereas on warming it above 27°
the formation of racemate occurs after a more or less prolonged
period, the water set free giving rise to partial liquefaction.

The formation of potassium sodium racemate, a salt which
was first prepared by WYROUBOFF, 3 has been investigated by VAN
'T HOFF and (JOLDSCHMIDT, 4 who found it to be completely analogous
to that of the sodium ammonium salt. The transition tempera-
ture in the equilibrium

1 Rendi conti di Napoli, 1865, p. 250. See also VAN 'T HOFF, Die Lagerung der
atome im Raume, zweite Aufl. 1894, p. 34.

2 Zeit. phys Chem. 1, 170, 1887. See also Zeit. pliys. Chem. 17, 47, 1895.

3 Ann. Chim. Phys. (6) 9, 224, 1886.

4 Zeit. phys. Chem. 17, 505, 1895.

THE TRANSITION TEMPEBATURE. DOUBLE SALTS. 171

2 (C4H606 K Na. 4EJ20) ^±L (C4H406 K Na. 3H20)2 + 2 H20,
is about — 6°.

3. The decomposition of sodium ammonium, and
of sodium potassium racemate.

Sodium ammonium racemate, which is formed from the dextro-
and laevo-tartrates at 27°, decomposes again according to VAN
'T HOFF, GOLDSCHMIDT, and JORISSEN * at 35° into sodium and am-
monium racemates.

2 (Na NH4 C4H406. H20)2 ^=± (Na2 C4H406)2 + [(NH4)2 C4H406]2 + 4H20.

The change in the case of potassium sodium racemate is, ac-
cording to VAN 'T HOFF and GOLDSCHMIDT 2, quite similar.

2 (K Na C4H406. 3 H20)2 ^=± (Na2 C4H406)2 + (K2 C4H406 2 H20)a+ 8 H20.

The transition temperature is about 41°.

A similar change occurs in the case of a mixture of sodium
ammonium laevo- and dextro-tartrates which changes into a
mixture of sodium and ammonium racemates at 30°, and also in
the case of the analogous mixture of the potassium sodium salts,
with which the change occurs at 33°.

4(NaNH4 C4H406. 4H20) ^ (Na2C4H406)2 + [(NH4)2 C4H406)]2 + 16H20.
4(K Na C4H406. 4H20) ^=± (K2C4H406. 2H20)2 + (Na2 C4H406)2 + 12H20.

4. The decomposition of copper calcium acetate.

It has been observed by H. KOPP that from solutions containing
the acetates of copper and calcium in equal molecular quantities
the salts sometimes crystallise out separately, sometimes in the
form of the double salt ; he thought it probable that the temper-
ature might be the determining factor.

REICHER 3 showed that this is the case, an equilibrium ocurring
which may be represented as follows, 4

1 Zeit. phys. Chem. 17, 47, 1895.

2 Zeit. phys. Chem. 17, 505, 1895.
:' Zeit. phys. Chem. 1, 221, 1887.

4 The composition of copper calcium acefate is often erroneously given as CuCa(C2H:jO.>)j.
MI._,0 on the authority of ETTLING (LIEU. Ann. 1, 286. 1832). It has heen more fully
investigated by RUDOUFF (Berichte, 21, 279, 1888) who found that the formula is CuCa
(,11,0.,) ,.011,0.

172 CHEMICAL EQUILIBRIUM.

Cu Ca (C2H302)4. 6 H20 ^=± Cu (C2H302)2. H20 -f- Ca (C2H302)2. H20 -f- 4 H20

the transition point lying between 76°. 2 and 78°.

The formation of astrakanite and of the double racemates,
which we have already considered, occurs on raising the temp-
erature, while in this case the double salt is the stable system
at temperatures lower than about 77°, while above this temp-
erature decomposition into its components takes place. The
transition from one system to the other is accompanied by a
change of colour from blue to green which is due to the facts
that the tetragonal double salt is blue, while the monosym-
metric copper acetate is green, and the small needle-shaped
crystals of calcium acetate are colourless.

5. The decomposition of copper bi-potassium
choride and of schonite.

The first-named salt was studied by W. MEYERHOFFER l and
J. VRIENS 2 by different methods. It was found that the salt,
CuCl2. 2KC1. 2H20, which crystallises in blue tabular crystals,
decomposes into copper potassium chloride, CuCl2. KC1, potassium
chloride, and water at about 92°, while below that temperature
it is formed from its constituents.

CuCl2. 2KC1. 2H20 ^=± CuCl2. KC1 -f- KC1 -h 2H20.

This case is quite analogous to that of copper calcium acetate.
If a molecule of copper chloride, CuCl2 2H20, be added to the
double salt to begin with, the transition temperature is depressed 3
to about 56°, which is to be regarded as the transition temp-
erature in the equilibrium

CuCl2. 2 KC1. 2 H20 -+- CuCl2. 2 H20 ^=± 2 CuCl2. KC1 -f- 4 H,0.

The researches of J. VAN DER HEIDE 4 show that the double
salts which may be formed from K^SO^ and MgS04, i. e. schoenite,

1 Zeit. phys. Chem. 3, 336, 1889; 5, 97, 1890.

2 Zeit. phys. Chem. 7, 194, 1891; Inaugural Dissertation, Amsterdam, 1890.

3 This depression of the transition temperature is quite analogous to the depression
of the freezing-point of a solvent by the addition of a foreign substance.

4 Inaugural Dissertation, Amsterdam, 1893. Zeit. phys. Chem. 12, 416, 1893.

THE TRANSITION TEMPERATURE. DOUBLE DECOMPOSITION. 173

K2Mg(S04)2. 6H20, and potassium asfcrakanite, K2Mg(S04)3. 4H20,
undergo decompositions which are quite analogous to that which
has just been considered.

d. The transition temperature in cases of double
decomposition.

SCHIFF * observed that on grinding together potassium chloride
and Glauber's salt, the mixture liquefied, which he supposed to
be due to a double decomposition accompanied by the formation
of water. VAN 'T HOFF and REICHER 2 subsequently showed that
this supposition is correct, and that the double decomposition
which occurs is represented by the equation

Na2 S04. 10H20 + 2KC1 ^=± K2S04 + 2NaCl -f- 10H20,

the transition temperature being 3°. 7.

If the potassium chloride be replaced by ammonium chloride
an analogous double decomposition occurs, the transition temp-
erature of which is 10°. 8.

e. The transition temperature of isomeric compounds.

According to TROOST and HAUTEFEUILLE 3 the vapour of cyanic
acid condenses in the form of cyanuric acid or of cyamelide
according as the temperature at which the condensation occurs
is above or below 150°. WELTZIEN 4 succeeded in converting
cyamelide into cyanuric acid by heating it with concentrated
sulphuric acid until decomposition began ; after some days crystals
of cyanuric acid separated out. From these facts it would appear
that a point of transition exists for the change

cyamelide ^rz±: cyanuric acid.

These observations have been confirmed by VAN DEVENTER :>, who
found that the vapour of cyanic acid when maintained at a

l LIEB. Ami. 114, 68, 1860.
'-' Xt-it. phye. Chern. 3, 482, 1889.
- Compt. Rend. 67, 1345, 1868.
' LIEB. Ann. 132, 222, 1864.

:> By experiments \vhich have not yet been published, kindly placed at my disposal
by the author. (E. COIIKX.)

174 CHEMICAL EQUILIBRIUM.

temperature of 125° for six hours, under a pressure of two
atmospheres, condensed in the form of a finely divided film, which
was insoluble in water and under the microscope appeared to
be mainly amorphous, isolated crystalline fragments being visible
in several places. When the condensation is allowed to take
place at 175°, the product is completely soluble in water and
consists of well formed doubly-refracting crystals.

In order to convert cyamelide into cyanuric acid directly, VAN
DEVENTER heated small tubes containing cyamelide, subsequently
determining the quantity of cyanuric acid contained in the mixt-
ure produced. The determinations were made by titration with
baryta solution, it having been found that phenol phthalei'n is
reddened when sufficient baryta has been added to convert the
cyanuric acid into the di-hydrogen salt. It was found in this
way that the change of cyamelide into cyanuric, acid occurs at
temperatures higher than 135° (uncorr.), and that it is con-
siderably facilitated by the addition of ready formed cyanuric
acid. No increase in the quantity of cyanuric acid could be
detected after heating to 135° for 40 hours.

The reversal of the change at temperatures below 135° could
not be produced; perhaps a better result might be obtained by
the use of a solvent. l

3. Solubility and vapour pressure ab the
transition temperature.

The transition temperature has been defined as the temperature
at which all the substances belonging to two systems in equili-
brium can separate out of a solution containing them when it is
evaporated, so that at this temperature a solution may exist which
is saturated for both systems. The curves of solubility of the
two systems therefore intersect at the transition point; at
temperatures above or below it, only the first or the second
system can separate out in the solid state, because, as has already
been proved, a solution which is saturated for one system is
unsaturated for the constituents of the other.

1 Compare page 87.

UNIVE1

THE TRANSITION TEMPERATURE.

175

Although, at any given temperature, only one of the systems
is in a condition of stable equilibrium, the change of the unstable
(or meta-stable) system into the stable condition may fail to take
place, especially in the absence of the stable system. It is,
therefore, generally possible to prepare two different solutions
saturated at the same temperature, by bringing together one or
other system with the same solvent. These solutions will possess
different concentrations, the solution of the system which is stable
at the temperature in question being the more dilute, while that
of the meta-stable system possesses the characteristics of a super-
saturated solution, allowing salt to crystallise out when placed
in contact with the constituents of the stable system.

The existence of these supersaturated solutions, which do not
deposit the dissolved material spontaneously but only when placed
in contact with the substances for which they are supersaturated,
is very intimately connected with the existence of a transition
point ; the two phenomena constantly accompany each other,
every transition temperature giving rise to two series of solutions
supersaturated with respect to the one system, or the other,
according to whether the temperature is above or below the
transition point.

It was observed by LOEWEL l that two distinct saturated solutions
of sodium sulphate may be obtained by mixing water with pure
Glaubers salt, or with the pure anhydride. The quantities of
Na2S04 contained in these solutions is given in the following
table together with the temperatures at which they are saturated.

Temp.

Saturated for
Na2S04. 10H20.

Saturated for
Na2S04.

31°.84

50.37

32 .73

50.76

49.71

The above mentioned point of intersection of the curves of
solubility therefore exists here at 32°. 65, and thus coincides with
the so-called melting point (the transition temperature). There

Ann. Chim. Pins. (3), 29, f>2, 1850; (3), 37, 157, 1853; (3), 49, 32, 1857.

176

CHEMICAL EQUILIBRIUM.

are also two different supersaturated solutions, viz., above 32°. 65,
the saturated solution of Glauber's salt supersaturated with respect
to the anhydride, below 32°. 65, the saturated solution of the
anhydride supersaturated with respect to Glauber's salt ; at 32°. 65,
the solution is saturated for both salts.

Similarly, the following numbers were obtained with astrakanite \
the numbers giving the percentages of salt in the solution.

Temp.

Astrakanite.

Mixed sulphates.

MgS04.

Na2S04.

Total.

MgS04.

Na2S04.

Total.

15°. 5

20.9

10.2

31.1

17.8

9.7

27.5

24°. 5

16.4

31.4

19.7

17.1

36.8

Below 21°. 5, where the mixed sulphates form the stable
system, the solution of them is less concentrated than that of
the astrakanite, above 21°. 5, the reverse is the case; in other
words, below 21°. 5 we have a solution of astrakanite super-
saturated with respect to the mixed sulphates, above 21°. 5
a solution of the mixed sulphates supersaturated with respect to
astrakanite.

It is further possible to obtain a relation between the
transition temperature and the solubilities of the different salts
which take part in the equilibrium.

Taking, for example, the simple case of two salts each con-
sisting of two ions, say the chlorides and bromides of two metals
M and m; we will calculate the temperature at which the four
salts MCI, MBr, mCl, and mBr are in equilibrium with each other
and with their saturated solution.

We shall suppose the salts to be sparingly soluble, so that
their saturated solutions are very dilute, and the dissolved salts,
therefore, almost entirely dissociated into their ions. The con-
centrations of each of the ions may then be regarded as the
same as those of the salts themselves in their saturated solutions,
call the latter CMC1, CMBr, etc.

1 See also BARHUIS ROOZEBOOM, Rec. des Trav. Chim. ties Pays-Bas, 6, 342, 1887;
Zeit. phys. Chem. 2, 518, 1888.

2 2

MBI Cm- CBr — CmBr.

THE TRANSITION TEMPERATURE. 177

In the equilibrium between a salt and its saturated solution
the product of the concentrations of the ions is a constant
quantity, at constant temperature, so that we obtain,

CMBI- = k2 etc.

Again, calling the concentrations of the ions in the solution
which is saturated with respect to all the four salts simultane-
ously Ccl, CBr, etc., we obtain

CM- CCi — KI,
CM. CBr = ka, etc.
and therefore,

From which

that is, the products of the solubilities of the bodies belonging to
the opposing systems are equal at the transition point.

It is also easy to see that above and below this temperature
the product of the solubilities of the stable pair of salts is
smaller than that of the ineta-stable pair.

When the salts dissociate into more than two ions, the above
concentrations must be raised to a power equal to the number
of ions; if the dissociation into ions be incomplete, each con-
centration must further be multiplied by the activity coefficient.

At greater concentrations deviations from the rule which has
just been established will occur; this detracts, however, but little
from its practical utility, since it is still able to give valuable
information as to the probable existence, and approximate
position of a transition point, which may then be sought and
its position accurately determined by experiment.

For example, the equilibrium

Na2 S04. 10H20 4- 2 KC1 ^^ K2SO, -h 2 NaCl 4- 10H20
was examined with the following results.

178

CHEMICAL EQUILIBRIUM.

Temp.

Na2 SO,.

KC1.

C'NasSOi-C'KCl-

K2 S04.

NaCl.

C'K^soi-C'Naci-

0°

29.5

2.8

35.5

5.6

10°

9.5

6.7

20°

34.5

36.5

7.9

The table contains, under the formulae of the different salts,
their solubilities, at the given temperature, in parts in 100 of
water.

The products of the concentrations of the saturated solutions
(in gram equivalents per litre) calculated from these numbers
show that the transition temperature probably exists at about
10°, the mixture of Glauber's salt and potassium chloride being
the stable system below this temperature, that of potassium
sulphate and sodium chloride above it. ' This has been con-
firmed 2 by direct experiment, the transition temperature being
found at 3°. 7.

The curves of solubility are not the only ones which intersect
at the transition temperature ; the curves representing the vapour
pressures of the saturated solutions do so also. That this is
necessarily the case is at once obvious when we consider that
at a given temperature the vapour pressure of a solution depends
only on its concentration.

The experimental proof was obtained by means of the BREMER-
FROWEIN tensimeter described on p. 159, which was used here
as a differential instrument.

The two bulbs were filled with moistened astrakanite and with
a moistened mixture of the two sulphates respectively, so as to
insure the presence of saturated solutions ; the difference in the
level of the oil, observed at different temperatures, gives the
difference between the vapour pressures of the solutions, which
corresponds to the difference in their concentrations. The following
results were obtained.

1 Cf. SCHIFF, LIEB. Ann. 114, 68, 1848

2 Page 173.

THE TRANSITION TEMPERATURE.

A. With falling temperature.

179

Temperature.

Astrakanite.

Mixture of
sulphates.

Difference.

22°. 15
21 .43

20 .75

344.5
344.9
345.5

345.7
344.9
344.1

— 1.2
0
-f- 1.4

B. With rising temperature.

Temperature.

Astrakanite.

Mixture of
sulphates.

Difference.

21°. 15

345.8

344.8

-f- 1

22 .95

343.4

347.5

- 4.1

The point of intersection of the curves of vapour pressure is
therefore very well marked; below 21° .5, the more concentrated
astrakanite solution has the smaller vapour pressure, while above
21°. 5 the reverse is true.

4. Relation between the transition temperature

of a hydrated salt and the vapour pressures

of the salt and of solutions of it.

The transition temperature of a hydrated salt is the temperature

at which the vapour pressure of the crystals is exactly equal to

that of the saturated solution of the salt ; below this temperature,

the former is smaller than the latter, above it, it would be greater,

if the solid salt continued to exist as such, and did not melt.

The following experiment with Glauber's salt (melting point 33°)
shows this in the clearest way. The vapour pressure of the
salt is compared with that of its saturated solution ; above 33° the
salt exhibits a greater vapour pressure than the saturated solution
only for a very short time, as owing to the fusion the two
become identical. The point of intersection of the vapour
pressure curves is therefore in this case, the point at which
the vapour pressure of the salt, and of its saturated solution
attain the same value, the equality continuing on further elevation
of the temperature. The following numbers show this.

180

CHEMICAL EQUILIBRIUM.

Temperature.

Level of the oil.

Difference.

Moist salt.

Dry salt.

33° .05

268.2

32 .85

32 .6

32 .5
31 .79

Difference ;
265.4

3erceptible.
271

5.6

2563

280.1

-23.8

At 32°. 5 — 32°. 6, therefore, the vapour pressure of Glauber's
salt becomes equal to that of its saturated solution, while below
this temperature it is smaller. The temperature at which the
vapour pressures become equal coincides thus with the melting point,
and with the point of intersection of the curves of solubility l.

5. Methods of determining the transition
temperature.

The different methods which, up to the present, have been
used for the determination of the transition temperatures of
condensed systems are the following: —

a. The dilatometric method.

b. The thermometric method.

c. The crystallisation method.

d. The identity methods.

x. By determinations of solubility.

/3. By determinations of the vapour pressures

1. of solutions.

2. of dissociation.

7. By determinations of the solution pressure

1. of solutions.

2. of dissociation.

See also R. LOWENHERZ, Zeit. phys. Chem. 13, 490, 1894.

DETERMINATION OF THE TRANSITION TEMPERATURE. 181

S. Electrical methods.

1 . Electrical method with both stable and meta-stable

phases.

2. Electrical method with stable and without meta-

stable phases.

Each of these will be considered separately and examples of
its application given, after which some less general methods
will be briefly noticed.

a. THE DILATOMETRIC METHOD.

This has been most extensively employed by
REICHER l in his researches on the conversion of
rhombic into monosymmetric sulphur.

The method depends on the fact that, in
the majority of cases, the substances present
before and after the change have different specific
volumes, so that the transformation is accomp-
anied by an increase or diminution of volume.
The temperature being maintained constant, a
change of volume therefore indicates that the
reaction has taken place

The specific volume of rhombic sulphur2,
for example is 1/2.07, that of monosymmetric
sulphur 1/1.96, so that the conversion of rhombic
into monosymmetric sulphur is accompanied by
an expansion.

The dilatometer (fig. 27, p. 94), which is
used in determining the transition temperature by
this method, consists of a cylindrical glass bulb
to which a thick-walled capillary tube is fused,
the whole having the appearance of a large
thermometer.

The bulb is partly filled with the substance
which is to be examined, evacuated by means of a water air-

1 See also W. SCHWAKZ, Beitrage zur Kenntniss der umkehrbaven Umwandlungen
pohmorpher Korper, Preisschrift, Gottingen, 1892; also KOPP, FOGG. Ann. 80, 175, 1850.

2 LANDOLT und BORNSTEIN, Physikalisck-Chemiscue Tabcllen, 2te Aufl. p. 119.

182 CHEMICAL EQUILIBRIUM.

pump, and then filled completely with some indifferent liquid,
such as oil, petroleum, or mercury, so that the position of the
latter can be observed on a paper scale which is glued to the
capillary tube.

The form of dilatometer shown in fig. 35 may be used in
cases in which only a small quantity of substance is available.
The reservoir b'c, which is 12 cm. long and 1 cm. in internal
diameter, is prolonged into a narrower tube ab, of about 4 mm.
diameter, which serves for filling it. The capillary cd is about
70 cm. long and 1 mm. wide ; at c there is a small glass bulb
with a narrow stem which fits loosely into the capillary and prevents
its stoppage by particles of the substance contained in the bulb.

In order to introduce the petroleum, the apparatus is sealed
up before the blowpipe at a, inverted, and the end of the capillary
d connected with the tube f by means of a caoutchouc stopper;
petroleum is then introduced at /', and the whole evacuated by
means of the water air-pump. The air escapes through the
petroleum, which takes its place in the apparatus, In order to
bring the oil to a convenient level in the capillary tube the
excess of it remaining at f is poured out, and the apparatus
again evacuated, the small quantity of air remaining in the bulb
expands and forces a quantity of petroleum out of the capillary
which is easily regulated. The height of the oil is read on a
paper scale glued to the capillary tube.

The observations are made by heating the dilatometer in a
thermostat for a considerable time at temperatures rising by
successive increments of a degree. The change in the mixture,
which gives rise to the change of volume, is indicated by a slow
alteration in the height of the oil in the capillary, which goes
on for several hours.

Taking sulphur for example, if the bulb be filled with the
rhombic modification alone, the change into the monosymmetric
modification may be delayed very considerably even when the
temperature is higher than the transition point. It has therefore
been found advisable in all cases to add, to begin with, a little
of the system which is formed by the change, as in this way
the delay in the commencement of the reaction is avoided.

THE TRANSITION TEMPERATURE. DILATOMETER.

183

By alternately heating the bulb above, and cooling it below the
transition point several times, the change is caused to take place
much more rapidly, so that dilatometers which have been used
several times (with the same contents) allow of much more rapid
measurements. The addition of a solvent is also often favourable
to the change. REICHER, for example, filled the bulb of a dilato-
meter with rhombic sulphur and a mixture of 1 volume of carbon
bisulphide to 5 volumes of turpentine. About half of the sulphur
was converted into the monosym metric modification by hesat, after
which the position of the liquid in the capillary was read off at
the following temperatures : —

Temperature 95° . 1

Time in minutes.

Level of the oil.

5
30
55
65

343.5
340.5
335.75
333

At this temperature monosymmetric sulphur still changes into
the rhombic modification.

Temperature 96° . 1

Time

in minutes.

Level of

the oil.

342

.75

354

.75

360

.50

361

.50

The rise of the oil shows that the change at 96° . 1 takes
place in the reverse direction.

Temperature 95° . 6.

Time in minutes.

Level of the oil.

5
100
110

368.75

368.
368.75

184 CHEMICAL EQUILIBRIUM.

At this temperature the height of the liquid in the capillary
tube is practically constant, that is, the two systems are in
equilibrium, and the transition temperature is 95° . 6. l

The dilatometric method may be applied in all cases in which
the chemical reaction is accompanied by a change of volume ;
this is not invariably the case, for example, no change of volume
occurs in the conversion of Glauber's salt into anhydrous sodium
sulphate and water. 2

In order to calculate the amount of expansion or contraction
which accompanies a change it is necessary to take into account
the composition of the systems in the immediate vicinity of the
transition point.

For example, in the formation of astrakanite from a dry
mixture of hydrated sodium and magnesium sulphates, the sub-
stances really formed are astrakanite and a solution saturated
with astrakanite, so that the equation which represents the
actual change is 3
5.9 (Na2 S04. 10 H20) -h 7.6(MgS04. 7 H20) -*=* 3 (Na2 Mg(S04)2. 4H20)

b. THE THERMOMETRIC METHOD.

This method is based on the fact that all changes of the kind
under consideration are accompanied by an evolution or absorption
of heat, that system which is stable at the higher temperature
being formed with absorption of heat.

The transition point may be determined by this method by
observing the times which are required in order to heat or cool
the system through equal intervals of temperature, or by observing
the changes of temperature which occur in equal intervals of
time. The occurrence of the chemical reaction coincides with
the maximum retardation of the change of temperature, in fact
the sign of the change of temperature is often reversed.

1 To prevent evaporation the dilatometer was sealed up ; the pressure within it was
4 atmos. at 95°. 6. T. E.

2 E. WIEDEMANN, WiED. Ann. 17, 575, 1882.

3 BAKHUJS ROOZEBOOM. Zeit. phys. chem. 2, 515, 1888. ROOZEBOOM uses the

sign 100 H2O™ ' 4 to indicate that 4.6 mols. MgS04and 2.9 mols. Na2S04

are dissolved in 100 mols. of water.

THE TRANSITION TEMPERATURE. THERMOMETRIC METHOD.

185

The method is practically carried out as follows : —

The substance which is to be investigated is placed in a wide
test-tube surrounded by cotton wool, in which a thermometer is
placed, it is then heated or cooled and well stirred with the
thermometer, and its temperature read from time to time.

The following results were obtained in the decomposition of
schoenite represented by the equation l

K2 Mg(S04)2. 6 H20 + H20 :^± K2 S04 + MgSO,. 7 H20.
Falling temperature.

Time t.

Temperature T.

AT
At

lOhrs. 4 3 min.

+ 6°

1.7

»» 46 „

+ 1

0.75

„ 50 „

— 2

0.13

, 54 „

— 2.5

0.08

11 hrs. 0 min.

— 3

0.5

11 * 11

0.5

1 „

— 6.5

Rising temperature.

Time t.

Temperature T.

AT
At

12 hrs. 4 min.

11 5 ,,

— 6

0.5

9 „

0.33

12 „

— 3

16 „

- 3

0.05

25 „

— 2.5

0.14

32 ,.

- 1.5

A very decided retardation of the change of temperature
takes place at - 3°, both on heating and on cooling, from

1 Sec note 4 on page 172. Compare also W. SCHWAHZ, loc. cit. (note 1,- p. 181).

186 CHEMICAL EQUILIBRIUM.

which we may conclude that the decomposition takes place at
this temperature.

c. THE CRYSTALLISATION METHOD.

This method was employed in the investigation of the equil-
ibrium

2 Na NH4 CJIA- 4H20 ^~± (Na NH4 CJ3A)2. 2 H20 + 6 H20.

By allowing the salts to crystallise out from solution, WY-

KOUBOFF l and SCACCHI have shown that above 27° sodium ammonium

racemate is deposited, while below it a mixture of the dextro-

and Isevo-tartrates crystallises out.

d. THE IDENTITY METHODS.

W. MEYERHOFFER 2 has pointed out that at - the transition
temperature the solutions of the mutually convertible systems
become identical in every respect. We have already seen that
the solubilities, and also the vapour pressures of the saturated
solutions of the two systems are identical at the transition
temperature. MEYERHOFFER says further, " There is no doubt that
if all the other properties of the solutions such as specific volume,
refractive power, viscosity, conductivity, etc. were to be represented
graphically as functions of the temperature, the curves would
intersect at the transition temperature."

The methods which will now be described all depend on the
experimental proof of the identity of the saturated solutions of
the mutually convertible systems. According as solubility, vapour
pressure, or some other property of the solution be used as the
criterion, the methods of determining the transition temperature
vary in experimental detail, so that we obtain the different methods
mentioned on p. 180, which will now be explained fully.

a. Determination of solubility.

We have already seen that the solubility curves of the two
mutually convertible systems intersect at the transition temper-

1 Bull. Soc. Chim. 41, 210, 1884; 45, 53, 18S6.

2 Zeit. phys. Chem. 5, 105, 1890.

THE TRANSITION TEMPERATURE. VAPOUR PRESSURE.

187

ature, and have found by interpolation the temperature at which
the solubilities of Glauber's salt and anhydrous sodium sulphate
become equal from the observations of LOEWEL (p. 175).

BAKHUIS ROOZEBOOM l has determined the transition temperature of
astrakanite by means of determinations of solubility, the results of
which are given in the following table. The numbers are molecules
of the salts to 100 molecules of water in the saturated solutions.

Temp-
erature.

Astrakanite.

Astrakanite +
Sodium sulphate.

Astrakanite -f-
Magnesium sulphate

Na2S04

MgS04

Na2S04

MgS04

Na2SO*

MgS04

18°.5

3.41

4.27

2.95

4.70

2.95

4.70

2.85

4.63

24 .5

3.45

3.68

3.45

3.62

2.68

4.76

According to these determinations, therefore,
the solubilities of the systems astrakanite + sodium
sulphate, astrakanite + magnesium sulphate, and
magnesium sulphate -f sodium sulphate become equal
at 22°, that is, 22° is the transition temperature.

ft. Determination of vapour pressure.
1. Vapour pressures of solutions.

From what has already been said on p. 178
it is clear that a comparison of the vapour
pressures of the saturated solutions of the mutually
convertible systems leads to a determination of
the transition temperature.

VAN 'T HOFF and VAN DEVENTER 2 made use of
the differential tensimeter in the investigation of
astrakanite in the way described on p. 179. A
form of the tensimeter which is to be preferred
to that shown in fig. 34 is represented by the
accompanying diagram, fig. 36 ; the porcelain

Fig. 36.

1 Zeit. phys. Chem. 2, 513, 1888; Rcc. des Trav. Chira. des Puys-Bas, 6, 333, 1887.

2 Zeit. phys. chera. 1, 169, 1887.

188

CHEMICAL EQUILIBRIUM.

millimetre scale allows the difference of level of the oil to be
read without using the cathetometer. The vapour pressures of
saturated solutions of Glauber's salt and of anhydrous sodium
sulphate have been determined by E. COHEN, l the results are
contained in the following table. 2

Temperature.

Vapour pressures
of the saturated
solutions of
Na2S04. 10H20.

Vapour pressures
of the saturated
solutions
of Na2S04.

28°.3

26.20

24.07

30 .1

28.03

26.60

32 .6

30.82

The point of transition is 32° . 6.

Further applications of this method have already been mentioned
in the cases of the racemates, copper potassium chloride, etc.

2. Pressure of dissociation.

This method depends on the relation, described on p. 179,
between the dissociation pressure of hydrated salts and the vapour
pressures of their saturated solutions. The table on p. 180 shows
clearly how the tensimeter may be used in order to determine
the transition temperature by means of this relationship.

7. The solution 'pressure method.
1. In the case of solutions.

This method, which has been worked out by J. VERSCHAFFELT, 3
is an application of NERNST'S 4 conception of solution pressure.

1 Zeit. phys. chem. 14, 90, 1894.

2 The vapour pressures are -in mm. of mercury at 0°. Compare the values obtained
with what is said on p. 174.

3 Zeit. phys. chem. 15, 437, 1894.

4 Zeit. phys. chem. 4, 150, 1389. Theoretical chemistry, p. 133.

THE TRANSITION TEMPERATURE. SOLUTION PRESSURE. 189

Just as a liquid possesses a certain power of expanding, in con-
sequence of which it evaporates into any vacant space until the
pressure of its vapour reaches a certain maximum value known
as the vapour pressure of the liquid, so a liquid, if brought into
contact with another liquid, in which it is soluble to a limited
extent, will dissolve until the dissolved part has reached a certain
maximum osmotic pressure which, on account of the complete
analogy between the processes of evaporation and solution, NERNST
has called the solution tension l ot the liquid.

If a foreign body be dissolved in the liquid its solution pressure
is diminished in the same way as its vapour pressure.

If some liquid in which water is soluble to a limited extent
be placed in contact with a hydrated salt which is insoluble in
it, the hydrate will give up water to the liquid in the same
way as it would effloresce in the air; if a sufficiently large
amount of the salt be used a maximum osmotic pressure of the
dissolved water will be attained, corresponding to the vapour
pressure of dissociation of the salt in vacua, and which may
therefore be called the solution pressure of dissociation. 2

Since at a given temperature the solution pressure only depends
on the concentration of the dissolved water, VERSCHAFFELT deter-
mined the latter only, using amyl alcohol as the solvent and
water as the soluble liquid.

In order to determine the concentration of the water in the
amyl alcohol solutions, a series of measurements of the solubility
of water in amyl alcohol at different temperatures was made;
the concentration of any solution could then be obtained by
cooling it until it just became turbid, and interpolating the
concentration corresponding to the temperature at which the
turbidity appeared.

The determinations were made in the following way: -
Exactly weighed quantities of the liquids were brought into
the flask of an EYKMAN'S freezing point apparatus 3 and the

1 " Losungateusion" is generally translated " solution pressure", which is perhaps
preferable to the more strictly equivalent term '•' solution tension". T. E.

2 LINKBARGKR, Zeit. phys. Chem. 13, 500, 1894.

;! The apparatus is described in the Zeitschrift fur phys. Chem. 2, 964, 1888, and
also in OSTWALD'S Lehrbuch der allgem. Chem. 1, 766.

190 CHEMICAL EQUILIBRIUM.

thermometer placed in position, after bringing the mercury to
a suitable position on the scale, and comparing its readings with
those of a standard thermometer. The apparatus was then slowly
warmed in a water bath, and vigorously shaken until the mixture
was homogeneous, after which it was placed in a beaker of
water which was allowed to cool by radiation.

The temperature at which the turbidity appeared could be
observed with an error of a few tenths of a degree ; in the table
which follows, the temperatures are given to the nearest whole
number so that they may be affected by a maximum error of
0°.5, a degree of accuracy which is sufficient for the present
purpose.

The following is an example of the numbers obtained.

Amyl alcohol 8 . 046 grams = Ga

Water 0.769 „• = Gw

Concentration of the water •=. 100 ^ — ^~rT — 8-72 per cent.

(jw -f- (ja

Temperature at which saturation took place — 6°.

The following are the percentage concentrations of the saturated
solutions of water in amyl alcohol at different temperatures.

Temperature. Concentration.
6° 8.72

15 9.14

25 9.67

32 10.00

36 10.20

The following equation represents the connexion between the
concentration c and the temperature t, between 0° and 40°.

c = 0.05 (168 + t).

To obtain the concentration of any solution, it is only necessary
to introduce the observed temperature at which turbidity appears
in it into this equation, and calculate c.

If the temperature at which turbidity appears is inconveniently
high or low, a known quantity of amyl alcohol, or water, may
be added in order to bring the temperature between suitable

THE TRANSITION TEMPERATURE. SOLUTION PRESSURE. 191

limits (20° — 40°). From the temperature at which the turbidity
now appears the initial concentration of the solution is easily
calculated; for example, 8.591 grams of a solution were taken
and 0.207 grams of water added to it, the turbidity appeared at
30°, so that the concentration of the new solution was
Cl = 0.05 (168 + 30) = 9.90 per cent.

The whole amount of the water is therefore,

o on
Wl = —- (8.591 + 0.207) = 0.871 grams,

and the initial quantity,

w =i 0.871—0.207 = 0.664 grams.

from which the concentration, which is to be determined, is

66.4

c — Q KOI =7.72 per cent.
0.591

After these preliminaries, it was possible to determine the
transition temperature of Glauber's salt in the following way : —
The finely powdered salt was placed in a flask of about 100 cc.
capacity, and treated with amyl alcohol which had been saturated
with water ; the salt takes up water from this forming a saturated
aqueous solution. 1 The flask was well closed and maintained at
a constant temperature in a thermostat, being well shaken from
time to time. In order to obtain a supercooled solution of
anhydrous sodium sulphate the flask with its contents was pre-
viously heated for some time to a temperature above 33°.
Equilibrium having been attained, after about an hour, the salt
was allowed to settle and the amyl alcohol filtered, after which
the concentration of the water contained in it was determined
in the way described. 2

1 This aqueous solution dissolves a little amyl alcohol, but sinco the two systems
become identical at the transition temperature, they both dissolve the same quantity
of amyl alcohol and though the solubility of the salt is changed a little the transition
temperature is unaffected.

2 PFEIFFEK, Zeit phys. Chem. 9, 445, 1892, has shown that the addition of foreign
bodies to a mixture of two liquids may displace the temperature at which the turbid-
ity appears to a considerable extent. Special experiments on this point showed, however,
that sodium sulphate is not sufficiently soluble in moist amyl alcohol to have any
appreciable effect.

192

CHEMICAL EQUILIBRIUM.

The following table contains the results of the experiments.

Percentage
concentration of

Temperature.

the water taken
up from a saturated
solution of

Temperature.

the water taken
up from a saturated
solution of the

Glauber's salt.

anhydrous salt.

20°

7.80

40°

6.48

7.49

6.29

6.92

6.09

6.7i

5.88

6.41

6.11

The concentrations of the water taken up by the amyl alcohol
from the saturated solutions of Glauber's salt at temperatures
from 31° — 33° lie on the straight line,

c - 16.01 — 0.3 t,

those of the water taken up from the solutions of the anhydride
are represented by the formula

c = 4.88 4 0.04 t.

These two lines intersect at a temperature of 32°. 74, which
is therefore the transition temperature.

2. Solution pressure of dissociation.

The transition temperature was also determined by means of
observations of the solution pressure of dissociation of Glauber's
salt in amyl alcohol ; in order to make the measurements Glauber's
salt may be placed in contact with dry amyl alcohol, or amyl
alcohol saturated with water may be brought together with
anhydrous sodium sulphate. The salt was ground to fine powder ,
01' when the anhydride was used, Glauber's salt was allowed to
effloresce in the air, because the powder formed in this way is
so finely divided that it remains suspended in the liquid for a
long time. Equilibrium is attained only after some hours.

TJNI

THE TRANSITION TEMPERATURE. ELECTRICAL METHODS.

193

Temperature.

Concentration of the water. l

20°

4.41

5.09

5.8 i

The concentrations are reproduced by the formula

c = 1.60 + 0.14 t.
This curve cuts that of the saturated solutions of Glauber's salt,

c - 16.01—0.3 t,
at 32°. 75.

£. Electrical methods.

1. Electrical method with both stable and
m eta-stable phases.

This method, which is also one of the identity methods, was
devised by E. COHEN. 2

If two solutions of a salt (say ZnSOJ, of different concentrations,
be placed in vessels connected together by means of a syphon
with limbs of equal length, and an electrode consisting of
the same metal as that contained in the salt be placed in
each vessel, then, on connecting the electrodes by means of a
wire, a current of electricity will flow round the circuit in a
direction such that the difference of concentration will tend to
disappear. The concentrations having become equal, no further
difference of potential will exist ; the cause of the current being
removed, the current itself ceases. MOSER 3 has shown that, in

1 In agreement with LESCOKIR'S observation that the dissociation pressure is constant,
it was found that the solution pressure of dissociation is independent of the quantity
of water of crystallisation in the hydrate. At 20° the salt Na^SO^ 3.88H20 had the
same pressure as the salt Na.2S04. 0.22H2O.

2 Zeit. phys. Chem. 14, 53 and 544, 1894.

3 The literature of the subject of concentration currents is given in OSTWALD'S
Lehrlmch, 2te Aufl. II, 824.

194

CHEMICAL EQUILIBRIUM.

the combination described, the direction of the current is the
following :

Zn, dilute ZnSO±-solution — >• concentrated ZnS04-solution, Zn.

Concentration cells have been constructed by NERNST 2 which
differ from those of MOSER'S type in the fact that, with ZnS04
for example, S04 electrodes are used instead of zinc ; with this
arrangement the current flows from the more concentrated to the
more dilute solution.

We know then, first, that in an equilibrium between condensed
substances the solubilities of the two systems, which are different
at temperatures above or below the transition point, become
equal at that point, and secondly, that when a concentration
current flows between two solutions it will disappear when the
concentrations of the solutions become indentical.

From these facts it is evident that the disappearance of the

concentration current

77iermomcfer
.S" Glass tube

Sealing

agiBg

^-^

which flows between
the saturated solutions
of the two mutually
convertible systems
may be used to deter-
mine the temperature
at which the solutions
have the same concen-
tration, that is, the
transition temperature.
Just as in the titration
of a base with an acid
an indicator is used in
order to determine the point at which the whole of the base
has been neutralised, so here the concentration current is employed
as an indicator of the temperature at which the solubilities of
the mutually convertible systems become equal, that is, the
transition point.

Woolen thread.

Transition cell.

Fig. 87.

gggp

'a ling

wax.

ad.

l Zeit. phys. Chcm. 4, 117 and 157, 1889.

THE TRANSITION TEMPERATURE. ELECTRICAL METHODS. 195

As an example, the transition temperature in the reaction
ZnS04. 7 H20 = ZnS04. 6 H20 + H20

will be taken.

The apparatus with which the determinations are made may be
called the transition cell with meta-stable phase ; it is represented
in fig. 37, and consists of two \essels, A and B, which are
connected by a syphon with limbs of equal length. Zinc
sulphate, which has been finely powdered and moistened with
a few drops of water, is placed in the narrower parts of
the vessels ; ' in this way the solutions, being in contact with a
great excess of the solid salt, are maintained in a saturated
condition when the apparatus is warmed.

The syphon is filled with cotton wool saturated with a solution
of zinc sulphate, and the projecting ends of the wool are pressed
into the moist salt in A and B.

Two amalgamated rods of zinc, which are covered with
sealing-wax with the exception of about i/g cm. of their, lower
extremities, serve as electrodes. A small thermometer, graduated
in Yio0? is introduced through the glass tube which is shown in
the figure. The wider parts of the vessels A and B are filled
with some indifferent substance, such as sealing-wax, in order
to prevent any movement of the electrodes during the experiment. 2

When a salt, such as sodium sulphate, the metal of which
cannot be used as an electrode, is under examination an electrode
which is unpolarisable with respect to the anion of the salt
must be employed ; with sodium sulphate, for example, an electrode
of mercury, the surface of which is covered with mercurous
sulphate, is used. Connexion with the mercury is made by means
of a platinum wire fused through a glass capillary tube. 3

1 Only a few grams of the salt are needed, so that, on warming, the solution very
quickly becomes saturated.

2 Any dissimilarity of the electrodes, which would give rise to a current, is
avoided by short-circuiting the cell and allowing it to stand in that condition for some
time; the cells when not in use should always be kept in this way. If after a
considerable time some inequality still remains, it may be allowed for by applying a
correction to the experiments.

3 The form of transition cell which will be described later may also be used in
these experiments.

196 CHEMICAL EQUILIBRIUM.

The transition cell is now to be arranged in the following order :

Unpolar-

Saturated solution

Unpolar-

isable

of the meta-stable

of the stable phase

isable

electrode.

phase of a salt.

of the same salt.

electrode.

The vessels A and B having been filled with a saturated sol-
ution of ZnS04. 7 ELO in the way described, the contents of B
are converted into a saturated solution of ZnS04.6ILO by heating
B in a beaker of water for an hour to a temperature higher than
the transition point. * In order to avoid heating A, a screen of
of asbestos card is placed between it and the beaker.

Fig. 38.

The transition cell is then placed in a thermostat (fig. 38) and
connected up in circuit with a galvanometer, a key to make or
break the circuit, and a variable resistance, such as the ENGELMANN 2
carbon plate resistance shown in the figure, which makes it
possible to bring the spot of light reflected from the galvanometer
mirror on to the scale by introducing a suitable resistance into
the circuit.

The thermostat is then brought to a temperature from 4 to 5
degrees below the supposed transition point ; it is not advisable

1 The transition point is determined approximately by a preliminary experimeut.
^ Archives Neerlandaises, 22, 1888. Zeit. phys. Chem. 2, 153, 1888.

THE TRANSITION TEMPERATURE. ELECTRICAL METHODS.

197

to depress the temperature much more than this, since the prob-
ability of the occurrence of the change of the system ZnS04.
7 H20 into the system ZnSO± 6 H20, which is stable at the lower
temperature, then becomes too great,

The temperature of the thermostat is now allowed to rise
very slowly so that the solutions remain constantly saturated.
Every five minutes the circuit is closed, and the deflection of
the galvanometer needle noted ; this becomes smaller and smaller
as the temperature rises, a point being finally reached where the
deflection is in the opposite direction. The temperature at
which the deflection is zero (the transition temperature) is then

30.8 3iS 3M 3M JW 3&S 362 37-f 3&g JM 40j 4l.g 4Zg «* US 454 4W 47.S

SIS 5SJI 53S 6M

Fig. 39.

obtained by interpolation. The explanation of the diminution of the
current is to be found in the diminution of the difference between
the concentrations of the solutions in A and B with rising
temperature; at the transition temperature, where the concen-
trations are the same, the current is zero, and on further
raising the temperature the current is reversed, as is obvious
from what is said on p. 174 on the course of the curves of
solubility. When the temperature is maintained above the
transition point for some time the solutions in A and B again
become identical, and the current disappears.

198

CHEMICAL EQUILIBRIUM.

The following table contains the results which were obtained
with Glauber's salt; the temperature is given under t, the deflection
of the galvanometer under &.

29°. 7

—122.5

34°. 1

74.5

30 .3

-104.5

38 .9

43.0

30 .9

— 87.0

42 .5

27.0

31 .6

— 60.5

48 .4

10.5

32 .1

— 38.5

50 .9

7.0

32 .7

- 1.0 '

53 .9

5.0

32 .9

+ 6,5

56 .9

5.0

33 .2

18.5

59 .9

0.0

33 .4

35.0

60 .9

0.0

33 .7

56.0

61 .9

0.0

Taking the deflections of the galvanometer as ordinates, and
the temperatures as abscissae, a curve is obtained, fig. 39, which
cuts the axis of abscissae at the transition point (32°. 8). 1

2. Electrical methods with stable and without
meta-stable systems.

The application of the method described in the preceding par-
agraph is limited by the fact that it is frequently impossible to
maintain the meta-stable system at the same temperature as the
stable system for a considerable period of time, especially when
that temperature differs much from the transition temperature.
For example, special precautions are necessary in order to super-
cool anhydrous sodium sulphate, in presence of its saturated
solution, several degrees below 32°. 6, without its passing over
into the more stable hydrate Na2S04. 10H20.

An arrangement has been devised by E. COHEN and Gr. BREDIG 2
which permits of the determination of transition temperatures by

1 Further applications of the method are described in the Zeitschrift fiir phys. Chem.
14, 53, 1894.

2 Zeit. phys. Chem. 14, 535, 1894.

THE TRANSITION TEMPERATURE. ELECTRICAL METHODS. 199

means of the transition cell without the presence of the meta-
stable system. The saturated solution of the meta-stable phase
is replaced by an unsaturated solution of known concentration,
which remains unchanged (neglecting the small thermal expans-
ion) at all temperatures.

The cell is put together as follows:

Unpolar-
isable
electrode.

Solution of the salt
of known strength,
without the solid.

Saturated solution
of the salt in
presence of the
stable solid phase.

Unpolar-
isable
electrode.

The electromotive force of a combination of this kind is a
function of the solubility of the stable phase of the salt. *

The temperature coefficient of the electromotive force will
therefore be a function of the temperature coefficient of the
solubility. The latter, as is well known, 2 experiences a per
saltum change at the transition point (though the solubility and
electromotive force themselves do not) and therefore the temperature
coefficient of the electromotive force must likewise undergo a sudden
change at this temperature. If therefore, a curve be drawn repres-
enting the connexion between the electromotive force of the cell
and the temperature, it will have a sudden change of direction
at the transition point, similar to those observed with the curves
of solubility and vapour pressure. Thus in order to determine
the transition temperature, we only need to draw the curves
representing the electromotive force of the cell below, and above
the transition point, and to determine their point of intersection.

The form of transition cell used is shown in fig. 40. It consists
of two tubes a and b, about 10 cm. long and 3.5 cm. wide, to
which capillary tubes are attached ; mercury is brought into each
of these and its surface covered with mercurous sulphate, elec-
trodes being thus produced which are unpolarisable for S04. Over

1 It is of course assumed that the solution or precipitation of the solid substance
in a reversible way occurs simultaneously with the passage of the current. See OSTWALD.
Lehrbuch allg. Chem. 2te Autl. II, 8(58.

2 The melting point may be considered as a special case of this; see J. WAI.KEK,
Zeit. phys. Chem. 5, 193r 1890; W. L. MILLER, Zeit. phys. Chem. 10, 459, 1892.

200

CHEMICAL EQUILIBRIUM.

the mercury in the tube «, a solution of sodium sulphate of known
strength is poured to a depth of 4 or 5 cm., while the tube b
contains a paste of finely ground Glauber's salt and the same solution.
Conducting communication between the two liquids is provided

Fig. 40.

by a Oj-tube about 1 cm. wide fille d with cotton wood soaked
in the sodium sulphate solution. This tube has a relatively small
resistance, which is of importance for the sensitiveness of the
method.

Just above the surface of the mercury in a and b, two J_-shaped
glass stirrers, r, are caused to rotate by means of a small water-
motor, so that the pasty mass of crystals and the solution at
the electrodes are kept in constant motion, and the solution in
b remains saturated. The parts of the apparatus are held to-
gether by a wooden frame easily taken to pieces, which also
serves to support the apparatus in the thermostat.

THE TRANSITION CELL.

201

\Vith Glauber's salt, the solution becomes saturated in about two
hours, after which the electromotive force remains constant. The
measurements of potential were made by means of the compens-
ation method of POGGENDORFF and Du Bois REYMOND ; with the
galvanometer used a difference of potential of less than Vsoooo
volt was appreciable. '

Three different cells were investigated, the solutions of constant
concentration being N, N/2, and N/4 respectively.

The other solution being a solution of sodium sulphate satur-
ated with respect to the modification which is stable at the
temperature given, the following values of the electromotive
force E (in millivolts) were obtained.

Cell I. Normal sodium sulphate solution.

20° .1

7. 2

35°

22.2

25 .4

11. 2

22.5

30 .2

16. 8

25.1

E! = 25.5 — 0.39 t + 0.006 t2.
E2= 12.8 — 1.097 t + 0.0407 t2.

Taking the temperatures as abscissae, and the corresponding
values of the electromotive force as ordinates the curves^ given
in fig. 41 result. The point of intersection obtained from the
curves, or calculated from the equations given above is 33° .8.

Cell II. N/2 sodium sulphate solution.

20°. 1

14.3

35°. 1

28.2

25 .2

18.7

40 .0

28.6

30 .1

24.1

45 .0

28.7

A Gouv cell was used as standard, a Leclanclie as the working cell.

202 CHEMICAL EQU1LIBBIUM.

E! = 16.63 -!- 0.548 t + 0.00622 t2.
E2— 10.12 — 0.297 t h 0.0253 t2.

The transition temperature obtained from these numbers is 33° .0.

30-

Cell fl '/> ru)rm,aL

20 c

Temperature

Fig. 41.

THE TRANSITION CELL.

Cell III. N/4 sodium sulphate solution.

203

20° .1

21.1

35°. 0

35.8

25 .1

25.7

40°. 1

36.7

30 .0

31.4

45 .0

37.1

E! = 16.32 + 0.889 t — 0.0095 t2.
E2= 15.00 — 0.190 t + 0.0245 t2.
The transition temperature is 32°. 9.

A. E. BAUK l has recently employed this method for the
determination of the transition point in the reaction

Na2HPO,. 12 H20 ^=± Na2HP04. 7 H20 + 5 H20,
which was found to lie between 36°. 5 and 36°. 8.

Further methods. 2

In addition to the methods of determining the transition temp-
erature described under at, — £, there are some others which may be
used, according to the nature of the system under investigation.

When, as in the case of mercuric iodide, a change of colour
accompanies the change, it may be employed to indicate the
transition temperature.

The mutual transformation of colourless polymorphous bodies
may be recognised by the occurrence of changes in the double
refraction, or by its appearance or disappearance. A change in
the electrical conductivity may also serve in many cases as an
indication of the change.

1 Zeit. phys. Chem. 18, 180, 1895.

2 Sec W. SCHWARZ (cf. p. 181) where the literature is given fully.

EQUILIBRIUM.

SECOND PART.
THE THREE FORMS OF PHYSICAL EQUILIBRIUM.

The occurrence of equilibrium between two different systems,
or in general between two different forms of the same kind of
matter, is not confined to the domain of chemistry. , An analogous
physical phenomenon, evaporation, was known long before anything
of the kind had been discovered in chemistry.

The equilibrium which, in the evaporation of water for example,
exists between water and steam, when the latter has reached its
maximum pressure, may be explained by the simultaneous occurrence
of two changes in opposite directions, the one being the conver-
sion of water into steam, the other the conversion of steam into
water with equal speed.

The symbolic representation which has been used in the case
of chemical equilibrium may therefore be employed here also, the
special case which we have taken being represented by the symbol: —

liquid water ^n±: water vapour.

There is, as we shall see, a far reaching analogy between
chemical and physical equilibria. The latter may be divided into
three classes, which are quite similar to those in which the
chemical equilibria were arranged, namely

1. Physical equilibrium in homogeneous systems.

2. Physical equilibrium in heterogeneous systems.

3. Physical equilibrium in condensed systems.

205

I. HOMOGENEOUS SYSTEMS.

The physical analogue of a homogeneous chemical equilibrium
such as

N204 ^ 2 N02,

is a phenomenon which, though not well marked, is of very
general occurrence, namely those molecular attractions which
cause the deviations from the laws of BOYLE and CHABLES (or
GAY LUSSAC); these attractions do not tend to the formation of any
sharply defined product ; were there any such tendency we should
have a case of chemical equilibrium.

II. HETEROGENEOUS SYSTEMS.
A heterogeneous chemical equilibrium, such as

NH4 HS ^=+ NH3 + H2S,

which has already been described, is to be regarded as completely
analogous to a physical evaporation, such as

Liquid water ^z±r Steam.

The equations which were used in the first case apply also to
the second ; we have

d T 2T3

, . , d log C q

from which ~r^ — - ^~,

where C is the concentration of the vapour, q the quantity of
heat which is evolved by the condensation of 18 kgrms. of water
vapour, without external work being performed.

From the above equation we obtain, by integration,

Ca _„ q /J_ l_\

where GI and C2 are the concentrations of the saturated steam
at the absolute temperatures T! and T2.

206 EQUILIBRIUM.

From this equation we can calculate the value of q by
introducing the vapour pressures pt and p2 at the temperatures
T! and T2; we have

n . r . P2 . Pi

^2 • ^1 — ^T • m »
J-2 A!

and therefore,

p2 i Pi q

log g --logT7 :

Introducing the following numerical values,

T! — 273 Pl = 4.54

T2 = 273 + 11.54 p2 =10.02

we find q = 10100.

The heat of evaporation of a kgrm. mol. of water at 5°. 7 7
is 10854 cals. To obtain q from this number, the external work
which accompanies the condensation must be subtracted ; this is
2T = 558 cals., and therefore q = 10296 cals., -which agrees
sufficiently well with the number calculated.

The solution of solid bodies is another example of this kind of
equilibrium, and may be represented as follows :

Undissolved substance ^z±: dissolved substance.

The equations which apply to chemical equilibrium are also
applicable to this case. In employing them to calculate q from
the solubility it is, however, necessary to remember that they are
only strictly true for very dilute solutions.

As is well known, the law of GULDBERG and WAAGE may be
written in the form

for very dilute solutions at constant temperature, 1 where ax and a2
are the numbers of each of the different kinds of molecules
which take part in the reaction, ix and i2 depend on the nature
of the solvent and of the dissolved substance, and the summations
extend to all the bodies belonging to each system.

L J. H. VAN 'T HOFF. Lois de 1'equilibre chimique dans 1'etat dilue, gazeui ou
dissous. Also, Archives Neerlandaises 20, 291, 1885.

SOLUBILITY. 207

Since Saiii relates to the dissolved bodies forming part of the
first system, we have, in the special case of equilibrium between
a solid body and its saturated solution, ^a^ = 0, and therefore

C2 is the concentration of the dissolved substance, and
is equal to the value of i for this substance, so that at constant
temperature

C1 = K,

that is, at a given temperature the soluble substance has a
definite solubility.

Introducing this value of K into the equation which represents
the influence of temperature on the equilibrium, we obtain

cUogC1 . _q_ f dlogG . _q
dT " 2T2' dT " 2iT2"

This equation represents the relation which exists between the
change of the solubility C with the temperature T and the heat
evolved by the separation of a kgrm. mol. of the substance
from the saturated solution, which is its molecular heat of
solution with reversed sign. By the molecular heat of solution
is meant here the heat of solution of the substance in its own
saturated solution. (Final, fictitious or theoretical heat of solution).1
This theoretical heat of solution and the heat of solution in a
large quantity of water (integral heat of solution) may differ
very considerably from each other, and even be of opposite sign.

REICHER and VAN DEVENTEE, 2 for example, have shown that
copper chloride dissolves in a large quantity of water with
evolution of heat, while it dissolves in its own saturated solution
with absorption of heat.

It is to be noticed however that with sparingly soluble bodies
the difference between the integral and the theoretical heats of
solution is negligible, for since there is very little difference
between the saturated solution and pure water, they have very
nearly the same action on the salt.

1 C. M. VAN DEVENTEU and J. VAN DE STADT, Zeit. phys. Cliem. 9, 43, 1892.
BAKHUIS ROOZEBOOM, Rec. des Trav. Chim. des Pays-Bas, 8, 96, 1888.

2 Zeit. phys. Chem. 5, 559, 1890.

208 EQUILIBRIUM.

J. J. VAN LAAR has obtained the following expression for
dlogC
dT : "

dlogC = _q^ 2 — x
dT 2 T2 2

where x is the so called activity coefficient l (z = i - - 1).
The formula is only applicable to dilute solutions of binary
electrolytes. It is to be noticed that when i •=. 1, i. e., with
non-electrolytes, and also when i •= 2, equations (1) and (2) become
identical.

Equation (1), p. 207, shows that the sign of the change of
solubility with rise of temperature is determined by that of the
heat of solution ; LE CHATELIER 2 obtained this result simultane-
ously with VAN 'T HOFF.

When the heat of solution is zero the solubility will not
change with the temperature. The solubilities of isobutyl-
alcohol (ALEXEJEFF 3), calcium sulphate (LE CHATELIER), and of
sodium chloride (VAN DEVENTER and VAN DE STADT 4) in water
illustrate the correctness of this result.

If the heat of solution q be positive, that is, heat is absorbed
when the substance dissolves, the solubility increases with rising
temperature; which is the case with the majority of substances.

Finally if the heat of solution be negative, that is, heat is
evolved when the substance is dissolved, the solubility decreases
with rising temperature. All the gases, and also ether, carbon
bisulphide, bromine, and nicotine (LE CHATELIER) belong to this
class. Lime and calcium sulphate may likewise be added to the
list, the latter having a maximum solubility at about 38 ° (MARIGNAC).*

According to VAN 'T HOFFG the equation

d log C q

dT " 2lT2'

1 The deduction of this relatiouship is to be found in the Zeit. phys. Chem. 17,
546, 1895.

2 Compt. rend. 85, 440, 1877, Compt. rend. 100, 50, 1885.

3 Compt. rend. 100, 442, 1885.

4 Zeit. phys. Chem. 9, 43, 1892.

5 Ann. Chim. Phys. (5), 1, 274, 1874. See also LANOOLT and BORXSTEIN, Phys
Chem. Tahellen, 2te Aufl. 238.

6 Loc. cit. p. 206.

SOLUBILITY.

209

may be employed to calculate the value of q, when the solubilities
of a substance at two temperatures, and the value of i are known.

By integration we obtain log C := — - r-™ + const.,
and therefore, log g = JL (^ - -|-),

q = 2i^-T-^ logg ...... (3)

where (^ and C2 are the solubilities at the absolute temperatures
Tj and T2.

The following table shows that the values of q calculated in this
way agree satisfactorily with those which are determined directly.

The substances examined are all rather sparingly soluble ; these
bodies were chosen because the equation by which q is calculated
only applies to dilute solutions. l

Substance.

Tem-
peratures.

Solubil-
ities. 2

1000

Calculated
by eq. (3)

_q_

1000

obser-
ved.

Oxalic acid

0° 10°

5.2 8.0

1.25

8.2

8.5

Acid potassium
oxalate

0 10

2.2 3.1

1.84

Succinic acid . .

0 85

2.88 4.22

1.00

Salicylic acid ....
Benzoic acid

12.5 81
45 75

0.16 2.44
0.182 2.193

0.93
0.93

8.4
63

8.5
65

Potassium bi-
chromate

0 10

4.6 7.4

2.36

173

Amyl alcohol ....
Aniline

0 18
16 55

4.23 2.99
3.11 3.58

0.93
0.83

— 3.1

— 2.8
0.1

Phenol

1 45

7.12 10.2

0.84

1.2

2.1

Baryta

0 10

1.5 2.22

2.69

16.3

15.2

Calcium hydroxide
Barium nitrate . . .

15.6 54.4
0 10

0 9.38

0.129 0.103
5.2 7.0
3.0 4.05

2.59
2.19
4.45

— 2.8
8.8
21.9

— 2.8
9.4
20.2

17.5 23

15.8 18.5

0.97

4.8

4.6

Mercuric chloride.
Potassium chlorate
Boric acid

10 50
0 15.4
0 12

6.57 11.84
3.3 6.03
1 95 2.92

1.11

1.78
1.11

3.0
11.0

5.8

3.0
10.0
56

Borax

0 10

2 83 4.65

3.57

27.4

25.8

1 In very dilute solution the theoretical heat of solution and that practically deter-
mined are identical, see p. 207.

2 Phys. chem. Tabellen, LANDOLT und BORNSTEIN, 2te aufl. 235. New determinations
of the values of q and i are very desirable, those given in the table not being
recent. Too much weight is therefore not to be attached to the agreement between
the calculated and observed values.

210 EQUILIBRIUM.

It is noteworthy that VAN LAAR'S formula, which applies to
binary electrolytes, gives ^ for KC103 = 10.1, the observed
value being 10.0.

III. CONDENSED SYSTEMS.

The class of chemical equilibria which is characterised by the
existence of a transition temperature possesses a complete analogue
in the physical changes of fusion and solidification. In the change

rhombic sulphur ~^^ monosymmetric sulphur,

there is a certain temperature above which the one system,
below it the other is stable ; precisely the same thing is found in
physics in the phenomena of fusion and solidification, the change,
taking water for example, may be written,

water ^~*~ ice.

The far reaching nature of the analogy will become more
apparent when we consider the influence of pressure on the
transition temperature of condensed systems.

So far, only the fundamental resemblance which exists between
chemical and physical phenomena has been pointed out. There
is, however, a considerable difference between them in one
respect, namely in the surprising variety of the phenomena encoun-
tered among chemical equilibria. The reason of this variety is
obviously to be found in the fact that, while the number of
different conditions of a substance which can take part in a
physical equilibrium is limited to three (solid, liquid and gas) no
such limitation exists in the case of chemical equilibrium. The
parallelism of the two classes will therefore be most evident
in those cases of chemical equilibrium in which only two bodies
take part.

Again, from what has been said it is evident that physical
equilibrium may be regarded as merely the most simple form of
chemical equilibrium. Chemical equilibrium in a homogeneous
system is found in its most simple form in the physical deviations
from the laws of BOYLE and CHARLES. Chemical equilibrium in a

FUSION AND SOLIDIFICATION. 211

heterogeneous system becomes, in its simplest form, evaporation
or condensation ; equilibrium of incompatible systems corresponds
to fusion.

A further difference between physical and chemical equilibrium
is found in the velocity with which the condition of equilibrium
is reached. While this is very great in physical changes, a
certain shuggishness is observed in similar chemical changes.
KAUMANN *, for example, found that in evaporating naphthalene, or
perchlor-ethane, the maximum vapour pressure is much more
rapidly attained than with ammonium carbamate. The equilibrium
in the dissociation of hydrated salts is generally attained only
after the lapse of a considerable time, and' the inaccurate results
of many measurements of the pressures of dissociation of such
salts may be due to this circumstance. 3

The same difference is also noticeable between the phenomena
of fusion and the similar chemical changes in condensed systems;
while the former change is complete almost immediately after
the change of temperature, the latter takes place very slowly
indeed.

It is therefore necessary, in the experimental study of the
changes which tend to bring about equilibrium, to take cases of
chemical change, for only in such cases is the course of the
change sufficiently slow to be susceptible of measurement.

1 Berichte, 4, 646 and 780, 1871.

2 FROWEIN, Zeit. pliys. Chem. 1, 1, 1887.

EQUILIBRIUM.

THIRD PART.

DIAGRAM OF THE INFLUENCE OF TEMPERATURE

ON EQUILIBRIUM. DETERMINATION OF THE

TRANSITION POINT OF SULPHUR.

The application of the laws governing equilibrium is greatly
facilitated by the diagram which will now be described; this
simplifies the expression of the complex phenomena very considerably,
and has made it -possible to predict the transition temperature
of sulphur.

In order to obtain a graphical representation of the equation

d log K q

~~dT~~ ~ 2T2'

we will take the values of K as ordinates and those of T as
abscissae.

The transition temperature of the two crystalline modifications
of sulphur may then be calculated in the following way.

Representing first the physical equilibrium which occurs between
solid rhombic sulphur and sulphur vapour, we obtain the curve
R! R2, the ordinates of which are the concentrations of the sulphur
vapour, the abscissae the corresponding absolute temperatures.
Since the concentration Cr of the sulphur vapour in equilibrium
with rhombic sulphur is equal to K, this curve represents the
equation

d log Cr qr

dT 2T2'

CALCULATION OF THE TRANSITION POINT OF SULPHUR. 213

where qr is the heat evolved by the condensation of the sulphur
vapour in the rhombic form, without the performance of
external work.

Monosymmetric sulphur also evaporates until its vapour has

reached a certain maximum pressure ; the equilibrium may there
fore be represented in a similar way by the curve MiM2, corres
ponding to the equation

d log Cm qm

dT " 2T2'

Cm being the concentration of the vapour of monosymmetric sulphur
at its maximum pressure, and qm the heat evolved by the condens-
ation of sulphur vapour in the form of monosymmetric sulphur,
without the performance of external work.

The two curves RiR2 and MiM2 intersect at A, corres-
ponding to the temperature Trm. At this point the concentrations,
and therefore the pressures of the vapour given off by the two
modifications of sulphur are identical ; above it the vapour
pressure of the rhombic is greater than that of the monosym-
metric modification, from which it follows that at temperatures

214 EQUILIBRIUM.

higher than Trm rhombic sulphur will change into monosymmetric
sulphur in consequence of a kind of distillation, since the rhombic
emits vapour at a greater pressure than the monosymmetric
sulphur.

At temperatures lower than Trm the opposite process will go
forward, so that Trm is the transition temperature.

A third curve FiFo may now be added to the two which
have been described ; this represents the physical equilibrium
which exists between fused sulphur and sulphur vapour, it corres-
ponds therefore to the equation

d log Cf _ qf
dT " 2T2'

where Cf is the concentration of the saturated vapour in contact
with liquid sulphur, and qf is the heat evolved by the condensation
of sulphur vapour to the liquid condition, no external work
being done.

The curve FXF2 cuts the curves M^M^ and RiR2 in the points
B and C, which therefore correspond to two transition temp-
eratures. B represents the temperature Trf above which rhombic
sulphur passes into the liquid condition and below which the
opposite occurs, so that Trf is the melting point of rhombic
sulphur on the absolute scale.

Similarly the point of intersection C corresponds to the melting
point of monosymmetric sulphur on the absolute scale.

We are now in a position to obtain, by means of the diagram r
the relationship which exists between the three transition temp-
eratures Trm, Trf, and Tmf, and the quantities of heat which are
evolved by the changes occurring at these temperatures. From
this relation it is possible to calculate the value of Trm, i. e.,
the transition temperature of the two crystalline modifications of
sulphur.

The triangle ABC may be regarded as bounded by straight
lines, since the angles B C A, and BAG are very small. This
follows from the fact that the concentrations of the sulphur
vapour in the neigbourhood of the transition temperatures (about
100°) viz. ATrm, BTrf, and CTmf, are very small.

CALCULATION OF THE TRANSITION POINT OF SULPHUR. 215

We have therefore,

AB : BC = sin BCA : sin BAG
in which AB : BC = Trf— Trm : Tmf — Trf , approximately.

Again, owing to the small values of A Trm, B Trf , and C Tmf,
the following relation holds good approximately ;

Q- RPA o- RAP d Cm — d Cf d Cr — d Cm
om JtJbA : sin JbJAO = - — - — — —

_dlogCm— dlogCf dlogCr — dlogC
dT dT

From our previous equations we have,

dlogCm— dlogCf __ qm — qf dlogCr — dlogCm qr —

dT 9T2 dT 2T2

^Imf ^-l-m

therefore,

Sin BCA : sin BAC = **

2Tmf 2Tmr

Trf-Trm:Tmf-Trf =l -f:-=^

2Tmt 2Tmr

In order to calculate the transition temperature Trm the different
numerical values must now be introduced.

Tmf and Trf, the melting points of monosymmetric and rhombic
sulphur respectively, have been determined by BRODIE l who found

Tmf = 273 + 120, Trf = 273 + 114.5.

qm — qf is the heat evolved by the conversion of fused sulphur
into the solid monosymmetric modification, that is its heat of fusion,
qr - - qf is similarly the heat of fusion of the rhombic modification.

According to BERTHELOT, 2

qm — qf : qr — qm = 0.15 : 0.04

1 Proc. Roy. Soc. 7, 24, 1856.

2 Essai de Mecanique Chimique 1, 413 aud 553.

216 EQUILIBRIUM.

So that we obtain

387.5— T™ : 5.5 =

3932 ^ ,

Trm = 273 + 96.3.

The transition temperature of the two crystalline modifications
of sulphur is therefore 96° .3. REICHER determined this temperature
by direct experiment as 95°. 4.

Experiment and calculation are therefore in very satisfactory
agreement.

EQUILIBRIUM.

FOURTH PART.

DISPLACEMENT OF EQUILIBRIUM WITH

THE TEMPERATURE. PRINCIPLE OF MOBILE

EQUILIBRIUM.

The observations which have been made on the different forms
of equilibrium lead to a simple general conclusion, which may
be expressed in the following way : -

Every equilibrium between two different conditions of matter
(systems) is displaced by lowering the temperature, at constant
volume, towards that system the formation of which evolves heat.

This principle applies to every possible case, both of chemical
and physical equilibrium. It indicates the effect of an elevation,
as well as of a depression of the temperature; it expresses,
finally, the fact that if no system is present the formation of
which evolves heat, a change of temperature will not displace
the equilibrium. This principle, which will be called the "prin-
ciple of mobile equilibrium" will now be demonstrated for all
cases of equilibrium. The three forms of chemical equilibrium,
and the three forms of physical equilibrium will accordingly be
considered.

I. THE PRINCIPLE OF MOBILE EQUILIBRIUM APPLIED
TO HETEROGENEOUS SYSTEMS.

a. Physical equilibrium in heterogeneous systems.
Evaporation and condensation.

The two different states of matter with which we have to do
in this equilibrium, are, on the one hand, the liquid or solid,

218 EQUILIBRIUM.

on the other hand the gaseous state; the liquid state being
that which is formed with evolution of heat from the gaseous
one, the principle requires that the quantity of liquid should
increase at the expense of the vapour when the temperature is
lowered ; that is to say, that cooling must favour condensation ;
nothing further need therefore be said on this point.

b. Chemical equilibrium in heterogeneous systems.
As we have already seen, the equations

Cf2 dlogK _q_

~ IK? an dT "2 T2'

hold good here, q being the heat evolved when the system
whose concentration is GI is formed, and ni and n2 relating to
those bodies which are not in the condensed condition. In demon-
strating the principle here, it is convenient to distinguish between
those cases in which n! and n2 both differ from zero, as in
the equilibrium between hydrogen, ferrous oxide, steam and
metallic iron,

H2 + FeO ^=± H20 + Fe,

where ii! and n2 are both unity, and those in which nt or n2 is
equal to zero, as in the classical equilibrium

CaC03 ^n^ CaO + C02,

where ni = 0, and n2 = 1.

We shall only consider the latter case here, since the former
will be explained later together with homogeneous chemical
equilibrium. Confining ourselves then to heterogeneous equilibria
in which only one of the systems contains substances in the
uncondensed condition, and calling the concentration of this system
C2, the equations, after putting i^ — 0, take the following form : -

„ nii2 1 dlogK _ q
Iv — L2 , and — r~ — —

and therefore

d log C2 q

2 dT 2 T*

THE PRINCIPLE OF MOBILE EQUILIBRIUM. 219

From this it is evident that the system whose concentration
is C2 will increase or diminish in quantity, at the expense of the
other system, when the temperature rises, according as q is pos-
itive or negative, while a fall of temperature will produce the
opposite result.

The equilibrium is therefore always displaced by a fall of
temperature towards the system which is formed with evolution
of heat, as the principle enunciated above requires.

The equilibrium above mentioned,

NH4HS ^=± H2S + NH3,

is a good example of the application of the principle ; the system
NH4HS, the formation of which from H2S + NH3 evolves heat,
is produced at the expense of the latter when the temperature falls.

II. THE PRINCIPLE OF MOBILE EQUILIBRIUM
APPLIED TO CONDENSED SYSTEMS.

a. Physical equilibrium in condensed systems.

Fusion and solidification.

The solid and liquid states of matter are to be considered
here. The principle of mobile equilibrium requires that the
solid, the quantity of which suddenly increases at the expense
of the liquid when the temperature sinks, shall be formed with
evolution of heat ; that is, solidification evolves, fusion absorbs
heat.

b. Chemical equilibrium in condensed systems.

Incompatible systems.

In the physical equilibria just considered the truth of the
principle is obvious, the phenomena being so well known ; we
shall see that it is also in complete harmony with the phenomena
of chemical equilibrium in condensed systems. These equilibria
undergo sudden displacement at a definite temperature ; the demon-
stration of the truth of the principle in this case, depends therefore
on showing that the change, which, at the transition point, is
brought about by lowering the temperature, will always lead to

220 EQUILIBRIUM.

the production of the system which is formed with evolution of heat.
Taking for example the change of rhombic into monosymmetric
sulphur, or that of cyanuric acid into cyamelide, cases in which
each system contains only one substance and in which the vapour
evolved by both systems is the same, the truth of the principle
may be shown as follows.

Fig. 43.

The equilibria which subsist between each of the two systems
and the vapour which it emits may be represented graphically
by taking the concentrations of the vapour, measured at its
maximum pressure, as ordinates, and the temperatures as
abscissae, fig. 43. Suppose that in the figure the lines MI M2
and K! K2 represent these quantities for the two allotropic
modifications of sulphur.

According to what is said on p. 213 the point of intersection,
A, which represents the temperature at which the vapour pressures
are equal, is the transition point ; above the temperature 0 B the
modification to which the line MI M2 refers will exist, below it
that referred to by KI K2. For sulphur, therefore, MI M2 would
refer to the monosymmetric, K! K2 to the rhombic modification.

It must now be shown that the modification which is stable

THE PRINCIPLE OF MOBILE EQUILIBRIUM. 221

at the lower temperature is formed with evolution of heat from
that which is stable at the higher temperature. The equations,
of which the curves MI M2 and K! K2 are the graphical represent-
ations, are

d log Cr qr_ dlogCm qm

dT " 2 T2' l dT " 2 T2'

Cr and Cm being the concentrations of the saturated vapour
given off by rhombic and monosymmetric sulphur respectively,
and qr and qm being the quantities of heat evolved by the
formation of rhombic and monosymmetric sulphur from sulphur
vapour, no external work being performed.

The heat evolved by the conversion of monosymmetric into
rhombic sulphur is qr - - qm, and from the figure it is evident that

dlogCm
dT

from which qr > qm, and therefore qr - - qm, the evolution of
heat accompanying the change, is positive, as is required by the
principle of mobile equilibrium.

The results of direct experiment are also in agreement with
this conclusion. MITSCHERLICH l found that heat is evolved when
monosymmetric sulphur is transformed into the rhombic modific-
ation. TROOST and HAUTEFEUILLE 2 observed that the conversion of
cyanuric acid into cyamelide, which takes place when the temp-
erature is depressed, is accompanied by an evolution of heat-
LEHMANN 3 found that the different changes which ammonium
nitrate undergoes while cooling give rise to liberation of heat.
The researches of FROWEIN and of VRIENS (pages 158 and 161)
likewise lend support to the principle that the system which is
formed at the expense of the other with evolution of heat is-
produced when the temperature falls.

1 POGG. Ann. 88, 328, 1853.

2 Compt. rend. 67, 1345, 1868.

3 GROTH'S Zeitschrift fur Krystallographie, 1, 106, 1877.

222 EQUILIBRIUM.

III. THE PRINCIPLE OP MOBILE EQUILIBRIUM
APPLIED TO HOMOGENEOUS SYSTEMS.

The physical equilibria which come under this heading may
be neglected, since the principle relates to equilibria between two
different states of matter, and there is no reason for assuming
the existence of two different substances in cases where, for
example, deviations from BOYLE'S law show that some molecular
action occurs which, however, is insufficient to give rise to any
sharply defined product.

In the case of homogeneous chemical equilibrium, the proof
of the truth of the principle depends on the equations

CD)

where q is, as before, the heat evolved by the formation of the
system of concentration Cj. at constant volume.

We may distinguish between cases in which q is positive and
those in which it is negative. When it is positive, that is, when heat
is evolved by the formation of the system of concentration GI,
the constant of equilibrium K will decrease with falling temp-
erature, and therefore GI will increase at the expense of C2,
because Ci + C2 remains constant, the volume being maintained
invariable. When q is negative the first system is formed with
absorption of heat, and the second, therefore, with evolution of
heat ; the second system, of concentration C2, will then be formed
at the expense of the first when the temperature falls. A
depression of temperature thus always increases the quantity of
the system the formation of which evolves heat.

The equilibrium

N204 ^i± 2 N02

may serve as an example of this. According to the principle of
of mobile equilibrium the system N20± will be formed at lower
temperatures at the expense of the system 2 N02, which is well
known to be the case.

The application of the principle of mobile equilibrium makes

THE PRINCIPLE OF MOBILE EQUILIBRIUM. 223

it possible to predict the direction in which any given chemical
equilibrium will be displaced at higher or at lower temperatures.
Since the equilibrium is displaced, on depressing the temperature,
towards those systems which are formed with evolution of heat,
these will predominate at lower temperatures, while at higher
temperatures they will disappear more and more, giving place to
those which are formed with absorption of heat.
In the equilibria

.N204 ^-*r 2N02
NH4.HS ^z± NH3 + H2S
Cyamelide y~*~ Cyanuric acid

for example, the quantities of the systems on the left hand side
will increase more and more at the expense of those on the
right as the temperature falls, so that at lower temperatures
the fraction of the substance which exists in equilibrium in the
form of the system to the left will be very considerable. Since
the temperature on the surface of the earth, at which the
majority of observations is made, is relatively low, about 273°
above absolute zero, it is a priori to be expected that under
ordinary conditions the majority of chemical equilibria have been
displaced towards those systems which are formed with evolution
of heat. This view is fully verified in all parts of chemistry;
to see this clearly, however, it is necessary to consider more in
detail those equilibria which are so completely displaced in one
direction that their true character is not at once obvious. Consider
for example, the equilibrium

2 H20 ^i± 2 H2 + 02,

which as is well known, was shown by DEVILLE to occur, owing
to the partial decomposition of steam, at about 1000°. According
to our principle, the equilibrium must be displaced towards the
system which is formed with evolution of heat, that is water,
when the temperature is allowed to fall ; this is corroborated by
experiment. This displacement is such that, at the ordinary
temperature, water represents the stable condition of a mixture
of oxygen and hydrogen, the latter being converted practically

224 EQUILIBRIUM.

entirely into water under the influence of the most diverse actions.

If, now, chemical equilibria in general are, at the ordinary
temperature, displaced towards the systems which are formed
with evolution of heat, it is evident that those chemical changes
ichich occur at the ordinary temperature must in the majority of
cases be accompanied by evolution of heat.

Similar considerations, based on the principle of mobile equil-
ibrium, show that at very high temperatures the opposite must
take place, and that the changes which occur under these con-
ditions will in general absorb heat. This conclusion also is fully
corroborated by experience.

It is perhaps not superfluous to point out that these conclus-
ions are based on the exact laws of thermodynamics, since the
principle of mobile equilibrium itself is deduced from them. The
principle may, further, be brought into a form which allows of
numerical calculations, the accuracy of which has been shown
by numerous applications.

It is also in place here to compare these results with the
views which have been expressed by THOMSEN and BERTHELOT on
this subject, more especially because the ideas of BERTHELOT, although
contradicted by the facts and recently abandoned ' by the author
himself, are still represented in many text books as being in
accordance with experience.

In 1853 THOMSEN 2 expressed himself thus : -

" Every simple or complex change of a purely chemical nature
is accompanied by an evolution of heat."

BERTHELOT a in 1867 put forward his views in the form of the
principle of maximum ivork, which states that: " Every chemical
change, accomplished without the intervention of external energy
tends towards the production of the bodies or of the system
which evolves the greatest quantity of heat."

There is a great similarity between these two statements; in
both of them the principal idea is that chemical change evolves

1 Compt. rend. 118, 1378, 1894.

2 POGG. Ann. 88, 349, 1853; 90, 261, 1853; 91, 83, 1854; 92, 34, 1854;
Berichte, 6, 423, 1873.

3 Compt. rend. 71, 303, 1870. Ann. Chim. Phvs. (4), 18, 103, 1869. Bull. Soc.
Chim. 19, 485, 1873.

THE PRINCIPLE OF MOBILE EQUILIBRIUM. 225

heat ; THOMSEN confines the application of the statement to purely
chemical changes, while BERTHELOT confines it to those which
occur u without the intervention of external energy" (une energie
et range re).

While THOMSEN, in his " Thermochemische Untersuchungen", l
recognises fully the exceptions to his earlier statement which
have been discovered, and seeks for a hypothesis which shall be
in better accordance with the facts, BERTHELOT, in his "Essai de
Mecanique Chimique", 3 upholds his view, attempting to bring
the facts into harmony with it, and it is only recently that he
has abandoned it.

The principle of mobile equilibrium possesses the advantage
that it is entirely free from any hypothesis, being a rigorous-
deduction from the laws of thermodynamics. It further allows
us to predict that under ordinary conditions equilibrium will
exist, in a great many cases, when the substances are present
almost entirely in the form of the system which is formed with
evolution of heat, and therefore that the majority of changes
which occur under ordinary conditions will be accompanied by
an evolution of heat. The application of the principle shows,
also, that at very high temperatures, equilibrium will exist in
the majority of cases when the system which is produced with
absorption of heat predominates, and therefore that most changes
which occur at high temperatures will absorb heat ; we might
in this case, following the example of BERTHELOT, speak of a
principle of minimum work. It is also to be noted that the principle
of mobile equilibrium places all equilibria, whether physical or
chemical, on the same footing, emphasising the great similarity
of the two classes of phenomena, and embracing all equilibria
between material systems.

Lastly, it is of importance that the principle is capable of
quantitative expression, and may therefore be applied to numerical
calculations, as has been shown in the examples already considered.

By means of this quantitative expression of the principle it is
possible to determine the conditions under ivhich the principle of

1 1883, vol. Ill, 523.

2 Vol. I, 421.

226 EQUILIBRIUM.

maximum work is rigorously true. To do this we have to find the
conditions under which any given equilibrium will be displaced
completely in the direction of the system which is formed with
evolution of heat ; we shall see that this only occurs at absolute zero.
In a case of homogeneous equilibrium the quantitative expres-
sion of the principle of mobile equilibrium is contained in the
equations

K C?2 ! dlogK . q

K- ....... (I)and - -

Suppose that the system whose concentration is C, is formed
with evolution of heat, and that q is therefore positive. The
problem is to find the conditions under which the concentration
of the second system C2 becomes zero. This is evidently the
case when K = 0. Integrating equation (II), on the assumption
that q is constant, we obtain

log K = - JL_ i Const.

This gives K = 0 when T = 0.

Since q is not quite independent of the temperature (see p. 123)
it is better not to employ the integrated equation, since the same
result may be obtained from equation (II) which gives K == 0,
when T == 0 and q is positive.

Quite similar considerations apply to heterogeneous equilibria;
taking for an example the equilibrium

S ^=± NH3 H- H2S,

only the system NH4. HS, which is formed with evolution of
heat, will be present in a condition of equilibrium at absolute
zero, in other words its dissociation pressure will have disap-
peared.

The application of the principle to the third form of equili-
brium, viz. that in condensed systems, is of considerable interest,
for, at absolute zero physical condensation will have reached its
limit, and therefore we might have dispensed with the consider-
ation of homogeneous and heterogeneous equilibria, in which

UNIVEI
5

THE PRINCIPLE OF MOBILE EQUILIBRIUM. 227

bodies in a condensed condition either do not participate or do
so only partially. It is possible to show that in an equilibrium
between condensed systems, only that one which is formed with
evolution of heat is stable at absolute zero. Suppose that at a
given temperature the system whose formation absorbs heat is
alone present in the condition of equilibrium, as, for example,
is the case with monosymmetric sulphur at about 100° C. in
the equilibrium

rhombic sulphur ^n± monosymmetric sulphur.

We have then to prove that on cooling the system it will
pass through a transition point, so that before reaching absolute
zero the system which is formed with evolution of heat will
have taken the place of the other. As before call Cr the con-
centration of the vapour of rhombic sulphur at its maximum
pressure, qr the heat evolved by its condensation to rhombic
sulphur, and Cm and qm the corresponding quantities for mono-
symmetric sulphur, then

log Cr Jlr_ , d log Cm qm

dT ' 2T2' ' dT 2T2'

and therefore,

__ qr -- qm _ .

dT 2 T2 2T2'

where qmr is the heat evolved by the transformation of mono-
symmetric into rhombic sulphur.

The conditions which must be fulfilled in order that the
system which is formed with absorption of heat (monosymmetric
sulphur) shall exist alone in stable equilibrium are,

Cr > Cm and qmr > 0.

According to the above differential equation ^- = 0 when

C
T = 0, and therefore the value of . - must be equal to unity

228 EQUILIBRIUM.

at some temperature intermediate between absolute zero and

C
the temperature at which ^- > 1 ; the temperature at which

~- 1= 1 is the transition temperature the existence of which

was to be proved.

From the preceding, therefore, all chemical equilibria without
exception are displaced completely at absolute zero towards those
systems which are formed -with evolution of heat, and only under
these circumstances is the principle of maximum work rigor-
ously true.

AFFINITY.

I. THE COMPARISON OF CHEMICAL AFFINITIES.

This section will be devoted to the determination of the mag-
nitude of chemical affinity in different cases by means of the
conceptions already obtained, and without using any special
hypotheses.

If affinity be considered as a force, it may be expressed in
kilograms or in atmospheres, and the work which it can effect
in kilogram-metres or in calories.

Regarding it as the force which produces chemical change
we shall arrive, by means of a more detailed consideration of the
equilibrium of condensed systems, at a conception which may
serve as the starting point of our further studies. Equilibrium
in such systems is characterised by the existence of a transition
point. For example, in the equilibrium l

CuCl2. 2KC1. 2H20 ^z± CuCL.KCl 4- KC1 4- 2H20,

it has been proved experimentally that above 92°. 4 the system
on the right completely replaces that on the left, while below
it the reverse takes place. This temperature, characterised
by the fact that at it both systems simultaneously exist in
equilibrium, is the transition temperature. The law of the
incompatibility of condensed systems makes it possible to predict
the existence of a transition temperature in every such equil-
ibrium, for example in the reaction

KI + NaCl ^7^ KC1 + Nal,

the affinity, that is the force which brings about the change,
or the difference between the affinities which are at work in
the two systems, is zero at the transition temperature; further

1 See p. 172.

230 CHEMICAL AFFINITY.

on passing through the transition temperature the value of the
affinity, or of the difference of affinities, changes sign.

In the case of copper bi-potassium chloride, for example, the
affinity which brings about the formation of the system to the
right is, at 92.° 4, equal to that bringing about the formation
of the system on the left, or, what is the same thing, the dif-
ference between the two affinities is zero at this temperature.

II. MEASUREMENT OF AFFINITY.

The magnitude of the affinity ivhich retains the water of
crystallisation in salts.

We will now taken up a question which was attacked by
MITSCHERLICH * in 1844, namely: What is the magnitude of

the affinity which binds the water of crystallisation in decahyd-
rated sodium sulphate ?

MITSCHERLICH expresses himself as follows : -

u If a crystal of hydrated sodium sulphate be introduced into
the Torricellian vacuum at 9°, the mercury falls 5.45 mm., owing
to the water evaporating after having escaped from combination.
Under the same circumstances water alone produces a depres-
sion of 8.72 mm. and therefore the affinity of the water of
crystallisation for the sodium sulphate is equal to a pressure of
3.27 mm., or about 1/84 kgrm. per sq. cm/'

Although the attraction which sodium sulphate exerts on its-
water of crystallisation is, as will be shown later, many thou-
sand times greater than MITSCHERLICH supposed, yet a connexion
may be shown to exist between the magnitude of this attraction
and the diminution of the vapour pressure.

Consider the attraction which a solution of a salt exerts on pure
water, or, as it might be called, the affinity between a solution
and water.

This attraction has been measured by PFEFFER 2 by means of
a piece of apparatus consisting of a porous cell, in the walls of
which a membrane of copper ferrocyanide has been precipitated.

1 Lehrbuch der Chemie, 4te Aufl. 565.

2 Osmotische Untersuchungen, Leipzig, 1877, p. 4.

OSMOTIC PRESSURE A MEASURE OF AFFINITY.

231

which contains the solution of the salt. The copper ferrocyanide
membrane is semi-permeable, that is, it possesses the property of
allowing water to pass through it, while the salt is unable to do so.

If now the cell, filled with the solution of the salt, be immersed
in pure water, after closing its open end and connecting it to a
manometer, the pressure within it will be seen to increase, the
water passing in through the membrane in consequence of the
attraction of the salt solution. After some time a condition
of equilibrium is attained, because the pressure in the porous
cell increasingly resists the inflow of water, finally stopping
it entirely. The pressure which is then indicated by the mano-
meter, i. e. the osmotic pressure of the solution at the temperature
of the experiment, is evidently a measure of the affinity between
the solution of the salt and pure water.

The following numbers were obtained by PFEFFER' with a
solution containing one per cent, of sugar.

Temperature.

Osmotic pressure
in atmospheres.

6°.8

0.664

13 .7

0 . 691

14 .2

0.671

15 .5

0.684

0.721

0.716

0.746

By means of this method it is possible to determine the mag-
nitude of the affinity between sodium sulphate and its water of
crystallisation. For this purpose it is first necessary to obtain the
relation existing between the affinity of a salt for water and the
decrease of the vapour pressure of water produced by dissolving
a salt in it. 2

1 Loc. cit. p. 85.

2 The equations which follow may be obtained from the laws of osmotic pressure,
depression of freezing point, etc. which have been discovered since the appearance of

the Etudes de Dynamique Chimique in 1884. The original form has, however, been
retained here since it possesses a certain historical interest.

232 CHEMICAL AFFINITY.

Suppose we have a closed vessel, fig. 44, filled partly with
steam E, partly with water. The lower part of the vessel, con-
taining the water, is divided into two compartments A and B
by a semi-permeable partition. The aqueous
vapour having attained its maximum pres-
sure at the prevailing temperature, and
being therefore in equilibrium with the
water, an infinitesimal quantity of some salt
is dissolved in the water in A. The equili-
brium, which is disturbed by the attraction
of the salt for the water, will tend to be Fig 44

re-established by the passage of water from

B into A by two different paths, first, directly through the
semipermeable membrane, secondly, indirectly in the condition of
vapour through E.

The direct passage of the water into A will produce an
osmotic pressure which might be measured by means of a
manometer as in PFEFFER'S experiments ; let its value be d D
atmospheres.

The pressure which brings about the flow of vapour from E
to A may be measured by determining the diminution in the
pressure of the vapour at E which would just suffice to prevent
condensation in A. This will be the case when the pressure of the
vapour in E is equal to the vapour pressure of the solution A.
The pressure which causes the flow of vapour from E to A is
therefore equal to the diminution in the vapour pressure of water
which is produced by dissolving the salt in it ; let this be — d S
atmospheres.

The attraction of the salt solution for water thus gives rise
to two forces, d D and — d S, according as it acts on liquid
water or on aqueous vapour. Assuming that the attraction of
the solution in A for a molecule of water is independent of the
state of aggregation of the water, the ratio between the two
forces of attraction will be the same as that between the quan-
tities of water contained in equal volumes of liquid and vapour.

The weight of 1 litre of liquid water may be taken as 1 kgrm., and
1 litre of aqueous vapour under the pressure of S atmospheres weighs

CALCULATION OF ITS VALUE FROM OSMOTIC PRESSURE. 233

S X 0.000806 r = j-j~ kgrms.
We may therefore write,

Integrating this expression we find,

- log S = ^ft + const.

If Sw be the vapour pressure of water at T, we have for
S :: Sw , D := 0.

The integration constant may be eliminated by means of this,
and we obtain

D = 4.55 T log |s

or. introducing common logarithms,

D = 10.5 T Log |S

where Ss is the vapour pressure of the solution of the salt.

As an example of the application of this equation, the values
of D may be calculated for the solutions of sugar the osmotic
pressures of which were determined by PFEFFER.

The value of ~- may be calculated approximately for a given

solution from its freezing point by means of thermodynamics.

GULDBERG l has shown that, the freezing point of an aqueous
solution being — t°, the following relation exists between it

and -^-: —
bs

hL- 1

Ss 1 — 0.00954 t

Introducing this into the equation for D, we obtain
D = - 10.5 Log (1 - - 0.00954 t)

1 Compt. veud. 70, 1349, 1870. OSTWALD, Lehrbuch der Allgem. Chem. 2te Auti.
I, 757.

234

CHEMICAL AFFINITY.

RAOULT * has found that the value of t for a one per cent,
solution of sugar is O.°054.

The following table contains the values of the osmotic pressure
of a one per cent, solution of sugar, at the different temperatures
given, (1) observed directly by PFEFFER, (2) calculated by means
of the above equation.

Temperature.

D observed.

D calculated

6°. 8

0.664

0.668

13 .7

0.691

0.684

14 .2

0.671

0.686

15 .5

0.684

0.689

22 .0

0.721

0.704

32 .0

0.716

0.728

36 .0

0.746

0.737

We are now in a position to calculate the magnitude of the
force with which a solution, or a hydrated salt, retains the water
in it; when the vapour pressure of the solution, or the dissociation
pressure of the hydrated salt, is known, and thus to answer the
question proposed by MITSCHERLICH in 1844.

The following table contains the results of the calculation made
by means of the equation

D = 10.5 T Log !*.

Name of the
salt.

Temperature.

D = 10.5 T Log %.

CuS04. 5H20

39°. 70

1300 atraos.

BaCl2. 2H20

43 .45

1642 „

ZnS04. 7H20

29 .95

532 „

ZnS04. 6H20

29 .95

709

1 Compt. rend. 94, 1517, 1882.

CALCULATION OF ITS VALUE FROM OSMOTIC PRESSURE. 235

The values of -^ have been calculated from the numbers

obtained by FROWEIN (pp. 160 and 161).

The statement that the value of D for CuS04. 5H20 at 39° .7
is 1300 atmospheres, means that if copper sulphate, from which
two molecules, for example, of its water of crystallisation had
been removed, were brought, at the temperature mentioned, into
PFEFFER'S osmometer, a pressure of 1300 atmospheres would be
required in order to prevent the water from penetrating the semi-
permeable membrane and combining with the copper sulphate.
The experiment could not of course be actually carried out in
the usual way, since we are here dealing with a solid substance.

III. DETERMINATION OF THE WORK WHICH
CAN BE DONE BY AFFINITY.

The quantity of work which can be done by affinity of known
magnitude will now be calculated.

If a kilogram-molecule of hydrated copper sulphate (249 kgrms.
of CuS04- 5H20) be taken, and a molecule of water (18 kgrms.)
be removed from it by means of the air pump, the vapour pres-
sure of the crystals remains, according to the experiments of
PAREAU *, completely constant, that is, the salt tends to retain
the water which is being removed from it, from beginning to
end, with a force of 1300 atmospheres (at 39°. 7). If the salt
CuS04. 4H20 were brought into a PFEFFER'S cell (under this
pressure) the work which would be done by the 18 kgrms, of
water on passing into it through the semipermeable membrane,
owing to the affinity of the salt for it, would be

18
A = 1300 X 10333 X = 241792 kgrai.metres, or 568 calories.

Generally, the problem may be treated as follows: the mag-
nitude of the affinity is, according to what is said on p. 233,

D = 4.55 T log f^.

1 De Pompbarometer. Inaugural Dissertation. Utrecht, 1875.

236 CHEMICAL AFFINITY.

The work which this force can do, during the transport of
18 kgrms. of water, is

D 1 ft ^

-, 10333 j±|L _ 2T log |= calories.

A more complicated case will now be considered. The force
will be calculated which comes into play when a salt, say
FeSO^. 6H20, takes up water from another hydrated salt, say
MgS04. 7H20, instead of combining with water in the free state.

We may say a priori that this can only take place when the
dissociation pressure of the FeSO^.TH^O is smaller than that of
the MgS04. 7H20 at the given temperature. The force D which
brings about the transference of the water is equal to the differ-
ence between the forces with which each of the sulphates retains
its water of crystallisation; it is, therefore,

D = 4.55 T (log % - log %) = 4.55 T log 4* ,

lOs 2QS/ i&s

iSs and 2SS being the dissociation pressures of the ferrous and
magnesium sulphates respectively.

The work which can be done by this affinity is therefore

T) 1 ft

A ~ 4257? 10833 TooeT kgrm* metres'

or, A — 2 T log ^~ calories.

This may now be extended by the introduction of the idea
of the transition point. The following table contains some of
the measurements of the dissociation pressures of magnesium
and ferrous sulphates made by Gr. WIEDEMANN l at different temp-
eratures.

1 Journ. prakt. Chem. (2) 9, 338, 1874. Although the numerical data contained
in the table are, according to FROWEIN'S determinations on MgS04. 7H20, decidedly
inaccurate, the truth of the principle which they serve to illustrate is not affected.

MEASUREMENT OF THE WORK DONE BY AFFINITY.

Temperature.

FeS04. 7 H20 dSs).

MgS04. 7 H20 (aS8).

40°. 2

40.1 mm.

46 . 3 mm.

50° .4

77
11

77 „

60° .0

131.3 „

122.5 „

From these observations it follows that at 40°. 2 the dissoci-
ation pressure of the magnesium sulphate, at 60°. 0 that of the
ferrous sulphate is the greater, while at 50°. 4 they are equal;
consequently, at temperatures lower than 50°. 4 water will pass
over to the ferrous salt in a mixture of FeS04. 6H20 and
MgS04. 7H20, producing FeS04. 7H20 and MgS04. 6H20, while
at temperatures higher than 50°. 4 the transference of water will
take place in the opposite direction in a mixture of'FeS04. 7H20
and MgS04. 6H20 forming the original pair of salts, and finally at
50° .4 the two systems will be in equilibrium. There is therefore
a transition point at 50°. 4 in the equilibrium

FeS04. 7 H20 + MgS04. 6 H20 ^z± FeS04. 6 H20 + MgS04. 7 H2(X

The force D which brings about the transformation of the
second system into the first, at different temperatures, may now
be calculated by means of the formula

D = 4.55 T log 2f ,

lOg

while the work A which can be done by this force, during the
transport of 18 kgrms. of water, that is, when the second
system changes into the first, is

A = 10333

1UUU

4.55 T log 2^ kgrm. metres,

A = 2 T log ^s calories.

238 CHEMICAL AFFINITY.

The following table contains the results of the calculation.

Temperature.

D in atmos.

A in
kgrm. metres.

A in cals.

40°. 2

+ 205

+ 38130

+ 90

50 .4

60 .0

— 105

- 19530

- 46

As the table shows, the difference between the affinities acting
in the two systems, that is, the affinity producing the reaction,
changes sign at the transition point (50° .4), passing through zero ;
the same is true of the work which it can perform.

We shall now obtain a general expression for the work which
a change of this kind can do.

As we have seen, the transition point is the temperature at
which the pressures of the saturated aqueous vapour in equili-
brium with the two systems are equal. The variation of these
maximum pressures with the temperature is given by the general
equation

dlogC _ _q_
dT : 2T2'

C being the concentration of the aqueous vapour at the pressure
which it has when in equilibrium with the salt, and q the quantity
of heat evolved by the combination of 18 kgrms. of this vapour
with the salt, no external work being performed.
For ferrous sulphate, therefore, we obtain

d log Of qf

dT " 2T2'

where qf is the quantity of heat evolved by the reaction

FeS04. 6 H20 -h H2Q = FeS04. 7 H20
Similarly for magnesium sulphate we obtain,

MEASUREMENT OF THE WORK DONE BY AFFINITY. 239

dlogCm qm
dT ' 2T2'

qm being the heat evolved by the reaction

MgS04. 6 H20 + H20 = MgS04. 7 H20.

The heat evolved by the conversion of the second system into
the first in the equilibrium

FeS04. 7 H20 + MgS04. 6 H20 z^r FeSO,. 6 H20 + MgS04. 7 H20
being q, we have

q = qf - - qm,

and therefore,

_ q

dT 2 T2'

This equation is easily integrated since q changes but little
with the temperature and may be regarded as independent of
it; we obtain,

log c7 = ~2T + const>

Since at the transition temperature P, Cf and Cm are equal,
we obtain

and therefore,

Cf - 2T

Since, further, the concentrations are in the same ratio as
the vapour pressures, we may write

Finally, introducing the value of the work which can be done
by the affinity,

240 CHEMICAL AFFINITY.

A = 2T log ^s.
we obtain

A = c

or. in words; the work, expressed in calories, ivliich the affinity
in a given chemical reaction can perform, when the reaction takes
place at a given temperature, is equal to the quantity of heat
evolved by the reaction, divided by the absolute temperature of the
transition point, and multiplied by the difference between the temp-
erature of the transition point and the temperature at which the
reaction occurs.

Considering that the maximum quantity of work which affinity
can perform is equal to the quantity of work done by the change
when it takes place in a reversible way, it will evidently be
possible to obtain equation (1) by means of thermodynamics.

Let us take any case in which one condensed system is trans-
formed into another, and let P be the absolute temperature of
the transition point, below which the first of the two systems is
replaced by the second completely with evolution of q calories.
Suppose the following cycle of reversible operations to be per-
formed: The first system is converted into the second at the
transition temperature absorbing q calories; the second system,,
formed in this way, is cooled to the temperature T, at which
it is allowed to change into the first. In doing so the work done
by affinity will be equivalent to A calories, if the process take
place in a reversible way !, and the heat evolved will therefore be
q — A calories. The temperature is finally raised to the transition
point in order to bring the system into its initial condition.

The changes which have occurred in this cycle being all rever-
sible, we have, (from the second law of thermodynamics)

q P

q — A ~~ T
and therefore,

P— T

A _ q — p .

1 The practical means by which this may be approximately realised, depend on
the nature of the case considered.

MEASUREMENT OF THE WORK 1)0\E BY AFFINITY. 241

In the special case P = T, we have A = 0, that is, the
work done by affinity at the transition temperature, (and there-
fore the force of affinity itself) is zero.

IV. APPLICATIONS.

1. Work done by affinity at absolute zero. Diagram of
the work done.

The equation

P — T
A := q -^p—

shows that at absolute zero A = q, that is, the work which
may be obtained from the change is equivalent to the whole of
the heat which it evolves. At absolute zero the change could
thus occur either with evolution of q calories and without doing
any work, or evolving no heat and doing a quantity of work
equivalent to q calories.

This is in complete agreement with the conclusion arrived at
on page 228, where it is pointed out that the "principle of
maximum work" is rigorously true at absolute zero, the quantity
of heat evolved being then a measure of the work which can
be done by affinity, and its sign therefore indicating the direction
in which the change will occur. This is no longer the case at
higher temperatures. The work which can be done by affinity
is then equivalent to a part
only of the heat evolved,
the two have the same sign,
however, until the transition
temperature is reached, at
this point the work which
can be done by affinity is
zero and at higher temp-
eratures its sign is reversed, Fio. 45
that is to say work must

be performed in order to bring about the reaction. The change
of sign accompanies the change in the direction of the reaction
which occurs at the transition point.

Employing the language of the views formerly entertained by

242 CHEMICAL AFFINITY.

BERTHELOT, we pass therefore at the transition point from a
"principle of maximum work" to one of " minimum work". This
may be represented diagrarnmatically by taking the quantities of
work which can be done by affinity at different temperatures as
the ordinates OA and the corresponding temperatures as the
abscissae of a curve.

For T = 0, A - q, and for T = P, A = 0.

The line q P passing through these points represents the work
which can be done by affinity at different temperatures.

Since the heat evolved by the change varies but little with the
temperature we may represent it by the straight line qq parallel
to OT. It is evident that A and q have the same sign up to the
point P, while beyond it they have different signs.

2. Influence of pressure on the transition point.

It has already been pointed out on page 210 that there is a
close analogy between the transition temperature of condensed
•systems and the melting point of solid bodies.

The connexion between the latter and the pressure is expressed
by the well known equation !

dp 425.7 r

dT
where -r— is the elevation of melting point produced by an increase

of one atmosphere in the pres-
sure, T is the absolute temp-
erature, v the volume of
unit weight of the substance
in the liquid, and T that in
the solid condition, and /• the
latent heat of fusion.

It is natural to inquire whe-
rig 46 ther, mutatis mutandis, the same

equation represents the influence

1 See R. CLAUSIUS, Die mech. Warmetheorie, I, 172, (1887). [1 atmosphere — 10333
kgvms. per square metre, 1 kgrm. degree calorie = 425.7 kgrm.metres].

INFLUENCE OF PRESSURE ON THE TRANSITION POINT. 243

of pressure on the transition temperature. That this is the
-case is easily shown by means of the diagram (fig. 46), in which
the temperatures are taken as abscissae, and the corresponding
quantities of work done by affinity as ordinates.

At temperatures higher than the transition point the work
•done is represented by the continuation of the line qP. The
work which can be done by affinity at a temperature Pi degrees
above P is represented by at. From the diagram we then obtain

_Pt at
OP == Oq'

Now Pt is equal to dT, the difference between the transition temp-
erature at atmospheric pressure and that at a pressure d p atmos-
pheres greater, OP = T, the absolute temperature of the transition
point, and

10333

at = AC)r „ (7 — T) dp calories,
4^o . §

{7 — T) being the increase of volume, in cubic metres, which
accopamnies the change of 1 kgrm. of the substance (for example,
the change of 1 kgrm. of rhombic into monosymmetric sulphur);
Oq = r, the quantity of heat absorbed by the change when it
takes place without doing external work.

Making these substitutions we obtain the equation

dT T (r - T

425.7 r'

which is thus true for a transition point as well as for a melting-
point when the quantities occurring in it have the meanings
given above.

The propriety of applying this equation in such cases has been
shown, by quantitative experiments, by REICHER !, MALLARD and
LE CnATELiER2, and quite recently by SILVIO LussANA3, while SPRING

1 REICHEII, Inaugural Dissertation, Amsterdam, 1883 ; GROTH'S Zeitschrift fur
Krystallographie, 8, 593, 1884; see also p. 185 ante.

2 Bull. Soc. Min. de France. 7, 478, 1884.

3 Nuovo Cimento, (4), 1, 97, 1895.

244

CHEMICAL AFFINITY.

and VAN 'T HOFF ' and LUSSANA have tested the accuracy of an
interesting deduction which may be made from it.

REICHER'S experiments refer to the change of rhombic into
monosymmetric sulphur. Having found,2 by means of the dilatometer,
that the transition temperature under atmospheric pressure is
about 95°. 4, he went on to investigate the influence of an increased

pressure by means of the apparatus
represented in fig. 47. This consists
of a dilatometer D the capillary of
which is connected, on the left, with
the apparatus A B serving for the
production of the pressure, on the
right, with the closed manometer E F,
by means of which the pressure is
measured.

The pressure is developed by heating
sodium bicarbonate, contained in the
bulb A, in an oil bath at constant
temperature. The small bulb B
Oerves to collect the water evolved

by the decomposition of the salt. A
millimetre scale is attached to the tube
of the manometer, which is filled with mercury. At C a thread
of wool is introduced into the capillary of the dilatometer in
order to take up any water which may pass over from B ; this
precaution is necessary since at 95° water decomposes the carbon
bisulphide in the mixture of carbon bisulphide and turpentine
filling the part of the dilatometer not occupied by sulphur (see
p. 183), and by evolving carbon dioxide renders the measure-
ments impossible.

The apparatus being thus arranged is heated to a constant
temperature of 95°. 6 and the pressure allowed to rise.

Fig. 47.

1 Zeit. phys. Chem. 1, 227, 1887. See also W. SCHWARZ, Beitrage zur Kenntniss-
der umkehrbaren Umwandlungen polymorpher Korper. Gottingen 1892.

2 See p. 184.

INFLUENCE OF PRESSURE ON THE TRANSITION POINT.

The following table contains the results obtained.

245

Time.

Level of the liquid
in the capillary.

Pressure in
atmos.

5 minutes

81.5

20 „

71.5

14.6

35 „

66.5

15.3

50 „

64.5

14.1

65 „

60.5

15.3

80 „

56.25

15.7

The regular fall of the liquid in the capillary shows that
monosymmetric sulphur changes into the rhombic form at 95°. 6
under a pressure of about 1 5 atmospheres ; the increased pressure
therefore causes the change to occur at a temperature at which
it would not take place under atmospheric pressure.

It was now attempted, by raising the temperature, to find a
point at which the change would not take place under the higher
pressure. The following results were obtained at 96°. 2.

Time.

Level of the liquid
in the capillary.

Pressure in
atmos.

5 minutes

59.5

15.7

20 „

60.5

15.3

35 „

58.5

50 „

58.75

15.7

65 „

58.5

15.7

80 „

15.9

95 .,

15.3

Since, then, as the table shows, an insignificant change of
level was observed at 96°. 2 under a mean pressure of 15.8
atmospheres, it may be assumed that the transition point is close
to this temperature.

246 CHEMICAL AFFINITY.

Under a pressure of 4 atmospheres the transition point was
found to be 95°. 6 \ an increase of pressure of 15.8 -- 4 = 11.8
atmospheres has therefore raised it from 95°. 6 to 96°. 2, orO°.6;
the elevation of the transition temperature by an increase of pressure
of one atmosphere is therefore given by experiment as 0°.05.

The same quantity may be calculated by means of the formula

= 10333

,
dp 425.7 r'

by introducing the following numerical values;

T = 273 + 95.6 = 368.6
c- - - r - 0.00001252

r = 2.52.
This gives

dT _ 10333 X 368.6 X 0.00001252

dp 425.7 X 2.52

a value which agrees sufficiently well with that obtained by
experiment.

The experiments of S. LUSSANA were made with the various
modifications of ammonium nitrate 2. He determined the trans-
ition temperatures at different pressures, the determinations being
made both with rising and falling temperature 3.

The results are given in the following tables in which, however,
only those results which were obtained with rising temperature
are included. The results obtained with rising temperature
always differ from those obtained with falling temperature by
some degrees, the influence of the pressure on the transition
point was however found to be the same in both cases. 4

1 See page 184.

2 See page 164

3 No agreement was found between the experiments and the values obtained from

the equation for -- in the case of HgI2; he ascribes this to the inaccuracy of ROD-

WELL'S determinations of the value of (<r — r).

4 For example, with ammonium nitrate (first modification).

Transition temperature at On heating. On cooling.

1 atmosphere 35°.45 30°.55

250 „ 42 .76 37 .95

A t = ~ 7°.31 A t = 7°.40

See also BELLATI and ROMANESE, Atti dell' Institute Veneto, (6), 4, 1395, 1885—6.

INFLUENCE OF PRESSURE ON THE TRANSITION POINT.

247

Pressure

Transition

A T

atmos.

temperature.

observed.

calculated.

Ammonium

35° .45

37 .05

+ 1°.60

-f 1.42

nitrate,

100

38 .59

3 .14

2.88

first

150

39 .77

4 .32

4.33

modification.

200

41 .47

6 .02

5.79

250

42 .76

7 .31

7.24

85°.85

Ammonium

85 .15

- 0°.70

-0.68

nitrate,

100

84 .38

1 .47

1.37

second

150

83 .73

2 .12

2.06

modification.

200

83 .03

2 .82

2.75

250

82 .29

3 .56

3.44

1 rr\

From the equation for — it follows that when <r — T is nega-

dT
tive — will also be negative, when r is positive ; this conclusion

is confirmed by the above results. According to the observations
of BELLATI and KOMANESE <7 — r zz — 0.00854 for the second mod-
ification of ammonium nitrate, and therefore, it is to be expected
that the transition temperature will be depressed by an increase
of pressure; as the table shows this is what occurs. Silver idiode also
shows a similar behaviour, being analogous to ice in this respect.
Another change of this kind is the decomposition of copper
calcium acetate into its components, studied by REICHER ; l

CuCa (C2H302)4. 6H20 ^=± Cu(C2H302)2. H20 + Ca(C2H302).2. H20 + 4H20.

This occurs between 76°. 2 and 78° at atmospheric pressure,
and since the change of the first into the second system is
accompanied by a contraction it is to be expected that the
transition temperature will be depressed by an increase in the
pressure. SPRING and VAN 'T HOFF have shown, experimentally,
that this is the case by exposing copper calcium acetate, in

l See p. 171.

248 CHEMICAL AFFINITY.

SPRING'S compression apparatus, ! to a great pressure. The change
occurred quite unmistakably at 40° under a pressure of about
6000 atmospheres, that is, the transition temperature w;is
depressed by the application of this pressure by about 40°.

3. Calculation of the transition point,
a. The allotropic modifications of sulphur.

The diagram on page 242, being quite generally applicable
to equilibrium in condensed systems, applies also to the simple
cases of fusion and solidification.

In these cases the line qP represents the work which can be
done by the forces producing solidification or fusion when Oq
represents the latent heat of fusion q, and OP the melting point
on the absolute scale of temperature. It must be pointed out,
however, that qP here, in contradistinction to the case of chemical
equilibrium, only represents the work in question near the trans-
ition point P, because q is a function of the temperature, the
difference between the specific heats of a substance in the solid
and liquid states being not inconsiderable 2.

By means of this diagram it is possible to calculate the trans-
ition temperature of
the allotropic modific-
ations of sulphur. To
do so, we will first
represent the work
which may be done by
the solidification or
fusion of the two mod-
ifications of sulphur in
rig. 48. a diagram, fig. 48.

Let the quantities of

heat qrf and qmf which are evolved during the solidification of
liquid sulphur to rhombic or monosymmetric sulphur respectively
be measured along 0 A, and let the melting points Trf and Tmf
(on the absolute scale) be measured along 0 T. The straight

1 Bull, de 1'Acad. Roy. de Belgique, 49, 344.

2 Appendix, note 3.

CALCULATION OF THE TRANSITION TEMPERATURE. 249

lines qrf Trf, and qmf Tmf will then represent the quantities of
work in question.

At any point P in OT erect a perpendicular, then P M and
P R are the quantities of work which can be obtained when
liquid sulphur solidifies in the form of monosymmetric or rhombic
sulphur respectively, and therefore their difference R M represents
the quantity of work which can be obtained from the change
of monosymmetric into rhombic sulphur at the temperature given.
Since there is a point of intersection at B, it is evident that at
the corresponding temperature Trm the sign of this quantity of
work will change and that its value at this temperature will be
zero ; these are the characteristics of the transition temperature
of the two modifications.

From the figure we see that,

lrf lrm : lrf — Jj lrm : qrf,

Qlirj T1 T . T — R T • n

ciHU. -i- mf -*- rm • •'-mf — •*-* •"•rm • *-Jmf'

Therefore

Trf — Trm Trf

A mf •*- rm -1- mf

— i . :HL

T - • - '

T —

^rm —

3* (JL M

q«nf ^Trf Tmf/

Introducing the numerical values (page 215)

*&- = - [5 Trf = 273 + 114.5, and Tmf = 273 + 120
qmf u . i o

we obtain

Trm = 273 + 95.2.

The transition temperature calculated is therefore 95°. 2, that
found experimentally being 95° .4. l

Another (approximate) calculation on page 216 gave 96° .3.

1 REICHER found 95°. 6 at 4 atmospheres pressure, p. 246 ; the change for 1
atmosphere being 0°.05, the transition temperature under the pressure of sulphur
vapour at 95°— 6° will be 95°. 4.

250

CHEMICAL AFFINITY.

b. The transformation of a mixture of sodium ammonium laevo-
and dextro-tartrates into sodium and ammonium racemates.

This case is analogous to that which we have just considered.

VAN 'T HOFF, VAN DEVENTER, GoLDSCHMIDT, and JoRISSEN ! llUVC

described the following changes: —
At 26°.6,

2 (NaNH4 C4H406. 4 H20) = (NaNH, C4H406. H20)2 + 6 H20 . . (1)
The so-called racemate of SCACCHI is here formed from the

mixture of Isevo- and dextro-tartrates.
At 34°.5,

0 t 4 H0

2 (NaNH4 C JI406. H20)2 = (Na2 C4H406)2 + [(NH4)2 C4H4(

The salt of SCACCHI decomposes at temperatures higher than
35° into the individual racemates.

The temperature at which the change of the mixture of laevo-
and dextro-tartrates into the individual racemates occurs, ac-
cording to the equation

4 (NaNH4 C4H406. 4 H20) - (Na2 C4H406)2 + [(NH4)2 C4H406]2 + 16 H20. .

may be calculated in the same way as before in the case of
sulphur.

The work which can be done by reaction (2) may be

represented as a function
of the temperature by
the line A B, fig. 49, OB
representing the transition
temperature on the abso-
lute scale (273 + 34.5)
and 0 A the heat absorbed
by the change.

Similarly the work

which can be done by the change (3) may be represented by
a line DC, C being the transition temperature to be calculated,
and 0 D the quantity of heat absorbed by the change.

The point of intersection P1? corresponds therefore to the temp-

P C

Fig. 49.

1 Zeit. phys. Chem. 1, 173, 1887; 17, 49, 1895; see also p. 170.

OF THJ--

UNIVER;

CALCULATION OF THE TRANSITION TEMPERATURE. 251

erature at which no work can be obtained from the change of
the mixture of Isevo- and dextro-tartrates into the racemate of
SCACCHI, that is, the transition point of change (1), (273 + 26.6).
The quantities of heat evolved by the changes may be taken
as approximately equal to the differences between the heats of
solution of the different systems concerned. These are as follows : -

NaNH4 C4H406. 4 H20 - 11726 cals.

NaNH4 C4H406. H20 7922 „

1/2 (Na2 C4H406 + (NH4)2 C4H406) - 5660 „

therefore

OD : OA - 11726 — 5660 : 7922 — 5660 = 6066 : 2262.
The figure shows further that

P! P : AO = PB : OB
and P! P : DO - PC : OC.

Since OC differs very little from OB, we may write

AO : DO = PC : PB.

Introducing numerical values we obtain, since
PB = 34.5 — 26.6 = 7.9,

The transition temperature required is therefore 26.6 f 2.9 = 29.5;
dilatometric experiments gave 29°.

V. THE ELECTRICAL WORK PERFORMED BY A
CHEMICAL CHANGE.

1. General considerations.

It has been proved above that the work which can be done
by the force of affinity which brings about a chemical reaction
may be represented by the equation

P — T

A = q - —5 — •

"252 CHEMICAL AFFINITY.

The magnitude of this quantity of work is independent of the
way in which the chemical reaction takes place, provided that
it is reversible.

HELMHOLTZ 1 has shown that a chemical reaction which occurs
in such a way that it does electrical work is reversible.

The chemical change may take place in the one direction
producing a current of electricity, or it may be made to
proceed in the opposite direction by passing a current from
an external source. In such cases the electromotive force pro-
uced by the reaction is the same as that required to reverse it.
It is evident, from these considerations, that the expression for
A represents the electrical work which the chemical change is
capable of producing. This may also be proved by means of the
following cycle of reversible operations: -

At the transition temperature P let unit quantity of the system
undergo chemical change absorbing q calories. Let the temp-
erature be then depressed from P to T. At the latter temper-
ature the chemical change, which will now occur in the opposite
direction, is allowed to take place in a galvanic cell so as to
produce a current of electricity; it will do a quantity of
electrical work equivalent to A calories, a quantity of heat,
q — A calories, being simultaneously evolved. The system
is then brought back to its initial condition by raising the
temperature to P.

This cycle of changes is reversible; we might begin by cooling
the original system from P to T, at which temperature it might
be caused to undergo the chemical change by passing a current
of electricity. This would do a quantity of work equivalent to
A calories on the system, and q — A calories would be absorbed.
The temperature might then be raised from T to P and the
chemical change allowed to take place, evolving q calories.

The cycle being reversible, we may apply the second law of
thermodynamics to it, and obtain

q :P

A — q ~~~~ T'

1 Sitzungsberichte der Kon. Preuss. Akad. 1882, p. 823. Gesammelte Abhandlungen,
II, 958 aud 979; III, 92.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 253

or P — T

A := q ~p — »

* \

This result may be further simplified by considering as unit
quantity of the system, its equivalent weight in kilograms. The
electrical work, A, which is done by the change of unit quantity
of the system is then proportional to the electromotive force
produced by the reaction l. The connexion between A and the
heat evolved by the reaction may therefore be expressed in
words as follows : —

The electromotive force which a chemical change can produce
is proportional to the heat evolved by the reaction, q, divided by
the absolute temperature of the transition point, P, and multiplied
by the difference between it and the temperature T at ivhich the
reaction occurs.

Since the electromotive force is thus shown to be proportional
to the work done by affinity, the diagram (p. 241) representing
the latter may evidently be applied to the former also.

By differentiating the equation for A with respect to T we obtain 2

dA q

dT = P'

Eliminating P by means of the original equation we obtain

dA A — q
dT T '

or m dA

A == q + T ^.

y™ is the temperature coefficient of the electrical work done by

the change.

HELMHOLTZ has already obtained this equation in another way
in his memoir " On the thermodynamics of chemical processes," :

1 [According to FARADAY'S law the quantity of electricity carried by an equivalent
of any substance is constant, it is found to be 96587 X 103 coulombs per kgrm.
equivalent. If E be tbe electromotive force produced by a reaction, the electrical work
done by a kgrm. equivalent of change will be A — E X 96587 X 103 volt-coloumbs.
1 volt-coulomb — 107 ergs — 0.0002395 kgrm. degree calorie, so that the above
quantity of electrical work A — 23116 E kgrm. degree calories. T. E.]

2 This is also evident from figure 45.

3 See the note on page 252.

254 CHEMICAL AFFINITY.

and it has been confirmed experimentally in a number of cases
by CZAPSKI ', GOCKEL 2. and JAHN 3.

As is well known, the view that in reversible processes the
chemical energy is completely converted into electrical has been
advanced by JOULE, WILLIAM THOMSON (Lord KELVIN), and also by
HELMHOLTZ ; accordingly we should have A = q. That this view
is incorrect has been proved by BKAUN 4, GIBBS, and HELMHOLTZ, the
latter giving the above-mentioned equation for the electrical work.

2. Thermodynamics of the transition cell.

The equation

P — T

A-q -p-

shows that if the electrical work in a galvanic cell be furnished
by the change of one of two mutually convertible systems
into the other, it being of course assumed that the change
takes place in a reversible way, then at the transition point,
where P =. T, this work will have the value zero.

COHEN'S electrical method of determining the transition temp-
erature, using both stable and meta-stable phases, (page 193) is
implicitly based on this deduction from the above equation.

Since the change in the transition cell used in this method is
reversible we may at once apply to it the equation

dA
A = q + T, ...... (1)

and see to what results it leads.

It has already been proved that A and q have the same sign
at temperatures below the transition temperature, while at temp-
eratures above it they have opposite signs.

Since A vanishes at the transition temperature it is obvious
that its magnitude (considered without reference to its sign)
must decrease, with rising temperature; below the transition

1 WIED. Ann. 21, 209, 1884.

2 WIED. Ann. 24, 618, 1885. See also W. NERNST, Zeit. phys. Chein. 2, 23, 1888.

3 WIED. Ann. 29, 21, 1886.

4 WIED. Ann. 5, 182, 1878; 16, 561, 1882; 17, 593, 1882.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 255

temperature, and increase above it. The values of the electro-
motive force which are proportional to A show similar behaviour,
as is shown by the table on page 198. A little consideration

dA
will show that q and T -r^- are always quantities of opposite

sign below the transition temperature; at this temperature
A = 0, and therefore

^-TTT V

This equation may be called the equation of the transition cell.

The results obtained with the transition cell with stable and
meta- stable phases show clearly that the view put forward by
W. THOMSON (Lord KELVIN), i. e. that A = q, is erroneous, for at
the transition temperature where q has a large value A is zero.

The value of -r^- at the transition temperature may be cal-
culated by means of equation (2); it may also be determined by
experiment and the two values so obtained compared. Taking the
case of Glauber's salt, which has been investigated experimentally,
q will be the heat evolved by the change which produces the
quantity of work A, A being the electrical work obtainabel
from the change when the quantity of electricity carried by one
equivalent of the salt is set in motion.

If a transition cell (fig. 37), in which the change occurring
below the transition point is the conversion of anhydrous sodium
sulphate and saturated solution of Glauber's salt into solid Glauber's
salt, were connected up against a Daniell cell and the current
allowed to flow, then after 1 kgrm. equivalent of zinc had passed
into solution in the latter an equivalent quantity (200 kgrms.)
of mercury would have separated in the metallic state at the
electrode contained in the saturated solution of the anhydride,
and an equivalent quantity of mercurous sulphate would have
been formed at the electrode in the saturated solution of Glauber's
salt. A corresponding quantity of Na and S04 ions would also
have passed through the solutions. The transference of the
S04 ions does not affect the concentrations of the solutions since
the S04 combines with mercury to form insoluble mercurous

256 CHEMICAL AFFINITY.

sulphate. If the transition cell were allowed to furnish the same
quantity of electricity everything would take place in the reverse-
order. Everything would also be reversed above the transition
point.

Suppose the cell to be working in its normal way below
the transition point, let n be the migration constant l for Na in
Na2 S04, then n sodium ions migrate from the more concentrated
(anhydride) solution to the weaker (Glauber's salt) solution, while

SO
(1 — n) —^ ions migrate in the opposite direction.

The n sodium ions combine with S0± from the mercurous
sulphate and so form — molecules of sodium sulphate, this causes

the precipitation of x molecules of Glauber's salt from the
saturated solution according to the equation

2- Na2S04 4- (x7n) Na2SO,. bH20 = ~ Na2S04. 10H20

& a £

where b is the number of molecules of water to each molecule
of sodium sulphate in the saturated solution of Glauber's salt.
We obtain from the above equation

zn^-- -16-

The migration of the sodium ions towards the Glauber's salt
solution has, further, the effect of removing — molecules of sodium
sulphate from the saturated solution of the anhydride, thus
causing — molecules of the anhydride to dissolve. The final
result is therefore
I Na2 S04 + | (^5) Na2S04. bH20 = j g-^ Na2S04. 1 0 H20,

or in words, -— — — molecules of Glauber's salt are formed from
J(b — lUj

— molecules of the anhydride and ^-7- — —-. molecules of the
saturated solution of Glauber's salt.

1 Appendix, note 4.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 257

The quantity of heat to be taken into account in equation (2)

is therefore the quantity evolved by the formation of — =^r-

2(b— 10)

molecules of Na2S04. 10H20; the value of b depends on the
temperature and may be obtained from the tables of solubility
given by LOEWEL '. The latent heat of fusion of Glauber's salt,
for a kgrm. molecule, has been determined by means of the
calorimeter as - - 16509 calories.2

Equation (2) (p. 255) may now be written

dA Q n b0

.... (3)

dT T0 2 (b0 — 10) '

where b0 is the number of molecules of water to each molecule
of sodium sulphate in the saturated solution of Glauber's salt at
the transition temperature T0.

The numerical values of the quantities occurring in equation (3)
are the following:

Q — 16509 calories,
n =: 0.36 according to HITTORF. 3
b0 = 15.6 ,, ,, LOEWEL.

_T0 = 305.6.

Introducing these into (3) we obtain

dA 16509 0.36X15.6

dT 305.6 2(15.6— 10)
or

rlA

^ = — 27.09 calories

and since (note p. 253) E = - ppr;;, -^ being the electromotive

£ol Ib

force in volts, we obtain

1.2 millivolts,
dl

1 Ann. Chim. Phys. (3), 49, 1857.

2 E. COHEN, Zeit. phys. Chem. 14, 85, 1894.

3 POQG. Ann. 100, 377, 1859. This value was obtained at 9°. At the transition
temperature of Glauber's salt it should be somewhat higher, since BREDIG, Zeit. phys.
Chem. 13, 191, 1894, found n ~ 0.4 at 25°.

258 CHEMICAL AFFINITY.

The electromotive force of this sodium sulphate transition cell
with both stable and meta-stable phases was determined by
E. COHEN and G. BEEDIG l by means of the apparatus represented
on page 196; the following numbers were obtained.

Electromotive force

Temperature. in millivolts. E.

28° .2 5.2

30 .2 2.9

32 .7 - 0.5

These data may be represented by the formula

E = --2.05+1.57t--0. 0466 t2,
from which we obtain, at the transition point, t = 32.6,

-TT= — - 1.5 millivolts.

This may be regarded as being in sufficiently good agreement
with the number obtained by calculation ( — 1.2 millivolts), the
smallness of the electromotive forces measured being taken into
consideration. 2

The equation obtained above is also applicable to the trans-
ition cell containing no meta-stable phase 3 described on page 198.

If we consider a cell of this kind (fig. 40) containing a solution
maintained in a condition of saturation by the presence of the
modification of the system which is stable above the transition
temperature T0, we have

A, = q, H T ^, (4)

where q! is the chemical energy of the cell, that is, the quantity
of heat evolved by the solution of the modification which is
stable at temperatures above T0, calculated for the quantity
which passes into solution at T during the passage of unit

1 Zeit. phys. Chem. 14, 540, 1894.

2 According to the note on page 257 the result given by the calculation should
probably be higher.

3 E. COHEN and G. BKEDIG, Zeit. phys. Cheni. 14, 535, 1894.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 259

quantity of electricity I through the cell, and A! is the electrical
energy obtainable under the same circumstances.

Similarly, for a cell containing the saturated solution of the
modification of the system which is stable at temperatures below
the transition point, we have

A, = q2 + T ^|- ...... (5)

Since the two saturated solutions have the same concentration
at the transition point the two cells have the same electromotive
force at that temperature, and therefore at To;

from which we obtain (at T0)

d. A2 d At qi - - q2
d T d T T

-r^r — —^ affords a measure of the angle between the two
dl dl

branches of the curve representing the connexion between the
electromotive force of the cell and the temperature, qi — q2 re-
presents the quantity of heat which is evolved by the trans-
formation of that modification of the system stable at tempera-
tures below the transition point into that stable at higher
temperatures, calculated for the quantity which dissolves at T0
when unit quantity of electricity passes through the cell.

The graphical representation, on page 202, of the connexion
between the electromotive force of a cell of this type and the
temperature shows that the curve consists of two parts meeting
at an angle. Each of these parts may be represented by an
empirical equation of the form,

Ei = QJL + R^ + S^ for temperatures between 35° and 45° (7)
and E2 = Q2 + B2t + S2t'2 for temperatures between 20° and 30° (8),
where t is the temperature centigrade.

By differentiating these empirical equations with respect to t,
and subtracting, we obtain the value of the sudden change in

1 Unit quantity of electricity is taken to mean that quantity which migrates with
A kgrm. equivalent of an ion (96587 X 1000 coulombs).

260 CHEMICAL AFFINITY.

the temperature coefficient of the cell which occurs at the
transition temperature (32°. 6): -

= (R2 - RO + 2 t0 (S2 - SO- • • .(9)

The values of -j~ • -~ found experimentally were: -

For cell I (p. 201) .... -h 1.6 millivolts.
„ „ II (p. 202) . . . . + 1.2
„ „ III (p. 203) . . . . + 1.1
The mean value being 1.3 millivolts.

The same "quantity may be calculated from other data by
means of equation (6), in which T0, the transition temperature
on the absolute scale, is 305° .6 ; q, for Glauber's salt at its

transition temperature is ~~ur\ ^' anc^ similarly ^2 —

L (b0 10)

W2, where n and b0 have the meanings already
2 (b0 — 10)

ascribed to them (page 257), and

Wx is the heat evolved by the solution of 1 kgrm. molecule of

Na2S04 at temperatures above T0, and
W2 is the heat evolved by the solution of 1 kgrm. molecule of

Na2S04. 10H20 at temperatures below T0.
W2 — Wi is therefore the heat evolved by the fusion of Glauber's-
salt ( — 16509 cals.). Equation (G) may thus be written

dAa ' d Wj— W2 nb0

dT dT T0 ' 2 (b0 - 10) '

From this, introducing numerical values,

dA2 dA, . 10504 X 0.36 X 15.6 ..
~dT~ dT" - 805.6X2(15.6-10) :

or, since A = 23116 E, where E is the electromotive force of

the cell, ^TT, = 1.2 millivolts.
dl

This number is in satisfactory agreement with that found
experimentally, i. e. 1.3 millivolts.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 261

VAN 'T HOFF, COHEN and BREDIG l have shown that the equation

dA A — q
dT T

may be used to calculate the electromotive force of transition
cells of the type which we have just considered. To do this we
may set out from the temperature at which A = 0, and sum
the increments of A with T, taking sufficiently small finite in-
crements of A and T to make it permissible to regard their
ratio as constant during the increment.

Taking first cell III, in which the one electrode is immersed
in a saturated solution of Glauber's salt and the other in a 1/4
normal solution of sodium sulphate, the temperature at which
A = 0 is that at which the saturated solution of Glauber's
salt is 1/4 normal ; this temperature, however, cannot be observed
since it lies below the cryohydratic temperature. It may be
calculated with considerable accuracy from the formula

dlogC _ Q

dT " T2 '

which is strictly true for dilute solutions, and in which C is
the concentration and Q a quantity connected with the heat of
solution and varying but little with the temperature.

According to LOEWEL 100 parts of water at 0° dissolve 5.02
parts of sodium sulphate and 9 parts at 10°. Substituting these
values in (2) (after integration), and replacing the Naperian
logarithm by that to the base 10, we obtain

_9_ Q / 10 \

J°g 5.02 " 2.3026 V273X283/'

At a temperature x degrees below zero the saturated solution
of Glauber's salt will be 1/4 normal, and will therefore contain
71/4o = 1.775 grams (approximately) of sodium sulphate to 100
grams of water, whence as before

5.02 Q / _ x_ _\

°g 1.775 "" 2.3026 V273 (273— x)/'

1 Zeit. phys. Chem. 16, 453, 1895.

262 CHEMICAL AFFINITY.

By eliminating Q from these two equations we obtain x = 16. 2r
that is, A = 0 at — 16° .2.

In order to calculate the electromotive force of the cell at

20° , it is sufficient to make use of the values of -7= at fairly

large intervals of temperature, say at — 16.2, 0°, 10°, and 20°.

The most important quantity entering into the calculation is
q in equation (1) ; it represents the quantity of heat which
is evolved by the process which produces the current. This-
process is the transference of 0.36 molecule of i/s(Na2 S04) from
the saturated solution, the composition of which may be repre-
sented by l/2(Na2 S04) bH20, to the 1/4 normal solution !/2(Na2 S04)
222.4H20. The heat evolved by this process may be considered
to consist of three parts: —

1. A! evolved by the removal of 1/2 (Na2 S04) b H20 from an
indefinitely large quantity of the saturated solution, and by the
return to it of b H20 which would then become saturated in
accordance with the equation

i/2(Na2S04) 5H20 + b H20 = r-^-p i/2(Na2S04)bH2(X

b — 5

The following are the quantities of heat evolved when
1/2 (Na2 S04) 5 H20 is dissolved in a quantity of water such that
the solution formed contains n molecules of water to i/2(Na2 S04).

n = 400 200 100 50 25 7.8

Heat evolved — 9430 -- 9380 — 9255 — 9021 - - 8689 -- 7495

The first five numbers have been determined by THOMSEN, the
last is calculated from COHEN'S determination of the latent heat
of fusion of Glauber's salt and from THOMSEN'S determination of
the heat of hydration of Na2 S04.

2. A2 is the heat evolved by diluting V2(Na2 S04) b H20 to
1/2 (Na2 S04) 222.4H20; it also ma^ be calculated from the
above numbers.

3. A3 is the heat evolved by removing 222.4 H20 from an
indefinitely large quantity of a 1/4 normal solution of sodium

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE.

263

sulphate. A! and A2 are negative quantities, while A3 is positive

9430-9380
and its value is approximately — -r— — - oo calories.

We thus obtain the following numbers.

Temperature.

b (LOEWEL).

A!.

dE
dT

- 16°. 2

222.4

9602

0.58

78.6

234

9773

9.4

0.60

43.8

450

- 10086

15.4

0.63

20.3

- 1023

-11096

21.7

0.72

A somewhat more exact result is perhaps obtained by using
the mean values of the temperature coefficients in the different
intervals of temperature. By doing so we obtain

E20o = 16.2 X 0.59 + 10 X 0.615 + 10 X 0.675 = 22.5

millivolts, the number found experimentally being 21 millivolts.
Following the curve to 33° .2, at which temperature COHEN
and BREDIG observed the transition to anhydride, it is necessary
to calculate the temperature coefficients at temperatures some-
what nearer to each other, since they increase more rapidly
with the temperature, this is done in the following table.

Temperature.

A2.

dE
dT

20°

20.3

- 1023

- 11096

22.5

0.72

14.1

-1453

- 12292

27.1

0.8

9.86

-1748

- 15496

32.9

0.99

32.6

7.8

-1891

-20879

36.3

1.27

A more exact result is again perhaps to be obtained by making

CHEMICAL AFFINITY.

use of the mean values of the temperature coefficients in the
different intervals of temperature; the following numbers have
been calculated in this way.

Temperature.

E observed.

E calculated.

20°

21 millivolts.

22.5 millivolts.

24.8

26.3

31.4

30.8

Using now the mean temperature coefficient between 30° and
33°. 2 the electromotive force at the latter temperature is found
to be 34 . 5 millivolts. At this temperature the change of Glauber's

salt into the anhydrous salt occurs and the value of -~= under-
goes a per saUum decrease owing to the change in AI. The
quantities of heat evolved by the solution of 1/2 (Na2 S04) are
obtained from the values of the heat of solution of i/2(Na2S04). 5H20
previously given, by adding to them 9610 cals. which is, ac-
cording to THOMSEN, the he it of hydration of l/2(Na2S04).
The following are the numbers obtained: —

Temperature.

A2.

dE
dT

33° .2

34.5

7.91

- 1883

+ 2107

34.8

0.101

8.08

- 1872

+ 2095

35.3

0.101

8.26

- 1859

+ 2083

35.8

0.101

Since the temperature coefficient here does not change appre-
ciably the values of E obtained should be fairly accurate; they
are compared in the following table with those found by
experiment.

ELECTRICAL ENERGY OBTAINABLE FROM A. CHEMICAL CHANGE.

Temperature.

E observed.

E calculated.

35°

35.8 millivolts.

34.8 millivolts.

36.7

35.3 „

37.1

35.8

The numbers observed and those calculated are therefore fairly
concordant. The electromotive force of cell I, containing a normal
solution of sodium sulphate (see page 201), may be obtained by
calculating the difference between it and that of cell III; this
difference was found to be

at 20°, 21 —7.1 = 13.9,

at 45°, 37.1—23.1 = 14.

The temperature at which the electromotive force of cell I is
zero is calculated, in the same way as before, from the equations

9 Q / 10

and

Log

2.3026
Q

2.3026 V273

273 X 283,

--}
x ' " 2837'

7.1

from which x = 5°. 8.

From the numbers already given, the electromotive force of
the cell containing 1/4 normal sodium sulphate is, at this temp-
erature,

E5o.8 = 16.2 X 0.59 + 5. S X 0.609 = 13.1 millivolts,

from which value, neglecting its small variation with the
temperature, the following numbers are obtained.

Temperature.

E observed.

E calculated.

E calculated with
temp. corrn.

20°

7 . 1 millivolts

9 . 4 millivolts.

8.7 millivolts.

2:»

10.8

13.2

12.3

16.6

17.7

16 6

22.2

21.7

20.4

22.5

22.2

20.7

23.1

22.7

21.0

266

CHEMICAL AFFINITY.

The agreement is satisfactory and becomes somewhat better
if the fact be taken into account that the difference between the
electromotive forces of the cells containing normal and 1/4
normal solutions of sodium sulphate, is proportional to the absolute
temperature just as in the case of a concentration cell l containing
dilute solutions; allowance has been made for this in calculating
the numbers in the fourth column.

The solutions of sodium sulphate contained in these cells being
dilute the electromotive force of cell II containing a 1/2 normal
solution may be calculated by taking the mean of those of the
cells containing normal and 1/4 normal solutions. The following
numbers are obtained in this way.

Temperature.

E observed.

E calculated.

20°

14.2 millivolts.

15.6 millivolts.

18.5

19.3

24.0

23.7

28.2

27.6

28.6

28.0

28.7

28.4

The electromotive forces of these cells may therefore be cal-
culated with a maximum deviation of 2 millivolts.

From equations (3) p. 257, and (10) p. 260, the following
deduction may be made : -

dAa. dA^ dA

dT dT " ar

The negative temperature coefficient of the transition cell with
both stable and meta-stable phases is, at the transition temperature,
equal to the difference between the temperature coefficients of the
two transition cells containing no meta-stable phase.

This has been confirmed by experiment ; on page 260,

JTjl

— -r was found to be 1.6 millivolts in cell I, while the

•ITjl

1 NERXST, Zeit. phys. Chcm. 4, 154, 1889.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 267

temperature coefficient of the cell with both stable and meta-
stable phases is --1.5 millivolts (p. 258).

3. Equilibrium constant and electromotive force.
From the equations

we find, by solving (2) for q and substituting the value ob-
tained in (1),

A T —

A " dT

__
2T2

and therefore, by integration, putting the integration constant
equal to zero,

log K = -

2T*

Since A is proportional to the electromotive force produced
by a reaction, each determination of the value of a constant 'of
equilibrium is at the same time a determination of this electro-
motive force !.

The case of ammonium sulphide may be taken as an example,

NH5S ^ NH3 + H2S.

The experimental data have been given on page 157. The
value of A at the temperature T may be calculated from them
by means of the equations 2

log K = — — , and K =

Since a gaseous system is under consideration
where ni — 0, and n2 = 2, and therefore

1 VAN 'T HOFF, Lois de 1'equilibrc cliiinique, p. 54.

2 See page 206.

268 CHEMICAL EQUILIBEIUM,

A z= - - 4 T log C2,

C2 being the concentration of the second system.

The unit of concentration of the second system is 17 kgrms.
of ammonia and 34 kgrms. of sulphuretted hydrogen per cubic
metre. If the pressure of the mixture of gases be p mm.,

the pressure of the ammonia will be -— mm.

Since the weight of a litre of ammonia gas at 0° and 760 mm.

is 0.761 grams, its concentration under a pressure of - - mm. is

—

_ 0.761XPX273 p

" 17X2X760XT " 124. 4T'
and therefore

124. 4T

A = 4 T log - — .

We thus obtain

Temperature. A.

9°.5 5992 calories.

25 .1 5132 „

The number found, 6000 calories approximately at 10°, in-
dicates that if the formation of ammonium sulphide from
ammonia and sulphuretted hydrogen at concentrations of 17 and
34 kgrms. per cubic metre, were to take place in a galvanic cell
at 10° producing a current, the electromotive force of the

combination would be approximately E == OQ = 0.129 volt.

& X «ol lo

On the other hand it is clear that, a determination of an
electromotive force, under definite conditions, must lead to a
knowledge of the condition of equilibrium towards which the
change tends.

For example, suppose that a DANIELL cell at 0° can furnish a
quantity of electrical energy equivalent to 50300 calories, during
the separation of a kgrm. atom of copper from the copper
sulphate solution of unit concentration, that is, containing 159
kgrms. of CuS04 per cubic metre, and the solution of the zinc

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 269

in a liquid already containing 161 kgrms. of zinc sulphate per
cubic metre, then the final condition of the equilibrium

ZnS04 + Cu ^ CuS04 + Zn,

at 0°, is known.
We have, namely,

therefore

A C

, and -— - = K,

^
I .

A 50300

log TYaTI - ' 2T - ' 2- =

In this expression
therefore

from which

p p 40

log £ = 92.1 or ^-l= 10 .

^2 ^2

At 0° therefore, equilibrium between the copper and zinc and
the sulphates will be reached when there is a certain definite
ratio between the concentrations of the two salts. The calculation
shows that the concentration of the zinc sulphate would be 1040
times that of the copper sulphate.

It is further possible to show that a general relationship
exists between the values of K in a cycle of chemical equilibria.

The equilibrium which is reached when an alkaloid is brought
together with the hydrochloride of another alkaloid has been
studied by JELLETT. l The alkaloids used were Quinine (Q),
Codeine (C), and Brucine (B), the following equilibria being
investigated : -

1. Equilibrium between Quinine, Codeine and their hydro-
chlorides.

Q + C. HC1. ^=± C + Q. HC1.

1 Transactions of the Royal Irish Academy, 25, 371, 1875.

270 CHEMICAL AFFINITY.

2. Equilibrium between Codeine, Brucine, and their hydro-
chlorides,

C + B. HC1 ^=± B + C. HC1.

3. Equilibrium between Brucine, Quinine, and their hydro-
chlorides,

B + Q. HC1 ^z± Q + B. HC1.

The determinations of the ratios of the quantities of the
different salts in these three cases gave the following results : -

Q. HC1 OHOl - RHC1

C. HC1 B. HC1 Q. HC1

JELLETT observed further that the product of the numbers
obtained is approximately unity.

2.03 X 1-58 X 0.32 = 1.026. -

It is possible to show that this relationship, found in a special
case by JELLETT, holds good quite generally.

Let the values of K in the three equilibria be K1? K2 and
K3 at any given temperature; the changes which lead to these
equilibria will be able to do quantities of electrical work A1?
A2, and A3 for a gram equivalent of change when the concen-
trations of the mutually convertible systems are unity. We
have then,

log K! = -- giji, logK2 = — ~, andlogK8=± •- 2T

and therefore,

Ai 4- AQ + A3

1™
log

Since the initial condition of the system remains unaltered
after these isothermal changes have taken place, the sum of the
quantities of electrical work done by them must be zero, that is,

A! + A2 + A3 = 0,
and therefore,

K! K2 K3 — 1,

that is, the product of the constants of equilibrium is equal
to unity.

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE.

271

Since the same is true of any similar series of equilibria,
independent of their number, the following general proposition
may be enunciated. The product of the values of K in a cycle of
chemical equilibria is equal to unity.

The case studied by JELLETT is an example of this, for since

K =

and the values of Zai differ from each other very little, the
equilibria studied being similar, and further

we obtain

We have also

K2 K3 == 1,

Q- HCl

0. HCl

C.HC1
B.HC1

B. HCl
Q. HCl '

from which the result obtained by JELLETT is found.

From the electromotive force produced by a change it is
possible to predict the direction in which it will proceed.

Taking for example a case of equilibrium between condensed
systems such as

2 Ag f Cu2 C12 ^z± 2 AgCl -f- 2 Cu,

the sign of the quantity of heat evolved determines the direction
in which the reaction will proceed at absolute zero ; that system
which is formed with evolution of heat will alone be present in
a condition of equilibrium at this temperature.

The following data have been obtained by F. BRAUN. 1

Reaction.

Heat evolved q.

Electrical work
A.

2Ag + C12

2Cu + C12
2Ag + Br2

117500
131600

90800

97000
99200
85000

l WIED. Ann. 17, 633, 1882.

272 CHEMICAL AFFINITY.

From these numbers the formation of the first system from
the second is accompanied by an evolution of heat of 131600—
117500= 14100 calories; at absolute zero, therefore, it will be
formed at the expense of the second. This is, however, not neces-
sarily the case at the ordinary temperature; the heat evolved
is no longer equivalent to the work which the change is capable
of producing, and it cannot therefore be used to predict the
direction of the reaction. The work which the reaction can do
may be measured by means of the electromotive force produced
by it. When the first system is formed from the second this
work is, according to the numbers given above, 99200 — 97000
— 2200 calories.

The first system thus represents the condition of the system
when it is in equilibrium at the ordinary temperature, the change
still occurring in the same direction as at absolute zero. The
first system will continue to be present alone, in equilibrium,
until the transition temperature is reached; at which point both
systems may exist together, above it the first system will give
place to the second.

We must now calculate the transition temperature ; having
done so the condition of the system in a state of equilibrium is-
known at all temperatures.

In the equation

P — T

A _ q p

all the quantities, are known with the exception of P. At T
(273° approximately) the value of A is 2200 calories, that of
q is 14100 calories. From these numbers we find P = 324r
that is, the transition temperature lies at 51° C. It is however
to be noted that small changes in the values of A, q, and T
have a considerable influence on the value of P obtained.

As a further example we may consider a case of heterogeneous
equilibrium such as

2 Ag Br ;^z±: 2 Ag + Br2.
According to the laws governing equilibria of this kind the

ELECTRICAL ENERGY OBTAINABLE FROM A CHEMICAL CHANGE. 273

bromine must, at each temperature, attain a maximum pressure,
which vanishes only at absolute zero.

Silver bromide, when placed in a vacuum at the ordinary
temperature, must therefore lose bromine until the latter has
attained the extremely small maximum pressure corresponding
to the prevailing temperature. This pressure may be calculated
in the following way.

The quantity of work which may be obtained from the com-
bination of metallic silver and liquid bromine is known ; it has
been determined by measuring the electromotive force to which
this reaction gives rise. From the table on page 271 it is
equivalent to 85000 calories.

This quantity of work may also be calculated from the equation

A = 2T log fsi.,

^AgBr

where SBr is the vapour pressure of liquid bromine, SAgBr that
of the bromine from silver bromide at the temperature T. At
the boiling point of bromine (about 60°) we have

T = 273 + 60, SBr = 760 mm.,
and therefore

SAgBr = 2.9 X 10 -53mm.

That is, silver bromide will decompose when exposed to a
vacuum at 60° until the bromine vapour evolved has reached a
pressure of 2.9X10"53 mm.

A similar calculation shows that the pressure of chlorine
evolved from silver chloride at the ordinary temperature is

SAgC1 = 5.4 X 10-75 mm.

THE END.

APPENDIX1.

Note 1, (page 2).

There are, to begin with, Co kilogram molecules of arsenic hydride
in a cubic metre. At the time t a fraction x of them has undergone
decomposition; the concentration of the arsenic hydride is then Ct —

Q -y O

(1 — x) Co , and that of the hydrogen molecules — — -. Since the pressure
of the gas is proportional to the concentration we have

Pt _(l-x)C0 + f xC0_

Ta ~ ~c f 2'

Therefore Ct = (1 — ^ - + 2) Co

-to

Note 2, (page 95).

32.7 cc. of pure air (saturated with aqueous vapour at 0°, and under
a, pressure of 760 mm.) would occupy 32.45 cc. when dry, and would
contain 6.78 cc. of oxygen. The hydrogen added (13.8 cc.) is in excess;
the quantity of electrolytic gas is thus 3 X 6.78 =z 20.34 cc. initially.
At the time t a fraction 11 has undergone change, that is 20.34 11 cc.
The fraction of the whole quantity of gas which has disappeared at this

~P — "P

time is - ^5 - , or, since the lengths L of the column of air are in-
-t o

versely proportional to the pressures,

•L<t

We thus obtain the expression

46.5 = 20.34 „

1 By the translator.

276 APPENDIX.

Note 3, (pp. 123 and 248).

The connexion between the quantities of heat evolved by the con-
version of a material system, A, into another, B, at different temperatures
may be obtained as follows: —

At the temperature T, let one gram of A be converted into B, qT calories
being evolved. Now let the temperature of B change to To, CB (T — T0)
calories being evolved, where CB is the specific heat of B. At T0 let
the substance be reconverted into A, with evolution of — q0 calories,
and finally let the system be brought back to the temperature T, the
quantity of heat evolved being CA (T0 — T) calories, where CA is the
specific heat of A. If the external work done during these changes be
zero or negligible we may write

qT — qo + CB (T — To) -f CA (T0 — T) — 0,
or qT=:qo +(CA— CB)(T-T0).

Note 4, (page 256).

If we call u the velocity with which Na ions move through a solution
of NaoS04 under the influence of a given E. M. F., and v the velocity
of the SO4 ions under the same circumstances, the quantity of Na ions
which move out of the solution surrounding the anode, i. e. the loss
of NaaSCh there, will be proportional to u, and similarly the loss of
Na2S04 from the solution round the kathode will be proportional to vr
the whole quantity of NasSCU decomposed being proportional to (u -j- v).
The migration constant for the Na ion is the ratio between the dimin-
ution in the quantity of Naa S04 in the solution round the anode, and

the whole quantity decomposed, i. e. 11 =2 r.

If we call the whole quantity decomposed unity, n is the quantity of
Na ions which moves out of the solution round the anode, and -

— (1 — 11) the quantity of SCh ions which moves out of the solution
surrounding the kathode.

Note 5, p. 89. Valvolin is a trade name for vaseline, used in Hamburg.

NAME INDEX.

Alexejeft*. 208

Arrhenius .... 123, 131, 133

Askenasy 42, 47, 48, 49

Anbel (van) , . 94

Baker .... 32, 33, 59, 81, 86

Baur 169, 203

Baeyer 92

Bellati 246, 247

Berthelot 28, 30, 36, 52, 92, 93,

123, 124, 145, 146, 151, 154, 163,

215, 224, 225, 242

Bodenstein 32

Boguski 27

Bois-lleymond (du) . . . .201

Bordet 168

Boyle 205, 210, 222

Braun 254, 271

Bredig 169, 198, 257, 258, 261, 263

Bremer 159, 178

Brodie 215

Buchanan 14, 32

Bunsen . . 33, 39, 48, 91, 93, 136

Cailletet 168

Chancel 168

Chappuis 83, 85

Charles 205, 210

Clausen 126

Clausius 242

Cohen 169, 188, 193, 198, 254, 257,
258, 261, 262, 263.

Conrad 125, 133

Czapski 254

Davy 51

Dent 25

Deveuter (van) 150, 165, 169, 170,
173, 187, 207, 208, 250.

Deville 152, 223

Dewar 81

Dixon 32, 33, 59

Docters van Leeuwen. . . 163

Duclaux 168

Dumas . . . , 51

Engelraann 52, 196

Esson . . . , . 13, 93, 124, 135

Ettling 171

Evans 125

Ewan 33, 56, 61, 82

Eykman 189

Faraday 253

Forcraiid (de) 168

Fourcroy 51

Friedel " 52

Frowein 158, 161, 162, 178, 211,
221, 235, 236.

Gay-Lussac 205

Gibbs 254

Gockel 254

Goldschmidt . . 81, 170, 171, 250

Graham 32

Guldberg .... 145, 206, 233

Harcourt ... 13, 93, 124, 135

Harker 33

Hautefeuille 173, 221

Hecht 125, 133

Heide (van der) 172

Helmholtz H . . . 252, 253, 254

Helmholtz E 82

Hemptinne (de) 116, 118, 119, li>l

Henry 12

Hittorf 257

Hoff (van 't) 24, 30, 32, 34, 36, 49,

57, 59, 82, 123, 138, 145, 147, 148,

151, 165, 169, 170, 171, 173, 187,

206, 208, 243, 247, 250, 261, 267

Hofmann ........ 36

Hood 20, 125, 132

Horstmann . . . 143, 145, 151
Houton de Labillardiere . 51, 52

278

INDEX.

Ikeda 56, 61

Isambert 156, 157

Jahn 254 ,

Jellett 269, 270, 271

Jorissen 52, 171, 250

Joubert 52, 61, 62, 66, 86, 141, 254
Joule 254

Kahlbaum 75

Konowalow 93, 125

Kooy 32, 49, 123, 125, 125, 126,
134, 169.

Kopp 171, 181

Krauel 42, 47, 48

Laar (van) 208, 210

Ladenburg 52

Landolt 28, 29

Le Chatelier 208, 243

Leeds 83, 96

Lehmann .... 164, 168, 221

Lemoine 36

Lescoeur 193

Leverrier 81

Ley 133

Linebarger 189

Loewel 168, 175, 187, 257, 261, 263
Lowenherz .... 118, 119, 180

Luff 92

Lussana . . . 167, 243, 244, 246

Mallard . - 243

Marchand 82

Marignac 208

Marum (van) 51

Meissner 82

Menschutkin . . 28, 29, 93, 95

Meyer L 28, 30, 136

Meyer V . . 42, 47, 48, 49, 137

Meyerhoffer 172, 186

Miller (Lash) 199

Mitscherlich . . . 221, 230, 234

Moser 193, 194

Mulder 168

Xaumann ... 43, 44, 93, 211

Nernst 188, 194, 254

Noyes. ...... 102, 104, 111

Ogier . 154

Ostwald 12, 13, 27, 115, 116, 119
125, 193, 199, 233.

Pareau 235

Parmentier 168

Pe"an de Saint Gilles 28, 30 36, 92,

93, 145, 146.

Pfaundler .... 143, 145, 161
Pfeffer 230, 231, 232, 233, 234, 235

Pfeiffer 191

Poggendorff 201

Pringsheim 33

Raoult 234

Raum •... 137

Reicher 4, 9, 30, 52, 94, 105, 115,

116, 119, 125, 130, 168, 171, 173,

181, 183, 207, 216, 243, 244, 247,

249.

Reinizer 81

Rennie . . . • 92

Rodwell 246

Romanese 246, 247

Rontgen 30, 31

Roozeboom (Bakhuis) 168, 176,

184, 187, 207.

Roscoe 33, 48, 91, 93

Rose 51

Riidorff 171

Sabatier ' . 125

Salzer 85

Scacchi 170, 186, 250

Schiff 173, 178

Schonbein 83

Schwab ... 15, 17, 28, 129, 130
Schwarz . . 167, 181, 185, 203, 244

Schwicker 105

Scott 104

Shenstone 34

Skalweit 83

Smithells 25

Spohr 125, 133

Spring 27, 30, 93, 94, 243, 247, 248
Stadt (van de) 20, 33, 54, 57, 58,
59, 60, 207, 208.

Stefan 63

Swart 152

Tammann .31

Than 33

Thomseii 161, 224, 225, 262, 264

Thomson J. J 80, 81

Thomson W 254, 255

Thorpe 86

Tollens 37

Troost 152, 173, 221

Tutton 86

Urech 32, 90, 91, 94, 107, 133
Verschaffelt . . . 169, 188, 199

INDEX.

Vriens

279
161, 172, 221

Waage 145, 206

Walker 199

Warder 4, 33, 116, 125, 130, 133

Weltzien 173

Wiedemann E 169, 184

Wiedemann G 236

Wilhelmi 13

Wittwer 13

Wright 92

Wyrouboff 170, 186

SUBJECT INDEX.

Acetamide, decomposition of, by

acids, 12, 125

Acetic acid, etherification of, 28

Acids, influence of the nature of,

on the hydrolysis of their esters

116, 120

Active oxygen, 82—86

Activity coefficient. .... 208

Affinity ......... 229

„ at absolute zero, . . 241
„ measurement of, 230—235
„ of salts for water of cry-
stallisation, . . 230, 234
work done by, . 235—240
Alcohol, influence of the nature of,
on the hydrolysis of its
esters, .... 116, 119

„ retarding action of, 28,

34, 35

Aldehyde, rate of oxidation of,73— 80

Alkaloids, 269, 271

Ammonia, decomposition of . 33

Ammonium carbamate, 34, 89, 94

„ carbonate, ... 34

„ nitrate, 164, 168, 221

246, 247

„ sodium racemate,

transition point of, 170,
171, 250

„ sulphide, dissociation

of, 155, 156, 157, 205

219, 223, 267

Arayl alcohol, solubility of, in wa-
ter 189, 190

Aniline, action of, on acetic acid,

28, 93

Anti-benzaldoxirne acetate . . 133

Arsenic compounds, preparation of

by pressure, .... 30

„ hydride, decomposition of

1, 2, 20, 32, 99, 134

Arsenic oxidation of, . . . .52

Astrakanite, transition point of

169, 176, 178, 179, 184, 187

Atomic condition of oxygen gas.

80, 82—86

Barium chloride, affinity of, for

water, . . 234

„ „ hydrated, heat

of formation of, 161

Benzene, nitration of,. . . . 28
Bimolecular reaction . . 4, 9, 15
Birotation of milk sugar, . . 32
Bloedite (astrakanite) 169, 176, 178
179, 184, 187

Bromic acid, action of hydriodic
acid on. 140

Cadmium choride (hydrated), tran-
sition point of, 169

Calcium carbonate, dissociation of,

218
Calcium oxalate, action of acids

on, 155

Cane sugar, inversion of, 30, 32

125, 133

Carbon, oxidation of .... 33
„ monoxide, explosion of
with oxygen, 33
„ „ action of, on me-

tallic oxides, 92
„ „ action of, on

water, . . 151

Catalytic action, 31 — 34

„ „ of hydrogen and

hydroxyl ions, . . . 116, 121

Chemical induction . . 91—98

Chloracetic acid, action of water on,

14, 32, 125, 130

Chloracetate of sodium, action of
NaOH on, .... 15, 125, 129

282

INDEX.

Chlorine, action of, on hydrogen,
83, 91, 93

Colour, determination of the tran-
sition point by, 203

Concentration currents, . 193, 194

„ gaseous, . . .18

„ of a system,. . 12

„ unit of, ... 4

Condensed systems, .... 163

„ „ incompatibility

of 165

Contact action, . .26—29,31—34
Copper, action of on ZnSO-i, 269
„ bipotassium chloride, de-
composition of, 161, 162,
172, 229

„ calcium acetate, 30, 171,
172, 247

„ sulphate, affinity of for
water, 234, 235
„ „ dissociation of

hydrated, 158,160
„ „ heat of formation

of hydrated, . . . . 160, 161
Crystallisation method of deter-
mining the transition temperature,

186

Cuprous chloride,action of, on silver,

271

Cyamelide, see cyanic acid. .
Cyanic acid, polymerisation of,
36—38, 43—45, 88, 96, 97,
107—110, 173, 174,220—223

Cyanogen, 25

Cyaiiuric acid, see cyanic acid
Cycle of chemical equilibria, 271

Depression of freezing point, 233

Devitrification, 47

Dibromsuccinic acid, 30, 113, 114,
115, 125, 127, 128

#-Dichlorhydrine, decomposition of

125
Differential tensimeter, . . . 178

Dilatometer, 94, 181

Dimethyl ethylene hydrochloride,

decomposition of, .... 125

Dissociation, . 144, 152, 155—157

„ pressure of hydrated

salts, 158—161, 188

Disturbing actions, elimination of

86—91

„ in gases, 31, 43, 50

„ „ in liquids, . 26

Double decomposition, transition

temperature in cases of, 169, 173,

229

Electrical conductivity, . . . 203

„ methods of determining

the transition point, 193-203

„ work done by chemical

change, 251, 252, 254, 255

Electrodes, unpolarisable, 195, 196,

199

Electrolytic gas, transformation into

water. . 36, 39—42, 45—49, 95

Electromotive force, . .253, 264

., „ connexion of

with equilibrium constant 267

Electromotive force, determination

of direction of change by means

of, 272

Electromotive force, measurement

of 196

Electromotive force, produced by

chemical change 253

Equilibrium, chemical, . . . 143
„ „ analogy with

physical, 211

Equilibrium, chemical, in conden-
sed systems, . . 163—180, 219
Equilibrium, chemical, in heteroge-
neous systems, . 155 — 168, 218
Equilibrium, chemical, in homoge-
neous systems, . 143—155, 222
Equilibrium, influence of tempe-
rature on, 148, 212, 217, 223-228
Equilibrium, constant. . . . 145
„ „ connexion of

of with E. M. F 267

Equilibrium, physical, . . . 204
„ „ in condensed

systems, 210, 219

Equilibrium, physical, in heteroge-
neous systems, . . . 205, 217
Equilibrium, physical, in homo-
geneous systems, . . 205, 222
Equilibrium, principle of mobile,

217, 228

TJNIVERJ

INDEX.

283

Esters, formation of, 28, 36, 92,

146, 151

Esters, hydrolysis of, 4, 11, 32,

115—121, 130, 131, 133

Etherincation, 28, 36, 92, 146, 151

„ influence of pressure

on, 30

Ethyl acetate, 4, 8, 11, 28, 115, 125,
130, 131, 133, 147
Ethylene hydrochloride, decompo-
sition of 125

Evaporation, equilibrium of, 204 —

206, 217

Evaporation, rate of, ... 63, 64
Explosive limit for dry phosphine

and oxygen, 56

Explosive limit for moist phosphine

and oxygen, 57 — 61

Explosion, velocity of, in dry gases,33

Fatty acids, action of bromine on, 94

Ferric chloride, action of, on SnCls,

110—112

Ferrous sulphate, action of, on
KClOs, 132

Formaldehyde, polymerisation of,

36, 89

Freezing point, depression of, 233
Fumaric acid, action of bromine on,

105, 106
Fusion, 210, 219, 243

Gaseous concentration ... 18

Glauber's salt, action of on ammo-
nium chloride, 173

Glauber's salt, action of on potas-
sium chloride. . 173, 177, 178

Glauber's salt, transition point of,
168, 169, 175, 179, 180, 184, 188, 191,
192, 193, 198—203, 230, 255—257

Heat evolved by reactions at high
or low temperatures, 224 — 228

Heat evolved by reactions, con-
nexion of, with equilibrium con-
stant, 148—150

Heat evolved by reactions, con-
nexion of, with velocity constant,
122—126

Heat of solution, . . . 207, 208

Hexane, rate of reactions in, 28

Hydrated salts, dissociation of,

158—161, 188

Hydrated salts, transition point of,
168, 179, 180

Hydrates, transition point of, 168
Hydriodic acid, action of, on bro-

mic acid, 104

Hydriodic acid, action of, on hy-
drogen peroxide, 104

Hydriodic acid, decomposition of,

32, 36
Hydrolysis of esters, apparatus and

methods, 6, 10

Hydrolysis of esters by acids,
116—121

Hydrolysis of esters by bases, 4,

11, 32, 115, 116, 130, 131, 133

Hypophosphoric acid, ... 85

Identity methods of determining
the transition point, . . . 186
Ignition temperature, . . 136 — 142
Incompatible systems. . 165, 219
Induction, chemical, . . .91 — 98
Initial acceleration, . . . 91 — 98
Inversion of cane sugar, 30, 32, 133
Invert sugar, action of, on Fehling's

solution, 90

lonisation, effect of pressure on, 31

Isodibrom succinic acid, 1 13, 114, 115

Isomers, equilibrium of optical, 151

„ transition point of, . 173

Lactic acid, action of bromine on, 92
Lactones, action of bases on, . 12
Light, effect of, on chemical change,
33, 91, 92, 93
Limiting equation, .... 146

Magnesium sulphate, heat of for-
mation of hydrated, . . . 161

Marble, rate of solution of, 27, 94

Maximum work, principle of,

224, 242

Medium, action of the, 26, 27, 43

Mercuric iodide, transition tempe-
rature of, ....... 203

Metaphosphoric acid, action of
water on, 125

Metaphosphorous acid, 21, 22, 23

284

INDEX.

Methyl ethylene hydrochloride, de-
composition of, 125

M ethyl iodide, action of, on sodium
ethylate, 125, 133

Micro-organisms, behaviour of, to
oxygen, 52

Milk-sugar, birotation of, . . 32

Minimum work, principle of, 225,

242

Mixtures, recognition of, 113 — 115

Moisture, influence of, on chemical
change, . . 32—35, 58, 59, 81

Moistening the walls of the vessel,

89—91

Molecular volume, influence ofoii
the rate of reaction, . . .15

Monomolecular reaction, . 1, 13

Nickel carbonyl, oxidation of, 52
Nitration of benzene, .... 28
Nitriles, formation of, ... 133
Nitrogen peroxide, 122, 144, 205, 222
Nitrogen peroxide, heat evolved by

the dissociation of, . . 152 — 155

Normal reactions, 1

Number of molecules participating

in a change, .... 99 — 112

Optical activity, 29

„ isomers, equilibrium be-
tween, 151

Osmotic pressure, . 189, 230—235
n n connexion of with
vapour pressure . . . 232, 233
Oxalic acid, action of, on perman-
ganate, 93

Oxidation of aldehyde, . 73—80

„ phosphine. 20— 25,33,

50-61

„ „ phosphorus, 32, 33,
5], 61—69, 81—86
„ sulphur, 33, 52, 69— 73
Oxygen, atomic condition of, 80, 82
Ozone, formation by the silent dis-
charge 34

Ozone, formation during the oxi-
dation of phosphorus, 82 — 86

Phosphine, decomposition of, 3, 20,
32, 43, 45, 49, 50, 99-101, 139

Phosphine, decomposition of, in-
fluence of temperature on, 126,
134, 135

Phosphine, oxidation of, 20 — 25.
33, 50—61

Phosphorescence, influence of tem-
perature and pressure on, 61, 66, 141
Phosphorescence, intermittent, 86

Phosphorous acid, 21

Phosphorus, formation of active

oxygen by oxidation of, . . 83

Phosphorus, oxidation of, 32, 33.

51, 61-69, 81—86

Platinum sponge, 27

Polymerisation, see cyanic acid and

formaldehyde.

Poly molecular reaction, . . 4, 19
Polymorphous substances, trans-
formation of, .... 167, 203
Potassium astrakaiiite . . . 173
„ chlorate, action of, on

FeO, 20

Potassium chlorate, action of, on

FeS04, 125, 132

Potassium hypoiodite, . . . 104

„ magnesium sulphates.

172, 173, 185

Potassium sodium racemate, 170,171
Pressure, influence of, on the lumi-
nosity of phosphorus, 61, 66, 141
Pressure, influence of, on the oxi-
dation of aldehyde,. ... 79
Pressure, influence of, on the oxi-
dation of phosphorus, . . 66, 69
Pressure, influence of, on the rate
of reactions in liquids, . . 30
Pressure, influence of, on the tran-
sition temperature, . . 242, 243
Pressure, influence of, on the tran-
sition temperature of sulphur,
244—246

Principle of mobile equilibrium,
217—228

Racemates, . . 170, 171, 186, 250
Respiration of plants,. . . . 126
Rochelle salt, decomposition of, 162
Rotativity 29

Salts, hydrated, dissociation of,
158—161, 188

INDEX.

285

Schonite, 172, 185

Semipermeable membrane,. . 231
Silicon hydride, oxidation of, 52
Silver bromide, vapour pressure of,

273

Silver chloride, vapour pressure of

273
Silver iodide, transition temperature

of, .247

Simonyite, see astrakanite.
Sodium ammonium racemate, 170,
171, 186, 250

Sodium ammonium tartrate, 170,
171, 186, 250

Sodium chloracetate, action of

NaOH on, .... 15, 125, 129

Sodium ethylate, action of, on

methyl iodide, .... 125, 133

Sodium hydrogen phosphate, hy-

drated, heat of formation of, 161

Sodium hydrogen phosphate, hy-

drated, transition temperature,

169, 203

Sodium potassium racemate, 170,

171

Sodium sulphate, anhydrous, 168,

169, 173, 175, 177—180, 184, 188,

191, 192, 193, 198-203, 230, 255-257

Sodium sulphate, decahydrated, 168

169, 173, 175, 177—180, 184, 188,

191, 192, 193, 198-203, 230, 255-257

Solubilities, product of, . . . 177

Solubility 206—209

Solubility at the transition tempe-
rature, . . 174—178, 186, 187
Solubility of water in amyl alcohol,

189, 190

Solution heat of, 207

pressure, . . . 188—192

„ „ of dissociation,

189, 192

Solutions, solid, . 143

„ supersaturated, at the

transition point, 175

Solvents, indifferent . . .27 — 29
„ use of, in eliminating dis-
turbing actions, . . . .87—89
Stannous chloride, action of, on

FeCls, 110—112

Steam, dissociation of, ... 2r2o

Sugar, osmotic pressure of solutions

of, 231, 234

Sulphur compounds, preparation of

by pressure, 30

Sulphur, oxidation of, 33, 52, 69—73
„ rate of change of rhombic

into monosymmetric, . . 94, 95
Sulphur, transition point, 30, 94, 95,

168, 181—183, 210, 212—216, 220,

221, 244—246, 248, 249

Surface of the walls of the vessel,

area of, ..43

Surface of the walls of the vessel,

nature of, 43—50

Synaldoxime acetates, . . . 133

System, unit of concentration of a, 12

„ „ quantity of a, . 253

Tartaric acid, action of bromine on,

Tartrates, transition temperature of,
163, 170, 171, 186, 250
Temperature coefficient of the tran-
sition cell, 199, 257—259, 266
Temperature, influence of, on equi-
librium, .... 148, 212, 217
Temperature, influence of, on the
velocity of reactions, 122 — 135
Temperature of ignition, 136 — 142

Tensimeter, 158, 187

Thermometric method of determi-
ning the transition point, 184, 185
Transition cell with stable and
metastable phases, 194, 195,
254—259

Transition cell with stable and
without metastable phases, 198 —
203, 258—266
Transition point (temperature),

164, 165

., point, calculation of,
212—216, 248—251
., determination of by
the dilatometer, . . . 181—183
Transition point, determination of
by electrical methods . . . 197
Transition point, influence of pres-
sure on 242, 243

Transition point, methods of deter-
mining the.. . . 180, 181, 203

286

INDEX.

Triethylarnine, action of, on ethyl

iodide, 28

Trimethylethylene hydrochloride,

125

Trimolecular reaction, 25, 110, 113
Turpentine, ...:... 29

Units of concentration, . . 4, 12

Unit quantity of a system, . 253

„ „ ,. electricity . 259

Valvolin, 89, 275

Vapour pressure at the transition

point, . . 178, 179, 180, 187, 188

Velocity constant, 1

„ „ influence of tem-

perature on, .... 122 — 135
Velocity of explosion, effect of

moisture on, ...... 33

Velocity of reaction in mixtures, 113
Volume, change of, at the transition

temperature, 184

Volume, influence of, on the rate

of bimolecular reactions, . . 13
Volume, influence of, on the rate

of monomolecular reactions, 3
Volume, molecular, influence of, on

the rate of reactions, 13, 15, 18

Walls of vessel, effect of moistening,
86, 89, 90

Walls of vessel, influence of area of,

43
Walls of vessel, influence of nature

of, 43, 50

Water, influence of, on chemical

change, 32, 33, 34, 37, 58, 59, 81

Work done by chemical affinity,

235, 236, 238, 240

Work done by chemical affinity at

absolute zero, 241

Work, electrical, done by chemical

change, 251, 252

Work, principle of maximum, 224,

226, 242

Work, principle of minimum, 225,

242

Zinc, action of acids on, . . 94
Zinc sulphate, action of coppei on.

269
Zinc sulphate, hydrated, affinity

of for water, 234

Zinc sulphate, hydrated, heat of

formation of, 161

Zinc sulphate, hydrated, transition

temperature of, 169

Zinc sulphate transition cell, 194, 195

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