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UC-NRLF

LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.
Class

PHYSICAL CHEMISTRY

FOR

BEGINNERS

DR. CH. VAN DEVENTER

WITH AN INTRODUCTION

PROF. J. H. VAN'T HOFF

AUTHORIZED AMERICAN EDITION FROM THE SECOND GERMAN EDITION

TRANSLATED BY

BERTRAM B. BOLTWOOD, PH.D.

Formerly Instructor in Physical Chemistry in the Sheffield Scientific School
,of Yale University

SECOND EDITION, RE VISED
FIRST THOUSAND

NEW YORK

JOHN WILEY & SONS

LONDON : CHAPMAN & HALL, LIMITED

1904

OF THE

UNIV::*SITY J

GENERAL

BERTRAM B. BOLTWOOD.

ROBERT DRUMMOND, PRINTER, NEW YORK.

INTRODUCTION

IN delivering in Amsterdam my lectures on Chem-
istry, chiefly to students of medicine, I was confronted
by a double task: on the one hand to present the
systematic side of the subject with relative complete-
ness and entirely on an experimental basis, on the
other hand to show how the fundamental laws of
chemistry might be deduced from these facts. The
scheme of presentation which I adopted therefore
comprised two topics: the first included the considera-
tion of certain elements, the second was confined to
a general summary.

I began with " Matter from a Qualitative Stand-
point,'* water, oxygen, hydrogen, air, and nitrogen
supplying me with the necessary material; then came
the concepts, compound, mixture, element, and the
whole table of atoms; the halogens furnished the ma-
terial for the second topic, in the course of which the
laws governing weight were introduced, and in this
manner I continued until the vacation.

This was all very well, but nevertheless a book was
required. For the systematic side I indeed recom-

iii

mended many, but for the theoretical side this was diffi-
cult, until as a welcome assistance this little book by
Van Deventer appeared. The author had attended
my lectures, had worked under me in the laboratory, had
pursued his studies still further, and had devoted con-
siderable time to the instruction of medical students.

But from a broader point of view it is indeed a
commendable task which the author has set himself
in presenting in his own way the subject of physical
or general chemistry to the students of medicine,
pharmacy and chemistry, without placing too great
stress on the physical and mathematical side of the
subject. A realm of science is concerned which in
recent years has proved extremely fruitful, a journal
especially devoted to physical chemistry having just
appeared in the New World, and from the corre-
sponding journal of the Old World a good word from
the pen of an eminent scientist will be quoted:

" The prospective development of all sciences in
which chemistry plays a part, from geology to
physiology, including the whole of chemical tech-
nology, can be more readily appreciated at the present
moment than perhaps at any time previously; they
will all undergo a fundamental reform through the
application of the facts recently acquired through the
agency of general chemistry. ' '

J. H. VAN'T HOFF.

AMSTERDAM, 1897.

AUTHOR'S PREFACE TO GERMAN
EDITION.

IN the book at hand the author has endeavorecj to
collect the most important results of physical chemistry
in such a manner that this important branch of modern
chemistry may be accessible to those who have not
made an exhaustive study of physics and mathematics.
The requirements of students of medicine and phar-
macy, as well as of elementary chemistry, have been
especially considered in the preparation of this work.

The author desires to express his sincere thanks to
Dr. Ernst Cohen, who has prepared the present edition.

CH. M. VAN DEVENTER.

BATAVIA, June, 1901.

CONTENTS.

CHAPTER I.

DEFINITIONS.
SECTION PAC8

1. Chemistry I

2. Substance or matter, element, compound, mixture, crys-

tals I

CHAPTER II.

FUNDAMENTAL LAWS OF COMPOSITION.

3. The law of constant weight 4

4. Law of constant composition 4

5. Law of multiple proportions » 5

6. Law of constant proportions 12

7. Law of equivalence of the elements 13

8. Explanation of the fundamental laws 14

9. Law of Gay Lussac on the combination of elements in a

gaseous state 15

CHAPTER III.

THE PROPERTIES OF GASES.

10. Law of Boyle-Gay-Lussac 17

n. Gay-Lussac's law on the reactions of substances in a

gaseous condition 1 8

12. Gas density 18

13. Some methods for determining the gas density 20

14. Abnormal gas densities 24

vii

viii

PACK

15. On the nature of gaseous bodies. Molecules. Atoms .. 25

16. Avogadro's hypothesis 26

17. Deductions from Avogadro's hypothesis :

a. Molecular weight 26

18. b. Atomic weight. Theoretical and experimental defini-

tion 28

19. c. Number of atoms in the molecule 30

20. d. Number of atoms in the molecules of the elements. ... 32

21. e. Deduction of the molecular formula of a substance. ... 33

22. f. The valence of the elements > 43

23. g. Theoretical demonstration of the law of Gay-Lussac

on the reactions of gaseous bodies. 46

CHAPTER IV.

THERMOCHEMISTRY.

24. Law of Dulong and Petit 48

25. Joule's Law 50

26. Application of the two laws to the determination of the

atomic weight c 52

27. Heat of formation and heat of decomposition of a com-

pound. Heat of reaction. Endothermic and exother-
mic reactions 54

28. Calorimetric methods 56

29. Law of Lavoisier and Laplace 58

30. Law of Hess 58

31. Applications of the law of Hess 59

32. Some general results of investigations on heat of forma-

tion 66

33. Principle of greatest work 81

34. Application of the principle of greatest work . . 83

35. Causes for the starting of reactions 91

36. Criticism of the principle of greatest work 92

37. Endothermic reactions which take place at normal tem-

peratures 92

38. Mass action 93

39. Dissociation..... 94

40. The principle of variable equilibrium 94

41. Chemical equilibrium 97

42. Graphic representation 98

43- Proof of the existence of equilibrium between simulta-
neous reactions TOO

4 \. The three kinds of chemical equilibrium 101

45. Effect of temperature on equilibrium 102

46. Effect of pressure on equilibrium. 104

47. Effect of chemical mass on equilibrium 106

48. Analogy between changes in physical and chemical state 107

49. Berthollet's law 108

50. Watt's principle no

51. Watt's principle applied to matter at normal temperature 115

CHAPTER V.

SOLUTIONS.

52. Definitions 121

53. General laws of solubility 122

54. Solubility of hydrates 122

55. Osmosis 123

56. Osmotic phenomena in dilute solutions 124

57. Experimental basis 126

58. Exceptions 129

CHAPTER VI.

ELECTROCHEMISTRY.

59. Definitions 131

60. Electrolytic, dissociation 131

61. Faraday's law 132

62. Conductivity of organic and inorganic compounds 133

63. Some laws governing electrolytic dissociation 134

64. Verification of the laws of electrolytic dissociation 137

CHAPTER VII.

PHENOMENA OF LIGHT.

65. Colored flames 140

66. The spectroscope 140

67. Absorption phenomena 142

FACE

68. Photochemical action 144

69. Photochemical extinction 145

70. Development and fixing of a photographic picture 146

71. Color photography 147

CHAPTER VIII.

THE PERIODIC SYSTEM.

72. Definition ' 149

73. Graphic representation 150

74. Tabular representation 151

75. Large and small periods 151

76. Variation of physical properties in periods 152

77. Application of the periodic system 154

78. Closing remarks on the periodic system 157

Table of the Elements arranged according to the
Natural System.

CHAPTER I.
DEFINITIONS.

§ i. Chemistry is the science which treats of the
conditions under which one substance of itself, or sev-
eral substances by reciprocal action, give rise to the
appearance of new substances. The province of
chemistry also includes the description of the sub-
stances, as well as of the phenomena which accompany
the formation of new substances.

§ 2. Substance or Matter is the name given in
chemistry to every homogeneous body, without refer-
ence to its form or state of aggregation.

An element is a substance which cannot be decom-
posed into other substances.*

A compound is a substance composed of two or
more elements; of the properties of the elements, the
weight only is retained in the properties of the com-
pound.

A mixture is a combination of substances in which
the essential properties of the substances are retained.

REMARK i. The substances which are now called ele-
ments are relative elements — i.e., non-decomposable by any

* A table of elements will be found at the end of this book.

known forces. For the introduction of the conception rel-
ative element we are indebted to Lavoisier.

REMARK 2. It is often difficult to plainly distinguish
the limits between compounds and mixtures. The differ-
ence may be most clearly stated as follows : in a compound
the elements are indeed present as such, but are so influ-
enced by one another that the properties of the whole,
with the exception of the weight, are not equal to the sum
of the properties of the components ; also the behavior of
the compound towards other substances is in no way sim-
ilar to that of the free elements. In a mixture, however,
the mingled components may be considered as side by side,
each part retaining its characteristic properties, these prop-
erties being so little influenced by one another that the
components act upon other substances in the same manner
that they would act if entirely separate.

REMARK 3. Solid bodies often form from liquids and
produce solid figures enclosed by planes. Bodies of this
sort are called crystals. They show certain regularities
upon which the systems of the crystals depend. They are
so divided into six groups that every crystalline chemical
compound is included in one of these groups.

Crystals grow by the addition of new layers of material
to the faces already existing. As a result of this process
the forms of crystals are not materially influenced by their
dimensions, but are dependent upon the angles between
their faces; since, by the parallel extension of the plane
faces of the crystals, these angles remain unaltered. It is
always possible, by shifting the faces of a crystal, to reduce
it to an ideal form in which a certain symmetry can be
detected. The degree of symmetry is dependent upon the
number of symmetry planes.

The position of the crystal faces is often expressed by
their intersections with certain a^es taken in the crystal ;
these axes being chosen with direct reference to the planes
of symmetry.

Each group of crystal forms in which an equal number
of symmetry planes can be detected is called a crystal sys-
tem. There are six of these : with nine, with seven, with
five, with three, with one, and with no symmetry planes.

Solid substances which are not crystalline are called
amorphous.

Some compounds can, however, crystallize in more
than one crystal system ; such cases are usually dependent
on the temperature.

CHAPTER II.
FUNDAMENTAL LAWS OF COMPOSITION.

§ 3. The Law of Constant Weight (Lavoisier's
Law). A system of matter on changing into another
system does not alter in mass (weight).

Differently formulated. On chemical action no
mass is either lost or gained. — The weight of a sys-
tem of matter is independent of the chemical form. —
On chemical action the total weight of matter before
and after the reaction is the same.

REMARK i. This principle was dogmatically employed
by Lavoisier as a fundamental doctrine in experimental
chemical investigation. But only after his death, and
chiefly as a result of his efforts, was it introduced as a
fundamental law of all chemical teaching.

REMARK 2. From the law of Lavoisier, in connection
with the conception element, it follows directly that not
only the entire system, by a change in the chemical form,
does not alter in weight, but also each element before and
after the reaction is present in exactly the same quantity.

§ 4. The Law of Constant Composition. The

composition of a compound is independent of the
method by which it is prepared.

Differently formulated. A compound, character-
ized by a definite number of physical and chemical

properties, has an invariable qualitative and quantita-
tive composition.

Example. Alcohol is obtained by the fermenta-
tion of sugar in water. The same substance is formed
also from the oxidation of ethane, by the action of
ethyl iodide on an aqueous solution of potassium hy-
droxide, and by other reactions. The product, which
has a specific gravity of 0.792 and a boiling-point of
78°, is always of the same composition : 46 grams of
the substance contains 24 grams of carbon, 6 grams
of hydrogen, and 16 grams of oxygen.

REMARK. This law was introduced by Proust at the be-
ginning of the present century.

§ 5. The Law of Multiple Proportions. When
two elements occur together in more than one com-
pound, then the different quantities of the one element
which are associated with the same quantity of the
other element, stand with respect to their weights in
proportions which can be expressed by rational num-
bers.

Differently formulated. A fixed quantity of one
element so combines with different quantities of another
element that the ratio between the latter may be ex-
pressed by rational numbers.

Example. In the compounds methane, ethane,
ethylene, acetylene, benzene there are to every 12
grams of carbon respectively 4, 3, 2, I, and I grams
of hydrogen. In the substances ammonia, ammonium
chloride, nitric acid, methyl-amine, amido-benzene,
nitrotoluene, hydrazoic acid there are to every 14
grams of nitrogen respectively 3, 4, I, 5, 7, 7, and
J grams of hydrogen.

REMARK i. This law was discovered by Dalton in 1802.

The law of constant weight permits, following Lavoisier's
example, of the expression of chemical reactions by means
of equations, in which the substances in the initial state
stand on the left of the equality sign, and the products of
the reaction on the right.

Thus : Sodium hydroxide -j- Hydrochloric acid = So-
dium chloride + Water.

REMARK 2. Since each separate substance has a fixed
composition, a substance is often named from its composi-
tion. Substances are also denoted by a symbol, a formula,
which expresses their qualitative and quantitative composi-
tion. These formulas consist of letters which represent the
element and a characteristic number belonging to it ; coeffi-
cients at the rear of the letters denote how many times this
characteristic number shall be taken. How these numbers,
the so-called atomic weights, are determined will be ex-
plained later.

The substance potassium chlonde is represented by the
formula KC1 ; it contains for every 39 grams of potassium
35.5 grams of chlorine. HNO9 is nitric acid, a substance
which in 63 grams contains i gram of hydrogen, 14 grams
of nitrogen, and 48 grains of oxygen.

When the formulas — frequently multiplied by a coeffi-
cient— of the substances which enter into a reaction are
assembled in an equation, an accurate idea is obtained of
the substances and the relative quantities in which they
enter into the reaction, and an exact expression for the qual-
itative and quantitative course of the reaction is secured.

The equation

KNO, + HaS04 = KHS04 + HNO,

states that by the action of sulphuric acid on potassium
nitiate each 101 grams of potassium nitrate requires for its
decomposition 98 grams of sulphuric acid, and as a result

of this process 136 grams of hydrogen potassium sulphate
and 63 grams of nitric acid are formed.
From the equation

2H, + O, = 2HaO

it is seen that 4 grams of hydrogen combine with 32 grams
of oxygen to form 36 grams of water.

When the substances exist in the form of gas or vapor,
the formulae have a special significance which will be ex-
plained later (compare § 17, Rem. 3 and § 23).

REMARK 3. Berzelius was the first to represent elements
by letters, and compounds by combinations of letters, and
it was he who gave a quantitative significance to the latter.

The characteristic numbers now associated with the let-
ters by all chemists were first used about thirty years ago.

REMARK 4. A chemical equation, according to the law
of Lavoisier and the definition of an element, shall have the
same elements, and of each element the same quantity on
both sides of the equality sign. If the formulas of the sub-
stances in the initial and final state are known, correct
results are not always attained by writing the formulas on
both sides of the equality sign. Hydrogen and oxygen
react to form water, but the equation

Ha + Oa = HaO *

is incorrect. What shall be done in this case is quite evi-
dent ; since by writing

2H, + O, = 2H,0

the equation is made to conform with Lavoisier's law.
But it is not always so simple to determine the correct

* Hydrogen and oxygen, as will be explained later, are not
denoted by H and O, but by H3 and Oa.

coefficients, and in some cases careful consideration is re-
quired. Since the coefficients determine the conformity
of the equation with Lavoisier's law, the law prescribing
only the equality of two quantities but not their absolute
values, it is evident that only the relative values of the
coefficients must be determined.

For explaining the method a special case will be con-
sidered.

When potassium manganate (K2MnO4) is added to a
considerable volume of water, potassium permanganate
(KMnO4), manganese dioxide (MnO,), and potassium hy-
droxide (KOH) are produced. The equation expressing
this reaction must have the following form :

/KaMnO4 -f ?HSO =*KMnO4 + jMnO, + sKOH.

From the definition of an element and Lavoisier's law
the following equations must be true :

/Ka = (* + s)K or 2/ = # + *... (a)

^Mn = (x -f~ y)Mn or ^> = x -{- y. (^)

/O4-{-^O = •^O4-|->yOi -f- sO or • ^p-\-q = 4^-j~2y~{~^' • (f)

^H, = j?H or 2q = z (d)

As is evident, there are five unknown quantities and only
four equations. But since, as already stated, the relation
only of the coefficients is required, the number of equations
is sufficient, and it is only necessary to choose some rational
value for one of the unknown quantities. If on carrying
out the calculation the values found for other unknown
quantities are fractions, the whole must be multiplied by
some suitable factor in order to reduce the coefficients to
whole numbers. Irrational quantities must not appear in the
results ; the equations must therefore be of the first degree
and the coefficients of the unknown quantities must be
rational.

If we now take z = i, then from (d) . . . . q = 4.

By the combination of (<r) and (b) we obtain

— q = 2y — z and y — \.

From (b) and (a) p= z — y, that is/ = f.
Finally : from (a) f = * -f- i, which gives x = J.
If now all the results of the calculation be multiplied by
4, and be inserted in the equation of the reaction, we obtain

3K,MnO4 + 2H,O = 2KMnO4 + MnO, + 4KOH.

More equations than unknown quantities cannot be ob-
tained ; but the case is not excluded where the number of
equations may differ by more than one from the number of
unknown quantities. For example, the reaction by which
potassium chlorate, on heating, forms oxygen, potassium
perchlorate, and potassium chloride:

/KC1O3 = ?KC1 + rKC!O4 -f sO,.

This gives for 2 independent relations 4 unknown quantities,
with which more than one system of values can be de-
termined. Experience has shown that the temperature de-
termines which system makes its appearance. The equa-
tions, however, are of the first degree and their unknown
quantities have whole numbers for coefficients, so that in
this case, also, only rational values can be obtained for the
unknown quantities.

// is therefore always possible to represent a chemical reac-
tion by an equation in which the coefficients are whole num-
bers.

An important application of this rule will be given later
in § 23.

REMARK 5. The fact must not be overlooked that the
quantities of the substances which appear in the equation
are only the portions which actually take part in the trans-
formation. In the equation

2K,MnO4 + 2H2O = 2KMnO4 -f 4KOH + MnO,

but a relatively small quantity of water appears. It must
not be assumed, however, that this small quantity of water
is sufficient to cause the transformation ; since the equation
merely states that in the reaction referred to — and this
occurs only in the presence of much water — the given quan-
tity of water has changed into another form.

REMARK 6. The methods which have been given for the
determination of the proper coefficients usually lead to the
desired results. Nevertheless it is often simpler to refer the
chemical change to an imaginary reaction, the coefficients of
which can be immediately determined ; when the latter are
known it is not difficult to write the actual equation with the
proper coefficients.

The action of water on potassium manganate will be again
considered. KaMnO4 is a derivative of MnOs ; with water
it gives KMnO4, a derivative of MnaO7, and the peroxide
MnO,. The imaginary change of the oxide is the forma-
tion of MnaO7 and MnO3 from MnOs.

For this imaginary reaction the equation can be imme-
diately found :

3Mn03 = Mn,07 + MnOa.

3MnO3 requires 3K3MnO4 ; MnaO7 assumes 2KMnO4 ; 4K
remains, appearing as 4KOH, and therefore 4H,O is re-
quired.

Finally : The action may be divided into a series of
phases ; each phase can be represented by a simple reaction,
the equation for each phase written, and then it is only
necessary to combine the separate phases in order to arrive
at an equation which represents the initial and final states of
the reaction.

It is known, for example, that by the action of potassium
bichromate on alcohol there are formed aldehyde, potassium
sulphate, and chromic sulphate. It is accordingly assumed :
that sulphuric acid and potassium bichromate give potas-
sium sulphate and chromic acid ; that chromic acid splits

up into water and anhydride ; that the anhydride oxidizes
alcohol with the formation of aldehyde and water, and
is itself reduced to chromium trioxide. These changes are
expressed in the following equations :

K,CraO, -f H,S04 + HS0 = KaSO4 + 2H,CrO4;
2HaCrO4 = 2HaO -f 2CrO,;

2Cr09 = CraO, + 3O;
3CaH.O + 30 = 3CaH40 + 3H,0;
Cr,08 +- 3HaS04 = Cra(SO)4 -f 3H,O.

By addition, similar members being cancelled on both sides,
we obtain

K3CraO, + 4HaS04 -f 3CaH60

= KaS04 + Cr,(S04)3 + 3CaH40 + 7HaO.

The disappearance — in the above addition — of so many
substances has not only a mathematical but also a chemical
significance. The division of the whole change into phases
is a purely mental operation, and the substances which occur
in this operation, but do not actually come into existence,
are not found in the final equation. The members of the
equation which disappear are all formulas of substances, the
existence of which is assumed in order to connect the equa-
tions with one another, and only those substances appear in
the final equation which can be identified in the initial and
final stages of the reaction.

Problems. The equations should be found which repre-
sent the following reactions:

1. The action of dilute nitric acid (HNO3) on copper
(Cu) causes the formation of copper nitrate (Cu(NO,)a),
nitric oxide (NO), and water (H,O).

2. The action of concentrated sulphuric acid (H,SO4) on
copper (Cu) gives copper sulphata (CuSO4), sulphur dioxide
(SO,), and water (H,O),

3. Oxalic acid (C3H3O4) in the presence of dilute sul-
phuric acid (H,SO4) is oxidized by potassium permanganate
(KMnOj to carbon dioxide (CO3) and water (H3O), while
potassium sulphate (K3SO4) and manganese sulphate
(MnSOj are formed as secondary products.

4. Potassium bichromate (K3Cr3O7) on heating with con-
centrated hydrochloric acid (HC1) is decomposed, with the
formation of chromic chloride (Cr3Cl6), potassium chloride
(KCl),and water (H3O).

5. Potassium iodide (KI) in neutral or alkaline solutions
is oxidized by potassium permanganate (KMnO4) to potas-
sium iodate (KIO,) with the formation of MnO, and KOH.

§ 6. Law of Constant Proportions. The elements
combine with one another in fixed relations by weight
and these relations are often retained when the same
elements appear together in combination with other
elements.

Example. Ethylene is composed of 6 parts
carbon and i part hydrogen. Carbon and hydrogen
occur in the same relation by weight in all other
hydrocarbon compounds of the ethylene series, also in
all fatty-acid, aldehyde, and dihalogen compounds of
ethylene ; the latter containing in addition both oxy-
gen and halogen.

200 grams of mercury combine with 32 grams sul-
phur, forming mercuric sulphide. The same quantities
are found in mercuric sulphate combined with 64 grams
of oxygen.

39 parts of potassium by combination with 35.5
parts chlorine form potassium chloride. In potassium
chlorate the same quantity of potassium is found com-
bined with the same quantity of chlorine and 48 parts
of oxygen.

In connection with this law the following rules will
be given :

The same relation by weight existing between two
elements, combined with a third, is often observed
when the two elements combine with another element.

Example. 48 parts oxygen and 14 parts nitro-
gen, form a compound with 108 parts silver: 48 parts
oxygen and 14 parts nitrogen are also found in com-
bination with 31.75 parts copper, with 103 parts lead,
with 100 parts mercury, with 32.5 parts zinc, with
68.5 parts barium, with 20 parts calcium, with 39
parts potassium, with 23 parts sodium, with I part
hydrogen.

32 parts sulphur and 64 parts oxygen combine with
216 parts silver; an equal quantity of sulphur and
oxgen is found combined with 206 parts lead, 63.5
parts copper, 200 parts mercury, 65 parts zinc, 137
parts barium, 40 parts calcium, 78 parts sodium, and
2 parts hydrogen.

§ 7. Law of Equivalence of the Elements. In
many cases the elements can enter into combination
with one another according to fixed relations by weight.
The number of grams of an element which can replace
one gram of hydrogen is called the equivalent of the
element.

Example. I gram of hydrogen combines with 8
grams of oxygen. But the hydrogen in combination
with 8 grams of oxygen can be replaced by 23 grams
sodium, 39 grams potassium, 20 grams calcium, 68.5
grams barium, 9 grams aluminium, 32.5 grams zinc,
31.75 grams copper, 103 grams lead, IOO grams
mercury.

REMARK. The equivalence of an element can therefore
be determined from the quantity of it which combines with
8 grams of oxygen, or with such quantity of another element
as forms a saturated compound with i gram of hydrogen.

§ 8. Explanation of the Fundamental Laws.

Only the first three of the six laws given are indepen-
dent laws, stating something which is in itself unre-
stricted. The law of constant proportion and the law
of equivalence can be considered as special cases of the
law of multiple proportion. Nevertheless the formula-
tion of these special cases is necessary, since they make
clear the existence of important phenomena: and
without this formulation the important special cases
would perhaps be overlooked.

In order to express the fact " that an element takes
the place of another in a compound," the word substi-
tute is often employed. It is said " that copper
chloride is hydrochloric acid in which the hydrogen has
been substituted by copper." Relative to this it is
to be remarked that the substitution is not always di-
rectly practicable. Although it is possible without
difficulty to substitute the copper in copper sulphate
by zinc, by introducing a rod of zinc in the solution of
the copper sulphate, the reverse substitution does not
take place so easily and is attained only by a relatively
complicated chemical process.

It is possible, under certain conditions, Jo effect
the substitution with quantities of the elements other
than the so-called equivalents. For example, a chlo-
rine compound may be obtained from hydrochloric acid
which in place of I gram of hydrogen contains, not 31.75
grams copper, but double that quantity. Especially

in organic chemistry this circumstance has made the
determination of the equivalents very difficult, — since
here the question : which substitution quantity shall be
called the equivalent ? often arose, — and the complex
substitutions increased the difficulty of representing the
substances by universally valid formulae at a time
when the significance of equivalence was attributed to
the letters representing the elements. The subse-
quently developed atomic theory saves us the trouble
of deciding on the proper equivalent, and furnishes us
with a method of formulation which is not affected by
the uncertainty of the notation previously used. It
is true that atomic weight and the equivalence do bear
a certain relation to one another, but in each stage of
experimental chemistry there is for each element a
fixed atomic weight, while the significance of the cor-
rect equivalent may always vary.

§ 9. Gay-Lussac's Law on the Combination of Ele-
ments in a Gaseous State. When a gaseous com-
pound is formed from gaseous elements, the volume of
a fixed quantity of the compound stands to the vol-
umes of the combining elements in a ratio which can
be expressed by whole numbers.

Example. Two liters of gaseous hydrogen chlo-
ride result from the combination of one liter of chlo-
rine and one liter of hydrogen. Two liters of water-
vapor can be decomposed into two liters of hydrogen
and one liter of oxygen, and can be formed from the
same quantities. Two liters of ammonia-gas give
on decomposition three liters of hydrogen and one
liter of nitrogen.

REMARK i. This law is a special case of a more general

law discovered by Gay Lussac in 1808, which will be given
later in § n.

REMARK 2. When substances in a gaseous condition are
compared with respect to their volumes, it is always assumed
that the pressure and temperature are the same in all cases.

CHAPTER III.
THE PROPERTIES OF GASES. .

§ 10. Law of Boyle - Gay - Lussac. Many sub-
stances, by heating or by a decrease of pressure, are
transformed into gaseous bodies ; many others are gas-
eous at normal temperature and normal pressure, i.e.,
at 15° C. and 760 millimeters of mercury. For most
gaseous bodies there exist certain limits, within which
for a certain quantity of substance the relation between
pressure, volume, and temperature is governed with
great exactitude by the following equation :

PV PV

In this formula V is the volume of -a certain quan-
tity of the substance at the absolute temperature T,
and P the corresponding pressure.

Example. I gram of hydrogen at o° C. and
760 mm occupies a volume of 11.16 liters; I gram of
chlorine a volume of 0.324 liters. 'Z'

* /= temperature in centigrade degrees.
C"= a constant,

REMARK i. This law is a combination of the law of Boyle,

PV=A (T constant),

with the law of Gay-Lussac (also called law of Charles),

T
VT = V^ (P constant),

Vt = P. ( i -r--^— ). . . . (P constant).

REMARK 2. The gases which conform to the above law
are called ideal gases. Vapors can be considered as ideal
gases when they are at temperatures relatively far above
their condensation-points. If gases show a considerable
deviation in their behavior from the Boyle-Gay-Lussac law,
their closer investigation belongs to the field of physics.
In this book only the case of the so-called abnormal gas
densities will be considered. (Compare § 14.)

§ ii. Gay-Lussac's Law on the Reactions of Sub-
stances in a Gaseous Condition. When gaseous
substances appear in a reaction, their volumes stand
to one another in most simple relations, which may
be expressed by whole numbers.

Example. Two liters of hydrogen combine with
one liter of oxygen to form two liters of water-vapor
(see Remark to § 12). — One liter of chlorine combines
with one liter of hydrogen to form two liters of hydro-
gen chloride. — One liter of methane with two liters
of oxygen gives one liter of carbon dioxide and two
liters of water-vapor. — I gram of diamond combines
with 1.9 liters of oxygen to form 1.9 liters of carbon
dioxide.

REMARK. This law was deduced by Gay Lussac from

investigations carried out in 1808 andfwas proved by Hum-
boldt. It includes the law given in § 9.

§ 12. Gas Density. In chemistry the density of
a gas is compared with that of air or, more generally.
with that of hydrogen at the same temperature and
pressure. The relation between the weights of equal
volumes of a gas and hydrogen under the same condi-
tions shall, according to the law of Boyle-Gay-Lussac,
be the same for all temperatures and pressures. If the
volume occupied by a definite weight of a substance in
a gaseous condition at a definite temperature and pres-
sure is known, then the weight of one liter of the gas
under normal conditions (o° and 760 mm) can be cal-
culated by applying the Boyle-Gay-Lussac law. This
weight, expressed in grams, divided by 0.0896 gram
(the weight of I liter of hydrogen at o° and 760 mm)
gives the gas density of the substance.

REMARK i. The weight of a substance in a gaseous con-
dition at o° and 760 mm is often only a mathematical
fiction, and this is true of those substances whose maximum
vapor pressure at o° is less than 760 mm. When it is stated
that one liter of water-vapor at o° and 760 mm has a
weight of 0.8 gram, this is not an actually true statement,
since water-vapor at a temperature of o° has a vapor pres-
sure of only 4 mm. The weight would, however, be 0.8
gram if water-vapor could be compressed at o° without
condensing until a pressure of 760 mm was reached and
obeyed the Boyle-Gay Lussac law at this pressure. This
imaginary value is used since it allows all gases and vapors
to be compared directly with hydrogen, of which the weight
of one liter at o° and 760 mm has been very accurately de-
termined, and since by this comparison the vapor density of
different substances may be readily obtained.

REMARK 2. The specific volume of a gas is the volume of
i gram of the gas, at o° and 760 mm, expressed in liters.
For hydrogen, for example, this value is

liters = 11.16 liters.

0.0896

REMARK 3. The knowledge of the gas densities is of
great importance in chemistry, not only because this is a
property of substances, but also because it has been shown
that relations exist between the gas densities and the
weights of substances which take part in reactions; also
relations exist between the vapor densities and the laws of
composition, and their most striking application is found in
the atomic theory, which will presently be considered.
(See § 14 ff.)

§ 13. Some Methods for Determining the Gas
Density. — General Principle. In order to calculate
the gas density of any substance — the weight of I
liter of hydrogen at o° and 760 mm being accepted
as already determined — there must be known : the
weight of the quantity of substance taken, its vol-
ume in the gaseous condition, and the pressure and
temperature at which the volume has been measured.
From these data the weight of I liter at o° and 760
mm can be calculated. This principle is the founda-
tion of the following methods:

a. Regnauli 's Method. A glass globe, the capacity
of which is known, is weighed first evacuated and
then filled with the gas, at the temperature and pres-
sure of the surroundings. This method is especially
suitable for substances which are gases at ordinary
temperatures, and gives very accurate results.

b. Dumas Method. This is much used for liquids

which do not have a high boiling-point. A small
quantity of the liquid to be examined is introduced
into a glass globe of known weight and capacity ; this
is then heated in a bath, the temperature of which is
several degrees above the boiling-point of the sub-
stance. The liquid boils, the vapor escapes through
the narrow neck, and the air is driven out. Finally
the globe is filled with the vapor at the temperature of
the bath and at the atmospheric pressure. The neck
of the globe is sealed by fusion, the globe is removed
from the bath and again weighed.

REMARK. By certain alterations, this method may be
used also for very high temperatures, the glass globe being
replaced by one of porcelain. The Dumas method has
the disadvantage that liquids are often mixed with small
quantities of substances having higher boiling-points ; as a
result the impurities play an important part in the final
state.

c. Gay Lussac s Method, modified by Hoffmann.
This is used for liquids having a low boiling-point. A
little flask, weighed first empty, then filled with
liquid, fused shut, and again weighed, is introduced
into the Torricellian vacuum of a graduated barometer.
The latter is surrounded by a jacket into which is led
the vapor of a boiling liquid. The substance is thus
transformed into vapor, the flask bursts, and the mer-
cury falls in the tube. The volume is then read off
by the graduations on the tube; the pressure of the
vapor is the atmospheric pressure minus the column of
mercury remaining in the tube; the weight is already
determined, and the temperature is that of the vapor
in the jacket.

d. Victor Meyer s Method. (Air-displacement
Method.) In this method the volume of the vapor is
not measured directly, but the
volume of air displaced by the
vapor is determined.

A long glass tube ec, having an
elongated bulb on its lower end,
is provided with a side tube d.
The jacket #, which surrounds the
greater part of the tube, contains
a liquid, the vapor of which on
boiling heats the part c to a con-
stant temperature. The opening
e is closed with a stopper, while d
extends into a vessel filled with
water, in which stands the gradu-
ated tube /, likewise rilled with
water. The liquid in a is heated
to boiling; the vapor surrounds
the bulb c\ the air in the latter
expands and escapes through d
until the expansion ceases. The
end of d is now brought under
the opening of /and, by remov-
ing the stopper, there is quickly
dropped into the tube through e
a little bottle containing a known
quantity of the substance the gas
density of which is to be deter-
mined, and the stopper is re-
placed immediately. The substance is now vapor-
ized in the lower part of the apparatus and a volume

of air corresponding to the volume of vapor is dis-
placed ; this volume of air escapes through the con-
necting tube d into /. When the substance is
completely vaporized the escape of air-bubbles ceases.
Now since the gas has displaced an equal volume of
air, the volume of the air is exactly equal to the
volume of the gas if this were to be cooled under
atmospheric pressure to the temperature of the room.
The volume of the air is suitably measured, the
pressure and temperature are noted, and the former is
decreased by the vapor pressure of water at the tem-
perature of observation. After the weight, pressure,
temperature, arid volume have been determined in this
manner, the weight of one liter of the vapor at o°
and 760 mm can be readily calculated.

Example. In a gas-density determination by
Victor Meyer's method 0.184 gram of a liquid was
vaporized and at the end of the operation 37.5 cc
of moist air were obtained. The height of the
barometer was 752 mm, the temperature of the room
14° C.

What is the gas density of the substance ?

The total pressure of air and water-vapor is 752
mm. But since the vapor pressure of water at 14° is
12 mm, the pressure of the air must be equal to 740
mm. At o° and 760 mm the volume of the air is
accordingly

740
37-5 X X - = 35 cc,

and this is equal to the volume of 0.184 gram of the
vaporized substance at o° and 760 mm. Therefore one

liter of this substance at o° and 760 mm has the
weight

0.184
1000 X gram = 5.3 grams.

The gas density accordingly is '— - = 59.

o.Ooo,o

REMARK i. When it is desired to determine the gas
density with only relative accuracy the Victor Meyer
method is usually employed ; in most cases a relatively
accurate determination of the gas density is sufficient for
chemical purposes.

As is evident from the description of this method, it is
not necessary to know the temperature of the bath, the only
requirement being that it be sufficiently high to effect the
complete vaporization of the substance under investigation.
If the tube ec is constructed of suitable material, this
method can be used for very high temperatures.

§ 14. Abnormal Gas Densities. Most gases and
vapors are so constituted that the volume occupied by
a given weight of the substance can be measured at
certain temperatures and pressures, and, after being
reduced to o° and 760 mm, for the same substance
always give the same value. Each substance has a
corresponding gas density, independent of the tem-
perature or pressure at which the measurements are
conducted. This rule holds good for all substances
which within certain limits of temperature and pres-
sure obey the law of Boyle-Gay Lussac.

There are, however, certain substances, as nitrogen
dioxide and acetic acid, which behave differently;
their gas densities are dependent upon the tempera-

tures and pressures employed. For such substances
there exists at low temperatures a maximum value for
the gas density, and at high temperatures a minimum
value, which does not alter on further increase of tem-
perature. These latter constant values are accepted
as the correct values for acetic acid and similar sub-
stances. Of certain other gases the density is con-
stant for a considerable range of temperature, but
decreases at still higher temperatures. Chlorine is
a gas of this nature. Especially noteworthy is the
behavior of sulphur, the gas density of which at 464°
is about four times greater than at 1 100°, and which
suffers no change between 1100° and 1700°.

The anomalies just mentioned are called abnormal
gas densities. An explanation of this behavior will
be given in the following. (See § 17, Rem. 5. Comp.
also § 21, Rem. 3.)

§ 15. On the Nature of Gaseous Bodies. Mole-
cules. Atoms. In physics and also in chemistry the
following conception is employed : a gas consists of
a great number of very small particles moving in
straight lines through space. Each of these particles,
called molecules, has the same chemical composition
as the entire mass of the substance. If the gas is a
compound, then the molecule consists of hetero-
geneous parts, each of which is composed of a single
element. These parts are called atoms ; according to
our present knowledge of chemical phenomena the
atoms in a chemical or physical respect are not further
divisible. The molecules of gaseous elements are also
composed of atoms which in this case are similar to
one another. The volume of the molecules them-

selves is small in comparison to the space in which
they move.

REMARK i. The theory of the constitution of liquids
has not been so far developed as that of gases. Still less
work has been done on the molecular theory of solid sub-
stances.

REMARK 2. The existence of atoms was assumed by
Demokritos as early as the fourth century B.C. Modern
chemistry is indebted chiefly to Laurents, whose work dates
from the middle of the present century, for the distinction
between the conceptions, atom, molecule, and equivalent.

§ 1 6. Avogadro's Hypothesis. In equal volumes
of different gases at the same pressure and the same
temperature there is an equal number of molecules.

REMARK i. This hypothesis was enunciated by Avogadro
in 1811 and by Ampere in 1814, but was not recognized by
many chemists as the foundation of a system until the latter
half of the present century.

§ 17. Deductions from Avogadro's Hypothesis.

a. Molecular Weight. The relation by weight be-
tween two equal volumes of different gases, under
similar conditions of temperature and pressure, is the
relation by weight between one molecule of the one
substance and one molecule of the other. If the
weight of one molecule of hydrogen is assumed to be
2, then the weight of one molecule of other gases is
equal to their molecular weight.

The molecular weight is therefore a ratio, which
expresses the relation between the weight of one
molecule of a substance in a gaseous condition and
the weight of one half-molecule of hydrogen. The
molecular weight may also be denned as twice the

quotient of the weight of one liter of the substance,
in a gaseous condition at o° and 760 mm, divided by
0.0896 gram.

Briefly stated : The molecular weight of a substance
is equal to twice its gas density. (Comp. § 12.)

REMARK i. The indefinite number 2 taken as the mo-
lecular weight of hydrogen is not an experimentally deter-
mined value, but is a conventionally assumed out ; therefore
all molecular weights which are used in chemistry are only
relative numbers. The determination of the absolute mo-
lecular magnitudes belongs to physics ; chemistry for the
investigation of its problems requires only relative numbers.

REMARK 2. The molecular weight of only those sub-
stances which vaporize without decomposing can be deter-
mined directly. Comp. § 21, Rem. 3.

REMARK 3. The weight of one liter of a substance in the
gaseous state can be determined directly from the molecu-
lar weight ; it is equal to one-half of the molecular weight
multiplied by 0.0896 gram.

REMARK 4. The molecular quantity of a substance is the
number of grams of the substance, which contains the same
number of units as the molecular weight.

Often this quantity is also called a gram-molecule of the
substance.,

REMARK 5. Explanation of the Existence of Abnormal Gas
Densities. Substances the gas densities of which vary with
the temperature vary also in molecular weight. This may
be explained by assuming that the structure of the mole-
cules is more complicated at a low temperature than at a
higher temperature, and that on an increase in temperature
the structure becomes simpler. This explanation of the
phenomenon is supported by the fact that the specific heats
of substances with abnormal gas densities are very great and
are variable ; only a portion of the heat added goes to in-
crease the temperature ; the rest is used for breaking down

the complicated molcular structure into a more simple one.

§ 18.

b. Atomic Weight. Theoretical and Experimental
Definition. The atomic weight of an element is the
weight of one atom of the element with respect to a
half-molecule or one atom of hydrogen.

REMARK i. An atomic weight also is only a ratio, i.e., a
relative quantity.

REMARK 2. In the table given in the back of this book
the unit taken for the atomic weights is, for certain reasons,
not the atom of hydrogen, but is one sixteenth of the atom
of oxygen. The value there given for the atomic weight of
hydrogen is accordingly 1.007. If all tne atomic weights in
the table are divided through by 1.007, their values with re-
lation to one atom of hydrogen are obtained.

The atomic weight of an element is the greatest com-
mon divisor of the different quantities of this element
which are present in molecular quantities of its com-
pounds.

Example :

I. Compounds of oxygen.

Name. Molec. Quant. Quant, of Oxygen.

Oxygen 32 32

Water 18 16

Carbonic oxide 28 16

Carbon dioxide 44 32

Sulphur dioxide 64 32

Sulphur trioxide 80 48

Nitric acid 63 48

Arsenic trioxide — ... 396 96

Greatest common divisor = 16 = atomic weight of
oxygen.

II. Compounds of chlorine.

Chlorine 71 7l

Hydrogen chloride 36.5 35.5

Methyl chloride 50.5 35-5

Ethylene dichloride.... 99 71

Chloroform 119.5 106.5

Carbon tetrachloride... 164 142

Greatest common divisor = 35.5 = atomic weight
of chlorine.

REMARK 3. The existence of a greatest common divisor
is in conformity with the law of multiple proportion, but is
not deduced from it. If molecular quantities of different
compounds of the elements A and B all contain equal quan-
tities of A, then the law of multiple proportion requires that
there shall be a greatest common divisor for the correspond-
ing quantities of B. But the other condition is not con-
tained in the law. The existence of these greatest common
divisors, which are the virtual foundations of the atomic
weights, is not a circumstance which can be assumed from
any of the earlier mentioned laws, but is a fact derived
from experience.

It is evident that the atomic weight of an element must
be changed if a new compound of it is discovered, the
analysis of which leads to the finding of another greatest
common divisor.

REMARK 4. Other methods for the determination of the
atomic weight will be considered later. In these, however,
the truth of Avogadro's hypothesis is accepted, so that the
results obtained by them in no way diminish the value of
the atomic weights obtained by the methods just described.
If the number of volatile compounds of an element is small,
much importance cannot be attached to the greatest com-
mon divisor, and other methods are required for determin-
ing and comparing the atomic weights.

REMARK 5. To determine the composition of molecular
quantities of a substance it is not necessary to analyze these
quantities. The numbers are calculated from the percent-
age composition of the substance and from the gas density.

REMARK 6. The greatest common divisor here mentioned
is a number the accuracy of which is dependent upon that
of the molecular weight and also upon that of the gas densi-
ty. The latter is indeed not very great ; but the degree of
the number sought is determined by the greatest common
divisor, and with the knowledge of this degree the number
can be accurately determined, since choice can then be
made from a great number of possible values, all of which
may be determined with great accuracy. If the analysis of
pure hydrogen chloride shows that the substance contains
35.46 grams of chlorine to i gram of hydrogen, and the
molecular weight is found to be 36.5, then the atomic weight
of the chlorine can only be either 35.46 or a rational frac-
tion of this number. The greatest common divisor is, how-
ever, of the degree 35.5, and it therefore directly follows
that the accurate atomic weight is 35.46.

REMARK 7. The molecular weight determined from the
gas density is only approximately accurate. Since this is
the case, it also is corrected with the help of analytical data,
as will be described later (comp. § 21).

§ 19-

c. Number of Atoms in the Molecule. When the qual-
itative and quantitative composition, the molecular
quantity, and atomic weights of the elements of a
compound are known, the number of atoms in the
molecule can be easily determined. This is done by
dividing the quantities of the elements which are
present in the molecular quantity of the compound by
the atomic weights of the corresponding elements.

Example. The molecular quantity of ethyl

alcohol is 46 grams ; these 46 grams contain 24 grams
carbon, 6 grams hydrogen, and 16 grams oxygen.
The atomic weights of carbon, hydrogen, and oxygen
are, respectively, 12, I, and 16. The ethyl-alcohol
molecule therefore contains 2 atoms of carbon, 6
atoms of hydrogen, and I atom of oxygen.

The molecular quantity of oxygen is 32. There are
accordingly 2 atoms in the molecule.

The molecular quantity of phosphorus is 124, the
atomic weight is 3 1 ; the number of atoms in the mole-
cule is therefore 4.

REMARK. Certain reactions lead to the determination of
the number of atoms in the molecule, without involving
the investigation of the molecular quantity or the atomic
weights.

One liter of chlorine and one liter of hydrogen combine
to form two liters of hydrogen chloride. If chlorine and
hydrogen were both monatomic gases, the total number of
molecules after the reaction had taken place would be only
half the number in the initial condition; and accordingly —
from Avogadro's hypothesis — the volume of the hydrogen
chloride would be only half the entire volume of the react-
ing gases. If, however, it be assumed that chlorine and hy-
drogen, as well as hydrogen chloride, are composed of dia-
tomic molecules, then the number of molecules and also the.
volumes of the gases will undergo no alteration. It is a fact
that in the reaction mentioned no contraction in volume
takes place.

This may also be stated as follows : one liter of hydro-
gen occupies after the reaction a volume of two liters ; each
molecule has therefore split up into two halves.

Similarly to this may be viewed the formation of 2 liters
of water-vapor from 2 liters of hydrogen and i liter of

oxygen, and also the decomposition of 2 liters of ammonia-
gas into i liter of nitrogen and 3 liters of hydrogen.

From these facts it can be assumed that hydrogen,
chlorine, oxygen, and nitrogen are not monatomic, but are
at least diatomic. Nevertheless such speculation does not
lead to positive conclusions ; since theory and fact would
also agree if the number of atoms in the mclecule was
greater than two. It is therefore better to solve the problem
with the help of the molecular quantities and the atomic
weights.

§ 20.

d. Number of Atoms in the Molecules of the Ele-
ments. Many substances in the gaseous state are
diatomic, i.e., nitrogen, hydrogen, oxygen, chlorine:
Na, Ha, O,, Cla.

Phosphorus- vapor at 1040° is P4, at still higher
temperatures it breaks up partially into Pa. Sulphur-
vapor at the boiling-point of sulphur is S8, at higher
temperatures the molecules split up into molecules S,,
which are stable at the highest temperatures. Mon-
atomic are: potassium, sodium, zinc, cadmium, and
mercury: K, Na, Zn, Cd, Hg.* The gas densities of
the first four monatomic elements mentioned are de-
termined at very high temperatures, and their atomic
weights are not deduced from the molecular quantities
of the compounds, but are found in another way.

The vapor density of mercury is 100, while the
molecular quantity is 200. The volatile compounds
of this element which have been investigated all con-
tain 200 grams of this element in molecular quanti-

*It is possible that the recently discovered argon is to be
counted among the monatomic elements.

ties of the compounds. The number of these com-
pounds is not large, and from this it might perhaps
be doubted that mercury was in fact monatomic. But
the specific heat of solid mercury also leads to the
atomic weight 200 (comp. § 24), and the researches of
Kundt on the velocity of sound in mercury-vapor have
shown that the so-called factor of Laplace for this gas
is 1.67: according to the kinetic theory of gases, this
value for this factor belongs to a monatomic gas.

§21.

e. Deduction of the Molecular Formula of a Sub-
stance. The molecular formula of a substance ex-
presses by certain symbols its qualitative and quan-
titative composition, as well as the number of atoms
which, when the substance is in the gaseous state, are
present in the molecule.

These symbols have already been used in this book.
The elements are represented by letters, and each
symbol denotes not only an element, but also its
atomic weight. Furthermore, the formula gives the
gas density, since this is equal to one-half the sum of
the weights of the atoms.

The substance H2SO4 for example contains to 2
grams of hydrogen 32 grams of sulphur and 64 grams
of oxygen ; its gas or vapor density is 49.

The deduction of the molecular formula from ex-
perimental data will be illustrated by an example.

The analysis of acetic acid has shown that 100 parts
of this substance contain 39.9 parts of carbon, 6.7
parts of hydrogen, and 53.4 parts of oxygen. The
atomic weights are: C = 12, H = I, O = 16. The
value 30.5 has been found for the vapor density.

From the latter fact it is assumed that the molecular
weight is equal to about 61.

With the help of the atomic weights the relative
composition is determined in the following manner:

The formula must have the form C^H^O,. and the
substance therefore contains \2p parts carbon, q parts
hydrogen and i6r parts oxygen. The quantities
stand in the proportion 39.9 : 6.7 : 53.4, and the
formula Cao.9Ha.,OM.4 represents the results of the

~77 TT

analysis. From this the formulas C3.mH6>7Os.837 and
CHt0ffcO,,M4 are derived. The latter may be rounded
off to CHaO.

The results of the analysis are accurately expressed
by the formula CHaO ; but by this alone its correctness
is not established, since the formula C^H^O^ would
also be in agreement with the results obtained. All
that may be correctly assumed, therefore, is that the
substance has a formula of the form C^H^O^.

A substance having this formula would give the gas
density \^x. By experiment the gas density was
found to be 30.5 ; therefore x = 2 and the formula of
acetic acid is C,H4Oa.

This example illustrates what has been stated in §
18, Rem. 6, namely, that it is necessary to determine
the gas density with only relative accuracy. A value
is required which will decide by what factor the sim-
plest formula, in this case CH2O, is to be multiplied.

Therefore in order to obtain the molecular formula
from the experimental data, the following operations
are necessary : the percentage composition of each ele-
ment is divided by the corresponding atomic weight ;

the quotients thus obtained are made into round num-
bers ; the imaginary gas density of the simplest formula
thus obtained is divided into the gas density deter-
mined by experiment; the quotient expressed in round
numbers is multiplied into the simplest formula.

Problems. An attempt should be made to solve
the following problems :

1. An organic compound has the following compo-
sition :

C = 51.9*

H= 13*1

0-35

The gas density is found to have the value 22.7.
What is the molecular formula of the substance?

2. A hydrocarbon contains

92$ of carbon
and 7.7$ of hydrogen.

The gas density is 38.8. Determine the molecular
formula.

3. A substance contains in 100 parts

73.8 parts carbon,
8.7 parts hydrogen,
17.1 parts nitrogen.

The gas density is 80.2. Determine the molecular
formula.

REMARK i. If the molecular quantity can be determined
by another way than by the gas density, it is likewise pos-
sible to arrive at the molecular formula.

The molecular formula gives the gas density and
the results of analysis, and in addition the number of

atoms of each element in the molecule, but not the
grouping of the atoms. This arrangement of the atoms
must be shown, however, when two substances are
different and yet have the same molecular formula.
This condition occurs frequently in organic chemistry
and is called isomerism. The representation of the
arrangement of the atoms in the molecule makes it
possible to express the behavior of the substance in
many reactions.

A formula in which the grouping of the atoms is
shown is generally called a constitutional formula ; it
may also be called a structural formula; and while too
great importance must not be attached to such a for-
mula,— since not all reactions lead to the same con-
clusions with regard to the grouping, and the question
often arises as to which reaction shall determine the
constitution, — in practical chemistry the need of such
formulas is very great, since they at all events express
many relations of the substances to one another.

Example. Ethyl alcohol and methyl ether are
isomers, the molecular formula for both being C2H,O.
The first of these substances is attacked by sodium
with the evolution of hydrogen and the formation of a
substance, sodium ethylate, whose composition is rep-
resented by the formula C2H6ONa. Sodium has no
action on methyl ether. If to the alcohol the struc-
tural formula (CaH5)OH be given, to the ether the for-
mula (CH3)2O, then the chemical difference mentioned
as existing between the two bodies is expressed, and
according to these formulae an analogy exists between
alcohol, (C9H6)OH, and water, HaO, which explains

the action of sodium. No such analogy is found in
the structural formula (CH8)aO.

Acetic acid and methyl formate are isomers having
the molecular formula C,H4O2. By the action of
sodium on acetic acid one hydrogen atom may be
substituted by sodium ; methyl formate, however,
allows no such substitution ; on heating with sodium
it is decomposed and is transformed into methyl
alcohol and sodium formate. This difference in be-
havior towards sodium is found expressed in the
formulas C,H3O.OH for acetic acid and HCO.O.CH,
for methyl formate.

The separation of the atoms into groups is carried
still further, and ethyl alcohol, for example, is repre-
sented by

CEEH, C = H,

I I

C = H, and acetic acid by C = O.

OH OH

The meaning of the dashes in these formulae will be
explained later (see § 22).

In the substances mentioned above it is sufficient to
show only the grouping of the atoms; but in many
cases this method of writing the formulae is not
adequate to express the difference of the isomers, and
it is necessary to determine also the spacial relations
of the groups in the molecule, and to represent the
molecule as a figure of three dimensions, and not as a
flat figure, whose parts lie in one plane, for example
a piece of paper.

With this point in view Van't Hoff and Le Bel have

proposed (1877) a theory which makes it possible to
explain many important cases of isomerism and to
denote them by formulae. One of the most important
propositions of this theory will here be stated and
explained.

There are cases where two substances have exactly
the same chemical properties and are both represented
by the same constitutional formula, but which differ
from one another in that in solution one of them
rotates the plane of polarization of polarized light to
the right, the other to the left, and both with an equal
intensity. These phenomena are in accord with the
following rule : if in the constitutional formula for the
molecule of an organic compound a carbon atom —
combined with four dissimilar atoms or groups —
appears, then the compound is optically active, and
exists in two modifications, one of which rotates the
plane of polarization just as far to the right as the
other to the left.

Example. The following is the constitutional
formula of malic acid :

C03H

HO— C— H

C03H
The carbon atom of the alcohol group

HO— C— H is

a so-called asymmetric carbon atom ; it is attached to
four dissimilar groups: (CO,H), H, (OH), and
(CH2CO3H); malic acid is therefore optically active.

Tartaric acid has the constitutional formula
C02H

H— C— OH
H— C— OH*
CO»H

In this substance there are therefore two asym-
metric carbon atoms; it is optically active.

As already stated, the presence of an asymmetric
carbon atom requires the existence of two active
modifications; there appears, however, in addition to
the first two, still another — an inactive modification —
which is formed by the combination of the two active
modifications. An important example of this double
molecule — which is ordinarily formed when the sub-
stance is artificially prepared — is racemic acid, which is
inactive, and results from the combination of dextro-
and laevo-tartaric acids. An inactive substance of this
nature can always be decomposed into its active con-
stituents.

There exists still a fourth modification of tartaric
acid, in addition to the two active compounds and
racemic acid, which, like racemic acid, is inactive, but
which can not be decomposed. Still this fact is not in
contradiction to the theory; since tartaric acid contains
two asymmetric carbon atoms, both having exactly
equal functions, the molecule being thus divided into
two exactly equal halves. Each half causes an exactly
equal rotation of the plane of polarization, and there-
fore the two, according to their geometric relations,

may both rotate the plane to the right, or both to the
left, or each in an opposite direction.

In the latter case a compensation of rotation occurs,
and a molecule is obtained which cannot be decom-
posed although it is inactive.

The following is the explanation of the behavior of
active substances :

Van't Hoff represents an active compound by a
figure of three dimensions. The asymmetric carbon
atom is located at the centre of a tetrahedron, from
which point four forces are exerted towards the apexes
of the solid angles, and connect the asymmetric carbon
atom with the four groups situated at these apexes.
If the central carbon atom is actually asymmetric, then
the groups at the apexes of the figure are dissimi-
lar, and the substance has the formula C R, R, R, R4,
which may be represented by the two following
diagrams :

These two figures are not the same ; since it is not
possible so to superpose them that similar groups only
will come together. Further, neither one of them pos-
sesses a single symmetry plane; they are absolutely
asymmetrical. If, however, two of the four groups are
similar, a symmetry plane results, and the two figures
are then superposable.

The representation of the molecule as a tetrahedron
makes it possible to denote the optical isomerism in
the formula. The correspondence of the structure
with the optical activity mentioned above is in so far in
accord with the observed facts, in that all active sub-
stances have been found to contain one or more asym-
metric carbon atoms. The theory is further supported
by the fact that solid bodies, which possess the power
of rotating the plane of polarization, appear in the
form of asymmetric crystals.

REMARK 2. A molecular weight exists, strictly speaking,
only for such substances as may be volatilized without
decomposition. The molecular weight is deduced fr^m the
gas density, or else is determined by some other method —
i.e., from the osmotic pressure of solutions (§ 57, Rem.
4), or from considerations on the constitution. If the
molecular weight is unknown, the simplest formula which is
obtained by analysis is made use of, and this formula is
then nothing more than an expression for the qualitative and
quantitative composition.

REMARK 3. In the case of a number of substances whose
molecular weights are not determined from the gas density,
but are deduced from other data, the experimentally found
gas densities do not correspond with those calculated from
the molecular formulas. The molecular formula of am-
monium chloride, for example, is NH4C1. From this the
gas density should be 26.75. In practice a number equal
to about one-half of this value is actually obtained. This
is due to the fact that ammonium chloride cannot be con-
verted into a gas without decomposition, but on volatilizing
splits up into NH9 and HCL One molecule of ammonium
chloride on vaporizing therefore forms two molecules,
which — according to Avogadro's hypothesis — occupy a
double volume. In general this phenomenon will appear in

the case of substances which on volatilizing split up into
simpler molecules.

If it is desired to include also these cases under abnormal
gas densities, then it may be said that the gas density of a
substance is abnormal when it does not correspond to the
molecular formula. (Comp. 14, Rem. 5.)

REMARK 4. Quite recently it has been possible to gain
an idea of the size of the molecules of liquids from a theoret-
ical inquiry into the phenomena of capillarity. It has been
found that in the case of the molecules of liquids chiefly as-
sociation occurs — that is, the molecules of a liquid are gen-
erally complexes of molecules of the same substance in
gaseous form.

Associated are the liquid molecules of water, all alcohols,
glycols and organic acids, most ketones, propio-nitrile,
nitro-ethane, phenol, nitric acid, and sulphuric acid.

Non-associated, for example, are the liquid molecules of
CS9, N,04, SiCl4, PCVPOCl,, SaClQ,SOClt, SO.C1., Ni(CO)4,
C9H;8, CC14, C.H.I, CaH6SH, (CaH§)aO, CC1.CHO,

CH,CaHsO CH.
HCOOCH,, ClCOOC,Ht, || , || C6H8,

^ — ^ x — *" COOC2H6 COC1

C6H6C1, C6H,NOa, pyridine, quinoline.

It has been found also that the degree of association is
dependent on the temperature. In general on an increase
of temperature the size of the liquid molecule approaches
that of the gas molecule, and at relatively low temperatures
there exists in the solution an equilibrium between the asso-
ciated and the non-associated molecules. In the following
table the relation between temperature and association is
given for several substances:

— 89°. 8 C. +2o°C. ioo°C. i40°C. 2oo°C. 28o°C.

Methyl alcohol.. 2.65 2.32 2.08 1.97 1.81

Ethyl alcohol.. 2.02 1.65 1.39 1.27 1.09

Water 1.64 1.41 1.29

Acetic acid 2.13 1.86 1.72 1.53 1.30

Sulphuric acid at medium temperatures has the liquid
molecule (H,SO4)la; above 130° C. this breaks up into sim-
pler complexes.

§22.

/. The Valence of the Elements. The so-called
theory of valence has a direct bearing on Avoga-
dro's hypothesis. If an investigation be made to
determine how many atoms of any one element will
combine with one atom of a certain other element to
form a saturated compound, it will be discovered that
the power of different elements varies in this respect ;
this power is called the valence of the element ; it is
measured by the number of hydrogen atoms with
which one atom of the element in question can com-
bine to form a molecule.

Of equal valence or equivalent are those elements
the atoms of which can combine with a similar number
of hydrogen atoms ; equivalent are evidently also such
elements as combine with one another to form a com-
pound, one molecule of which contains a single atom
of both elements.

Univalent are, for example, chlorine, bromine,
iodine, since they form the compounds HC1, HBr, HI.
Bi- or di-valent are oxygen and sulphur: H2O, H,S.
Trivalent are nitrogen and phosphorus: NH3, PH8.
Tetra- or quadri-valent are carbon and silicon : CH4,
SiH4. Equivalent are chlorine, bromine, and iodine;
oxygen and sulphur; nitrogen and phosphorus ; carbon
and silicon.

Under certain conditions the valence may also be
determined from the number of atoms of other univa-
lent elements with which one atom of the particular

element can combine. Elements having a valence
greater than one cannot in general be used for the de-
termination of the valence, since in the case of such
elements a mutual compensation of the valences may
take place. Further, such elements often have a
variable valence, i.e., the element appears in different
compounds with different valences.

In ferrous chloride (Fed,) iron is bivalent, in ferric
chloride (FeCl3) it is trivalent. From the formulas of
nitrogen dioxide (NO3) and su1phur trioxide (SO,) the
valence of the elements nitrogen and sulphur cannot
be determined with certainty.

If the theory of valence was a logically deduced
and sharply defined conception, it would be possible
to obtain a priori a knowledge of the valence of an
element from the formulas of its compounds. In prac-
tice, however, the application of the theory is very
much affected by the exigence of variable valences
and unsaturated compounds. Also, it is not in general
the rule that the highest valence of the element ap-
pears in its most stable compound. MnCl4 is less
stable than MnCl,, while ferrous compounds, on the
contrary, are readily oxidized to ferric compounds.
Only in the cases of the saturated compounds of C, O,
and H can it be in general assumed that these ele-
ments are tetra-, di-, and uni-valent respectively, and
this fact alone makes it possible to determine the con-
stitution of a saturated organic compound from its
molecular formula.

The molecular formula C2H6O, for example, can be-
long to only two isomeric substances. The carbon and
the oxygen possess together ten valences, and of these

ten valences six only are required to satisfy the six
univalent H atoms. If six of the valences of carbon
are saturated by hydrogen, there remain only two more,
which may be used by the oxygen, and this gives the
formula H,C.O.CH3, which is the formula of methyl
oxide.

But if one of the valences of oxygen is satisfied by
hydrogen (and in this case the oxygen cannot be com-
bined with two hydrogens), then the other valence
must serve to connect the oxygen to the carbon. This
latter element then uses five of its eight valences for
hydrogen, one for oxygen, and the remaining two
compensate one another, resulting in the formula
HO.HaC.CH3, the formula of ethyl alcohol.

Problems, i. Determine the constitutional formu-
las of the saturated compounds the molecular formu-
las for which are C,H8O.

2. Determine the constitutional formulas of the sub-
stances having the molecular formula CaH4Oa, noting
that in each of these compounds one oxygen atom is
attached directly to carbon.

3. Determine the constitutional formulas of the sub-
stances with the molecular formula C3HflO3, it being
understood that all of these contain the carboxyl
group OC.OH.

The valences, also called affinity units, are usually
represented by dashes which extend from the symbols
representing the atoms. Methyl oxide may be repre-
sented thus;

H\ /H

H-C-0— C-H ,
H/ \H

and ethyl alcohol thus :

/H
C-H

/H
C— H

\0— H.

In the case of unsaturated carbon derivatives (by
this expression it is meant that the valences of the
carbon atoms are not saturated), their state is denoted
by connecting the carbon atoms by two or by three
dashes.

For example, ethylene

r/H

L\H C— H

; acetylene |||
r/H C— H

These relations, however, must not be confounded
with forces ; they denote nothing more than certain
unsaturated states, such as appear in the cases of
ethylene and acetylene. Also the expressions double
and triple bonds never imply the actual existence of
forces, but signify merely a certain state of saturation.

The tetravalence of carbon is the basis of the stereo-
chemical theory of Van't Hoff and Le Bel. The
manner in which the unsaturated compounds are
represented in this theory cannot here be further
considered.

§23.

g. Theoretical Demonstration of the Law of Gay-
Lussac on the Reactions of Gaseous Bodies. In § 5,
Rem. 4, it was shown how the coefficients of a

chemical equation may be determined. It was evi-
dent that entirely rational values can always be ob-
tained for the coefficients, and that every chemical
equation has the form

pAB + qCD + . . . = rAD + sBC + . . .,

in which /, q, r, s . . . are whole numbers.

Now if gaseous substances are represented in the
equation, it follows — since according to Avogadro's
hypothesis each molecule occupies one volume — that
the volumes of these substances are to one another as
their respective formula coefficients; and, since the lat-
ter are rational numbers, the volumes stand to one
another in ratios which may be expressed by whole
numbers.

Problems. I . One liter of methane, CH^ with the
required volume of oxygen, is burned completely to
carbon dioxide and water. What is the volume of the
oxygen and of each of the products of the combustion?

2. Ten grams of ethyl alcohol are burned in air.
What is the volume of the air required and what is
the volume of each of the products of combustion?
(Note. Air contains one-Wh cf oxygen by volume.)

CHAPTER IV.

THERMOCHEMISTRY.

§ 24. Law of Dulong and Petit. The product of
the atomic weight and the specific heat is the same for
all elements in a solid state ; it is equal to about 6.4.

REMARK i. This law was discovered in 1818. It may
also be expressed as follows : The atomic heat of all solid
elements is a nearly constant quantity.

REMARK 2. The deviation from the value 6.4 is so great
for certain elements, namely, for C, Si, B, and Be, that
these cannot be included under the law of Dulong and
Petit. However, the atomic heats of these elements ap-
proach the normal value if these be measured at high tem-
peratures.

At ordinary temperatures :

Element.

At. Wt.

Spec. Heat.

Atomic Heat.

9.1

o 408

O.2^8

2 6

O 12

I 44

28.1

O 1 7O

4.77

At higher temperatures :

Element.

At. Wt.

Spec. Heat.

Atomic Heat.

Q.I

o. 58

5.28

O. 5

c . e

O.45Q

e . c

Silicon at 2^2° C

28.1

o. 203

c .7

TABLE OF THE ELEMENTS

WHICH CORRESPOND WITH THE LAW OF DULONG AND PETIT.

Element.

Atomic Weigh
(in round
numbers).

Specific Heat.

Product or Atomic
Heat.

Lithium • • • •

o 0408

6 6

Sodium . ...

27.

O 2Q74

6 76

Magnesium ... • - -

24 4

O 24QQ

6 oo

Aluminium

o . 214

5 80

Phosphor us (yellow)
Sulphur (rhomb.)...
Potassium

31
32

O.I74-O. IgO
0.1776

o 165 5

5-40-5.87
5-70

6 47

Calcium

o 169—0 172

6 74—6 O

Scandium

44.

O. T 57

6 7

Chromium

o 1216

6 "32

Manganese

o 1217

6 69

Iron

o 1138

6 77

Cobalt

o 1067

6 •*«;

Nickel

O JOQ2

6 44.

CoDoer.

6-3 6

O.OG7— O OQ5

5Q— 6

Zinc

65 4

O. OQ56

6 26

7°

O O7Q

5c^

Arsenic

o. 0814

6 ii

o 0746

Bromine ....

o 0847

6 74

Zirconium

9°

o 0660

5Q4

Molybdenum

IO2

0.0722

0.06 I I

6.92
6 2T

IO3

0.058

5 08

Palladium
Silver

106

108 -

0.0593

O.O57O

6.28
6 15

Cadmium
Indium

112

113.5

0.0567

O,O565—O O574

6.36

6 42—6 57

Tin

118

0.0562

6 64

Antimony
Tellurium

1 20

125

0.0508
O O474

6.II

127

o 0541

"V4

6 86

138.5

O.O448

6 20

Cerium

140

0.0448

6 27

Tungsten . . .

184

O. O774

V.4 1

6 15

Iridium

197

o 0326

6-IQ

Platinum . . .

105

O O724

6 7i

Gold

IQ7

O.O724.

V.^l
60 -J

Osmium. . . .

191

o 031 1

Mercury (solid)
Thallium
Lead

200

204

2O7

0.0319
0.0336
O O7I4

6.38

6.86

6 4.O

Bismuth

208

o 0308

6 4O

Thorium ....

233

o 0276

6 41

239

O.O277

6 65

It is to be noted also that the specific heats of the allo-
tropic modifications of a solid element are different.

§ 25. Joule's Law. An element in a solid com-
pound has the same atomic heat as in the solid, free
condition.

REMARK i. This law was enunciated in 1844. It may
also be stated in the following manner : The molecular heat
of a compound is equal to the sum of the atomic heats of
the elements of which it is composed. Elements which are
exceptions to the law of Dulong and Petit show similar
deviations in the cases of their compounds. The law of
Joule makes it possible to determine, with reasonable accu-
racy, the atomic heats of such elements as cannot be exam-
ined in the free state. By subtracting the atomic heat of
silver from the molecular heat of silver chloride the atomic
heat of solid chlorine is found to be from 6 to 6.4.

In addition, the following values have been determined
from the molecular heats of compounds :

Element.

Atomic Weight.

Atomic Heat.

H dro en

I
I
16
14
19
35-5

2-3
5-9
4
6.4?

6.4

Hydrogen (from palladium-hydrogen)
Oxygen . . « • r

The law of Joule is also employed with good results in
the case of elements which cannot be prepared so pure or
in such quantities that their atomic heats can be directly
determined. Example : From the atomic heat of lead and
the molecular heat of PbCO, the heat of the group CO, is
obtained ; if this quantity be subtracted from the directly
determined molecular heats of BaCO,, SrCO,, and CaCO,,
the results obtained are the atomic heats of Ba, Sr, and Ca.

In this way the atomic heats of the following elements
have been determined :

Element.

Atomic Weight.

Atomic Heat.

8*. 4

6.4

87 «;

6 4

1-77

6 4

REMARK 2. The following rule was mentioned by Neu-
mann as early as 1831 : Equivalent quantities of chemically
similar substances have the same capacity for heat. Thus,
for example, the product of the specific heat and the mo-
lecular weight is very nearly constant in the case of calcite,
dolomite, magnesite, siderite, and calamine.

REMARK 3. As a proof of the constancy of the molecular
heat of analogous compounds the following table is given :

Substance.

Specific
Heat.

Molecular
Heat.

Substance.

Specific
Heat.

Molecular
Heat.

o 0746

18 5

HgCla

0.0689

18 7

CoAsS

Cu2S

o. 1070

O 12

I7.8
IQ. I

MgCla
MnCla

0.1946
O. 142S

18.5
18.0

FeAsS

16 e.

PbCla

o 0664

18 «;

SnCU

o 1016

AsS

O IIII

II .9

SrCla

O . I I QQ

iy .&
I9.O

CoS

c 125

II .4

ZnCl2

0.1362

18.6

Ff»S

H^S

• * J57
O O5I 2

1 1 .y

II Q

AffBr..

O O73Q

I<J Q

NiS

o 1281

ii 6

KBr

o 1132

1^ «?

PbS

O O5OQ

12.2

NaBr (impure).

o. 1384

14. q

c_ c

10 f\

ZnS

o 1230

12 .O

Acl . .

o 0616

Cul

0.0687

H*I

AgCl .

O O9 I I

J-7 . I

Hgl .

O.O3Q5

12 .Q

CuCl . .

o i--8q

1-1.7

O.oSig

13.6

HffCl

o 0521

12.3

Nal

O.O868

13 .0

ICfl

LiCl

• ' 7 Ju

o '>- r

1 ^' V
12. 0

Cu2O

O. Ill

15.9

NaCl
Rhf*1

12.5

HaO (solid)

0.474

8-5

NH4C1

O 'iT'?

20 o

CuO

O 142

ii ^

H^O

o 0518

11 2

BaCla

o 0^96

iS 6

MgO

O 276*

II .O

CaCla .

o 1 642

18.2

MnO

O . I K 7O

II .1

According to other statements 0.2439.

Substance .

Specific
Heat.

Molecular
Heat.

Substance.

Specific
Heat.

Molecular
Heat.

NiO

o 1623

12 I

K2SO4

o 1901

•J-3 T

PbO

o 0512

114

Na2SO4

O 23 12

•32 8

ZnO

0.1248

10. 1

(NH4)2S04

0.350

46.2

A 1 O

BaSO4

o. 108

oc 2

•friars

& c (~)

0.2173

22.3

CaSO4

o. 1966

26 7

BoOi

0.1279

25-3
16 6

CuSO4

0.184

29.3

r>: o

*J"J.3/4

r>R i

MgSO4

0.2216

26 6

Ff O

20.3

MnSO4

0.182

27 5

cu r\

r>f\ 1

PbSO4

0.0872

26.4.

20-3

SrSO4

o. 1428

26 2

TO R

ZnSO4

o. 174

0.159

13-8

SiO2

O IQI7

II 5

SnO2
TiO2

0.0933
O 1 1O1

14.0
14 o

CoSO4 -f7H3O.
FeS04 + 7H2O.

0.343
0.346

96.4
96.2

MgSO4+7H,O.

0.407

100. I

K2C03

0.2162

29.9

ZnSO4 + 7H2O.

0.347

99-7

NaaCO3

0.2728

28.9

KNO3

o 2^88

Rb3C03

0.123

28.4

NaNO3

24. i

23.6

BaCO3

o. 1078

21 2

W H4J\U3

0.455

36.4

CaCO3

o 2085

2O 9

BaN2O6

OT CO'?

<JQ g

PbCO3

o 0791

21 I

PbN2O6

O I IO

•?6 j

SrCO3

0.1448

21.4

SrN2O6

O.lSl

38.3

§ 26. Application of the Two Laws to the De-
termination of Atomic Weight. — When an element
forms no, or only a small number of, volatile com-
pounds, the atomic weight cannot be determined from
the gas density. The knowledge of the specific heat,
however, leads to the desired value, as is illustrated
by the following example :

The atomic weight of platinum is required. The
correct formula for the chloride is not known; it is
therefore represented by the formula Pt^Cl^. The
quantitative composition may then be expressed by

the formula Pt^Cl ; from the analysis it is known that

i
35.5 grams of chlorine occur with 48.6 grams of

platinum. The specific heat of platinum has been de-

termined, and has been found to be 0.0324; therefore

6.4
the atomic weight is of the order = 197.5.

The fraction - shall be a proportion between rational

numbers, and cannot in fact be far from - It is

evident that this fraction is equal to about J, and
therefore - is taken equal to J. The formula of plat-
inum chloride would then be PtCl4 and the atomic weight
of platinum 4 X 48.6 = 194.4. The accuracy of this
conclusion is not affected by the possibility that the
formula of platinum chloride may be a multiple of PtCl4.
The law of Joule may be applied in the following
manner in order, for example, to determine the atomic
weight of barium : I kilogram of lead combines with
0.0582 kilogram of carbon and 0.233 kilogram of
oxygen to form lead carbonate, the specific heat of
which is 0.080. The heat capacity of 1.2912 kilo-
grams of lead carbonate is 0.1033 calorie.'55' The
capacity of I kilogram of lead is 0.031 Cal., so that
0.0582 kilogram of carbon and 0.233 kilogram of
oxygen together have a capacity of 0.0723 Cal. The
same quantities of carbon and oxygen, however, com-
bine with 0.665 kilogram of barium to form 0.956 kilo-
gram of barium carbonate. The heat capacity of this
quantity of barium carbonate is o. 108 Cal. X 0.956 =
o. 1032 Cal. Therefore the capacity of 0.665 kilogram of

* I Cal. denotes a large calorie, i.e., the quantity of heat which
is required to heat I kilogram of water from o° to i\ A small
calorie is equal to one one-thousandth of this value and is de-
noted by c. The quantity of heat equal to 100 small calories is
denoted by K, In this book all values will be given in large
calories.

barium isO.O3O9Cal. and of I kilogram of barium 0.0465
Cal. From this the order of the atomic weight is

*-$— = 138 (approx.). In barium chloride 35.5 parts
0.0405

of chlorine are combined with 68.5 parts of barium.
If the substance is given the formula Bad,, then the
atomic weight of barium is 137, in sufficiently close
agreement with the value 138.

§ 27. Heat of Formation and Heat of Decom-
position of a Compound. Heat of Reaction. En-
dothermic and Exothermic Reactions. The heat of
formation is the number of calories which are set
free (or absorbed) when the molecular quantity of a
compound is formed from the elements. For ex-
ample, when 78 grams of sodium sulphide are formed
from 46 grams of solid sodium and 32 grams of solid
sulphur, and the products of the reaction are brought
back to the initial temperature of the experiment,
then the number of calories set free in the calorimeter
by this change is equal to 87 calories, and this
quantity is the heat of formation of sodium sulphide.
This fact is denoted by the equation

Naa,S = 87 Cal.

The meaning of the term heat of decomposition should
be evident from the above.

The heat of reaction is the quantity of heat which is
withdrawn from molecular quantities of reacting sub-
stances if after the reaction the system is again brought
back to the initial temperature. Thus 87 Cal. is the
heat of reaction of the change

2Na (solid) + S (solid) = Na3S (solid).

The heat of reaction is represented in the following
manner:

2Na (solid) + S (solid) = Na,S (solid) . . . + 87 Cal.

NaOH (dissolved) + HC1 (dissolved)

== NaCl (dissolved) + H,O . . . + 13. 7 Cal.
Na (solid) 4 HaO (liquid)

= NaOH (dissolved) + H (gaseous) . . . +43. 4 Cal.

REMARK i. The state of aggregation of the reacting sub-
stances must in most cases be stated, since the heat of re-
action is dependent on it. Thus

NaOH (dissolved) + HC1 (dissolved)

= NaCl (dissolved) + HaO (liquid) . . . + 13.7 Cal.,

while

NaOH (dissolved) + HC1 (gaseous)

= NaCl (dissolved) + H,O (liquid) . '. . -f 31 Cal.;

C (diamond) -f Oa (gaseous)

— CO2 (gaseous) . . . -f 94.3 Cal.,

C (charcoal) -f- Oa (gaseous)

= CO3 (gaseous) . . . + 97.6 Cal.

The physical state of the substance is generally denoted
by printing the formulae in certain styles of type. In this
book, however, it has been considered preferable to mention
the physical condition, as has been done in the above
equations.

An exothermic reaction is one in which heat is set
free ; an endothermic reaction is one in which, on the
contrary, heat is absorbed.

The reaction

2 H, (gas) +0, (gas) = H,O (liquid) . . .+ 136. 8 Cal.

is exothermic, but

N2 (gas) + 3C12 (gas) = 2NC1, (liquid) ... - 77 Cal.
is endothermic.

REMARK 2. If a reaction is to be considered only from
a calorimetric standpoint, it is not necessary to adhere
strictly to the molecular relations. Thus, for example, it if
allowable to write :

2H (gas) + O (gas) = H2O (liquid) .; . . + 68.4 Cal.

REMARK 3. In the case of certain important reactions
the quantity of heat evolved is denoted by a special name.
Thus, for example, it is customary to speak of the heat of
neutralization.

§ 28. Calorimetric Methods. To be suitable for
examination in a calorimeter reactions must possess
one important characteristic, namely: they must pass
from the initial to the final state in a relatively short
period of time. Suitable reactions can be divided into
two classes: first, those involving the formation and
the reciprocal action of salts, and the phenomena of
solution and dilution; and second, combustion re-
actions.

The mixing-calorimeter is a vessel, sometimes of
glass, but usually of platinum, into which the solution
of one of the reacting substances is introduced. The
calorimeter is protected from the variations in temper-
ature of its surroundings by an insulating jacket, and
is brought to the temperature of the room. A sensi-
tive thermometer is inserted in the liquid and is moved
continually. A second insulated receptacle, placed near
the first, contains a small glass flask, likewise provided
with a thermometer, and in this flask is contained the

second of the reacting liquids. It is only in excep-
tional cases that the mercury columns of the thermom-
eters are motionless ; but as soon as the movement of
the menisci is regular, the contents of the flask are
poured into the calorimeter, the whole is stirred
briskly, the extreme position of the thermometer-
column is noted, and the variation in temperature
from the extreme position is observed for the first few
minutes.

In order to carry out the calculation we must know:
the heat capacity, in water units, of the liquids, the
calorimeter and the thermometer; the position of
both thermometers at the moment of mixing; the
extreme position of the thermometer inserted in the
calorimeter ; and the quantities of the reacting sub-
stances. In addition to this, a correction must be
made for the variations in temperature before and after
mixing.

REMARK. In calorimetric investigations of the forma-
tion and interreaction of salts, the work is conducted
with very dilute solutions, which have no appreciable
heats of dilution. With such solutions it is allowable to
consider their heat capacity as equal to that of the water
contained in them. For determining heats of dilution, the
solution is placed in the calorimeter and the glass flask is
filled with water.

The heat of solution of a substance is determined
by introducing the substance into the calorimeter,
which in this case is filled with pure water.

The combustion-calorimeter consists of a vessel of
water containing another vessel in which the combus-

tion is conducted. Into this second vessel the gases
required for the combustion are introduced, and the
arrangement of the apparatus is such that the gases
formed by the combustion, on escaping, transmit all
of their heat to the water of the calorimeter.

In the explosion method the second vessel has the
form of a bomb. This is filled with compressed oxy-
gen and an explosion of the contents is produced with
the aid of an electric spark. This method may be
used for both liquid and gaseous substances.

§ 29. Law of Lavoisier and Laplace. Every
compound has a fixed heat of formation, which is
equal to its heat of decomposition.

It is only from the truth of the first part of this law
that we are placed in a position to speak of definite
heats of formation. The truth of the second part is a
deduction from the law of the conservation of energy.

§ 30. Law of Hess. The quantity of heat which
is evolved on the transformation of one chemical sys-
tem into another is independent of the intermediate
states through which the system passes.

Special case. The heat of formation of a substance
is independent of its method of formation.

Second formulation. The evolution of heat which
accompanies a certain chemical process is always the
same, whether the process takes place in a single step
or consists of a series of phases.

Example •

K (solid) + HC1 (dissolved)

= KC1 (dissolved) + H . . . + 61.8 Cal.

This process may take place in two reactions:

K (solid) + «HaO*
= KOH (dissolved) + H+(» - i)H3O ... +48.1 Cal.

and

KOH (dissolved) + HC1 (dissolved) j

= KC1 (dissolved) + H,O . . . + 13.7 Cal.

The sum of the heats evolved in the last two reac-
tions is equal to the heat evolved in the first.

REMARK. This law was enunciated by Hess in 1840. It
is also called the law of constant heat summation. It is a
special case of the law of the conservation of energy, and
can, when so considered, be formulated as follows : The
energy of a system of substances is a function of its state,
and not of the manner in which this state is attained ; or
also, the alteration in energy on the change of a system
from one state to another is dependent only on the initial
and final states, not on the intermediate states through
which it passes.

§31. Applications of the Law of Hess.

a. The heat evolved in a reaction is equal to the dif-
ference between the heat of formation of the products
and the heat of formation of the substances in the initial
condition.

That this highly important law is to be considered
as a deduction from the law of Hess is evident from
the following:

The given reaction is

AB + CD . . . = AC + BD . . . + q Cal.,

in which AB, etc., are compounds of the elements A,
B, C, and D. The left, as well as the right, member

*wH3O denotes a large quantity of water.

of the equation represents a form of the system
(A+B+C + D).

The first form may be represented by the reaction

..+r Cal.,
the second by

A+B + C + D = AC + BD. . . + j Cal.
According to the method of notation employed in § 27,
r = A, B + C, D, and s = A, C + B, D.

If we now pass to the form (AC -f- BD), first pass-
ing from the elements to the form (AB -|- CD), and
then carrying out a double decomposition with the
latter, then, according to the law of Hess,

r -j- q = s or q — s — r,
and finally

q = (A, C + B, D) - (A, B + C, D).

REMARK. If the reaction under consideration involves the
formation of a compound from its elements, then the heat
of reaction is the same as the heat of formation of the com-
pound, and this reaction is a special case of the law men-
tioned. Thus in the reaction

K (solid) + Cl (gas) = KC1 (solid) . . . + 105.6 Cal.

the heat of reaction 105.6 Cal. = the heat of formation of
KC1.

b. Determination of the Heat of Formation with the
Help of the Above Law. This law is of great im-
portance, since by it the heats of formation may be
determined for those substances which are either not

formed at all, or only with great difficulty, by the
direct combination of their elements. If such a sub-
stance enters into a reaction which takes place quickly
and can be examined in a calorimeter, and if the heat
of formation of the other substances which enter into
the reaction is known, then the heat of formation of
the substance in question can be deduced from the
heat of the reaction and the heat of formation of the
other substances.

Example :

Heat of Formation of KOH. The following reac-
tion is known :

K (solid) + H3O (liquid) + Aq*

= KOH (dissolved) + H (gas) + Aq+ 48.1 Cal.

From the above law

48.1 Cal. = K, O, H, Aq - H2, O (liquid).
But

2H (gas) + O (gas) = H,O (liquid) . . . + 68.4 Cal. ;
that is: Ha, O (liquid) = 68.4 Cal.

and K, O, H, Aq = 116.5 Cal.

On the solution of KOH in water we find

KOH + Aq = KOHAq . . . + 13.3 Cal.,
which gives
K, O, H = K, O, H, Aq - KOH, Aq = 103.2 Cal.

* Aq here denotes much. wa(er,

Heat of Formation of KC I. The direct formation
of potassium chloride from its elements cannot be ex-
amined in the calorimeter; the heat of formation can,
however, be deduced from the following reaction,
which may be readily carried out in the calorimeter:

KOH (dissolved) + HC1 (dissolved)

= KC1 (dissolved) + H,O . . . + 13.7 Cal.

According to the rule,

+ 13.7 Cal. = K,C1, Aq + H,O (liquid) -Cl, H, Aq

- K, O, H,Aq.

Of the quantities appearing in the equation only K,
Cl, Aq is unknown. If the known values are substi-
tuted in the equation, we obtain

13.7 Cal. = K, Cl, Aq + 68.4 Cal. — 39.3 Cal.

- 116.5 Cal.;

therefore K, Cl, Aq = + 101.1 Cai.
But KC1, Aq = — 4.4 Cal. ;

therefore K, Cl = + 105.5 Cal.

From the heats of formation of KC1, KOH, and
H,O that of KC1O may be easily calculated with the
aid of the reaction, readily examined in the calorim-
eter:

2KOH (dissolved) + 2C1 (gas)

= KCl(dissolved)+KOCl (dissolved) . . .+25. 4 Cal.

Heat of Formation of Ammonia-gas. The combus-
tion of ammonia-gas in oxygen may be readily ob-
served in the calorimeter:

2NH8(gas)+30(gas)

= 2N (gas)+ 3H,O (liquid) ... + 181.2 Cal. ;

3H,, O (liquid) = + (3 X 68.4 Cal.) = + 205.2 Cal. ;
therefore

N, H, = £(205.2 Cal. - 181.2 Cal.) = + 12 Cal.

Heat of Formation of Carbon Monoxide. This is
deduced from the combustion of diamond to carbon
dioxide and the combustion of carbon monoxide to
carbon dioxide:

C (diamond) + 2O (gas) = CO, (gas) . . . + 94.3 Cal. ;
CO (gas) + O (gas) = CO, (gas) . . . + 68 Cal. ;
therefore C, O = C, O, - CO, O = + 26.3 Cal.

Heat of Formation of Hydrocarbons. Of all hydro-
carbons only acetylene can be prepared directly from
its elements, but this reaction is not suitable for calori-
metric determination. Most hydrocarbons, however,
burn readily in oxygen ; usually also it is possible to
produce an explosion of the two gases, and in both
these cases the heats of combustion may be measured.
The products of the combustion are always carbon
dioxide and water, the heat of formation of both of
these substances has been determined, and therefore,
in the calorimetric equation for the combustion, the
only unknown quantity is the heat of formation of the
hydrocarbon in question,

The following, however, is an objection to this
indirect method : The heats of combustion of hydro-
carbons are large; their heats of formation, on the
contrary, are relatively small. As a result of this
an error (not avoidable even in the most careful
determinations of the heat of formation and relatively
large in comparison to this quantity) is introduced
into the value of the heat of formation, and this
therefore differs considerably from the correct value.

This drawback often explains the variations in the
results of the best investigators. Thus J. Thomsen
found the heat of combustion of ethane to be 370
Cal. ; Berthelot, on the other hand, obtained the value
390 Cal. — a variation of 5—6 per cent. If the heat
of formation of ethane is calculated from these two
values, that of Thomsen gives 23 Cal. and that of
Berthelot 4 Cal., two numbers which show great
divergence.

The measurements of the heat of combustion of
acetylene show a fairly close agreement :

C,H2 (gas) + 50 (gas)

= 2CO,(gas) + H20 (liquid) . . . + 315 Cal.;

2C, O,= +188.6 Cal.; H,, O (liquid) = + 68.4 Cal. ;
therefore C,H, = — 58 Cal.

Heat of Formation of Compounds which are composed
of Carbon, Hydrogen, and Oxygen. The heats of for-
mation of these compounds are deduced from their
heats of combustion, the latter being determined by

burning or exploding the compounds with oxygen.
The same difficulties mentioned above also occur here.
For the heat of combustion of methyl alcohol in the
form of vapor Thomsen found :

CH40 (vapor) + 30 (gas)

= CO, (gas) + 2H2O (liquid) . . . + 182.2 Cal. ;

therefore

C, H4, O (vapor)

- 182.2 Cal.+ (94.3+ 136.8) Cal. = + 48. 9 Cal.

c. Application of the Law for Predicting the Heat
of Reaction. In the above cases the heats of reaction
were used for determining the heats of formation ; on
the other hand, the former can be calculated if the
heats of formation of the substances taking part in the
reaction are known. And although it is not always
known whether the reaction is actually practicable, still
it can be stated in advance how great the heat of reac-
tion would be if the reaction did take place according
to a certain equation.

If it is known that

Ht, S, O4, Aq = + 210.9 Cal.
and Zn, S, O4, Aq = + 248.5 Cal.,

then in the reaction

Zn (solid) + H2SO4Aq = ZnSO4Aq + H, (gas)

a quantity of heat equal to -f- 37. 6 Cal. will be set free.
If it is found that

K, Cl (solid) = + 105. 6 Cal.
and K, I (solid) = + 80, i Cal.,

then in a -reaction which takes place according to the
equation

KC1 (solid) + I (solid) = KI (solid) + Cl (gas),

a quantity of heat equal to 25.5 Cal. will be absorbed.

REMARK. In the determination of the heats of formation
of gaseous substances the following conditions must be ob-
served : If the total volume of the products of the reaction
is not the same as that of the substances in the initial con-
dition, as is the case, for example, in the reactions

2NH, (2 liters) = N, (i liter) + 3H, (3 liters),

2C,H, (2 liters) -f 50, (5 liters)

— 4CO, (4 liters) + 2H,O (2 liters),

2H, (2 liters) + Oa (i liter) = 2HaO (2 liters),

then the experimentally determined calorimetric quantity is
a result, not only of the chemical action, but of the work
done in the displacement of the air on increase in volume.
If the initial and final conditions are compared, it will be
found that both internal and external work are performed
in this process. As a result the value of the heat of forma-
tion is often given at constant pressure, containing, in this
case, the equivalent of the external work, and also at constant
volume, where a correction for the external work has been
introduced. Generally, however, this correction is of slight
importance in comparison with the actual heat of formation,
and has therefore been neglected in the above calculations.

§ 32. Some General Results of Investigations on
Heat of Formation. Stable and Unstable Compounds.
In general those compounds are stable with respect to
heat and shock whose heats of formation are positive,
and the stability increases the greater the heat of
formation. A negative heat of formation is, on the

contrary, in most cases an evidence of instability.
Water vapor and hydrogen chloride, the heats of
formation of which are + 58 Cal. and + 22 Cal. re-
spectively, are decomposed at high temperatures only
to a very slight extent, and are entirely unaffected by
pressure or shock. Nitrogen chloride, on the other
hand, with a heat of formation of — 38 Cal., is ex-
tremely unstable and on the slightest jar decomposes
into chlorine and nitrogen. Many substances having
negative heats of formation behave, nevertheless,
under many conditions like stable compounds. Thus,
for example, acetylene, although its heat of formation
is — 58 Cal., may be subjected to many operations
without undergoing decomposition. Nevertheless this
substance has been shown to be unstable under the
combined action of a suddenly applied high pressure
and a high temperature.

Substances having a positive heat of formation and
undergoing partial decomposition at high temperatures
have the property of regenerating themselves from
their decomposition products on cooling; they exhibit
the phenomenon of dissociation ; the alteration which
they undergo as a result of the increase in tempera-
ture is reversible — i.e., one which increases with an
increase in temperature, but which decreases when the
temperature is again lowered. The result of this
action is that when the original temperature is again
reached the state of the system is the same as it was
in the beginning. In the case of substances having
negative heats of formation the decomposition, when
it has once appeared, is, on the contray, complete

and is not reversible ; the term dissociation is not used
to express the decomposition of this class of bodies.

REMARK. The heat of formation of a substance which
undergoes dissociation must be considered as a latent heat,
comparable to the internal latent heat of vaporization of
water. As a matter of fact it is really determined as an
actual quantity of heat, but nevertheless it appears in the
theory as a latent heat, i.e., as the quantity of heat which
must be added to the system in order that an alteration of
condition can take place isothermically.

In the study of the phenomenon of dissociation, when
reactions which take place at high temperatures are under
consideration, it is necessary to employ the heat of forma-
tion, which is determined at a lower temperature and is
equal to the heat of dissociation. This is necessary since
the dissociation can be observed and studied only at very
high temperatures. It is, however, very evident that the
value of the heat of formation is influenced by the tempera-
ture at which formation and decomposition occur.

Values of the Heats of Reaction. Compounds of a
halogen with different metals follow the rule that the
heat of formation is large for the compounds of the
so-called strongly positive metals, and is in fact larger
the more positive the metal. In general the chlorides
have a greater heat of formation than the bromides,
the bromides greater than the iodides. Oxygen stands
intermediate between chlorine and bromine; sulphur,
however, is exceeded by oxygen and iodine.

Strong acids in dilute solution all give with strong
bases exactly the same value for the heat of neutral-
ization, namely, + 13.7 Cal.

The mixing of dilute solutions of neutral salts

which give no precipitates usually causes no evolution
of heat (law of t her mo-neutrality].

The heats of combustion of the hydrocarbons differ
for two neighboring members of the series by about
+ 158 Cal. The same phenomenon is observed in
the case of many homologous unsaturated hydrocar-
bons and homologous alcohols; and, further, in the
case of homologous fatty acids a constant increase in
the value of the heat of combustion can be observed.

A series of tables follow in which special results of
thermochemical research are summed up.

Concerning the heat of combustion of organic
substances it is again mentioned that Thomsen's
results generally differ considerably from those of
Berthelot.

It must be further noted that the elements are
taken in those states of aggregation in which they
normally occur. Thus in H, Br = + 8-4 Cal. H is
gaseous, Br is liquid, and HBr is gaseous. In HaS
the octahedral sulphur is taken. In the case of the
hydrocarbon compounds the carbon is always con-
sidered in the form of diamond. Thus C, H,, Br
= + 1 1 .6 Cal. is to be understood

C (diamond) + Br (liquid) + 3H (gas)

= CH,Br(gas). . . +u.6Cal.

HEATS OF FORMATION OF CERTAIN COMPOUNDS
THE METALLOIDS AT NORMAL TEMPERATURE.

Substance.

Formation.

Heat Evolved.

Gaseous.

Liquid.

Solid.

Dissolved.

HC1
HBr
HI
HaO
Hap,

HaS
HaSe
HaTe
NH9
NHaOH
H,P
H,As
N,0
NO
N308
NO,
N204
Na06
HNO,

HaSaO,
SO,
SOS
HaS04
SeOa
H9Se04
TeO,
HaTeO4
H3POa
H3P03
P.O.
CO,

C0a
CO

C0a
H3P04
AsaO,
As,O6
BaO,

H, Cl
H, Br
H, I
Ha, O
Ha,0a
HaO, 0
Ha, S
Ha, Se
Ha, Te
N, H,
N, Hs, 0
H8, P
H,, As
N,. 0
N, 0
Na, O3

N, 0,
Na>04
N,, 05

H, N, O3
4(Na. 06, HaO)
Ha. Sa, 0,
S, Oa
S, 0,
S, O4, Ha
Se, 0,
Se, 04, Ha
Te, Oa
Te, 03, Ha 0
i(Pa, 0, 3H20)
i(Pa, 03, 3HaO)
P«, 0.
C, Oa
(C diamond)
C, Oa
(C amorph.)

C, 0

(C diamond)
CO, O
H3, P, 04
Asa,O,

Asa, 0.
Ba.O,

+ 22

+ 8.4
- 6.1

+ 58

+ 68.4

+ '69.8

+ 39-3
+ 28.4
+ I3.I

+ 45-3
- 23.1

-f 7-3
- 16.1

+ 2.7

- 25.4

- 35
+ 12

+ 20.4
+ 19.4

+ 4-3
- 44-1
- 17-4
- 21.5

- 6.8

— 7-7

- 2.6
0

+ I3.I

+ 29.8
+ 49.1
+ 14-9
+ 145-3
+ 78.8
+ 142.5
+ 210.9
+ 56.3
+ 145-2
+ 77-3
-f 93.5
+ 37-3
+ 125.2
+ 406
+ 98.2

+ 101.5

+ 41-9

H- 7-7

+ 71

+ 189.9

+ 103.3

+ 57-2

4- 94.3

+ 97-6
+ 26.3
+ 68

-f 37-5
+ "5.3
+ 370

+ 302.9
+ 154.7
+ 219.4
+ 317.2

+ 305-6
+ 147
+ 225.4

+ 335-a

HEATS OF FORMATION OF CERTAIN COMPOUNDS OF
THE METALLOIDS.— (Continued.)

Substance.

Formation.

Heat Evolved.

Gaseous.

Liquid.

Solid.

Dissolved.

ClaO
HC10,
HC104
BraO
HBrOs
1,0,
HIOS
HI04
CSa

C1I
C13I
SaCla
SOCla

soacia

SeaCla
SeCl4
TeCU
PC13
PC16
it

PCUO
AsCl,
BC1,

coo,

IBr
SaBra
PBr,
PBr6
AsBr,
Sala
Pah
PI3
AsI3

Cla, 0
H, Cl, 03
H, Cl, 04
Bra, O
H, Br, O8
It, 05

H, I, Oa
H, 1.04
C, S,

(C diamond)
Cl, I
IC1, Cla

Sa, Cla
S,0, Cl,
S, Oa, Cla
Se, Cla
Se, C14
Te, C14
P, C13
P, C16

PC13, Cla

P, C13, 0
As, Cla
B, Cla
(B amorph.)
C, 0, Cla
(C diamond)
I, Br
Sa, Bra
P, Br,
P, Br5
As, Bra
Sa, I,
Pa, U
P, la
As, I8

-I7.8

- 8.4
+ 24

4- 38.6

- 16.2
-- 12.3
-- 43-5
- 55-7
+ 47.6

+ i83.a

+ 18.3

4- 45-3
H- 57-9

-28.7

— 22.3

+ 5.8

+ 14-3
-f 49-8
+ 89.8

+ 22.2

+ "75" 5

+ 146

+ 71.5
+ 104

+"ii'.7

+ ' 46.2
+ 77.4

+ 105
+ 29.7

+ 52.9

+ 2.5

+ I

+ 44-8

+ 59- 1

+ 44-9
o

+ 19-8
+ 10.9

+ 12-7

The heat of solution of a substance is determined from the differ-
ence between the heats of formation of the same for the dry and for
the dissolved condition.

HEATS OF FORMATION OF CERTAIN COMPOUNDS OF

THE METALS.
A. OXIDES AND HALIDES.

Substance.

Heat of Formation.

Substance.

Heat of Formation.

Solid.

Dissolved.

Solid.

Dissolved.

K, H, O

+ 103.2

+ H6.5

Ca, 0

+ 131

+ M9-5

K3, 0

....

+ 164.6

Sr,O

+ 128.4

+ J57-7

Na, H,0

-f 101.9

+ in. 8

Ba, O

+ 124.2

+ 158.7

Naa. O

-{- IOO.2

+ 155.2

Ca, 03, H3

+ 214.9

+ 217-9

Li, H, O

....

f H7.4

Sr, O2,H,

+ 214-5

+ 226.1

N, H,, Aq

....

+ 20.3

Ba, O3) H3

+ 214.9

+ 227.1

Mg, 0

+ 144

....

Mg, 02, H3

+ 217.3

Al,, 0,,H6

+ 594

....

Ca, Br3

+ M0.9

+ 165.4

Mn, O, H30

+ 94.8

....

Ca,I3

+ 107.3

+ 135

Zn, O

+ 85.3

....

Ba, Cla

+ JQ4-7

+ 196.8

Zn, O, H2O

+ 82.7

«...

Ba, Br2

+ 170

+ 175

Cd, O, H2O

+ 65.7

....

'Sr.Cl,

+ 184.6

+ I95.7

Fe, O, HaO

+ 68.3

....

Sr, Bra

+ 157:7

+ 173-8

Fea, Oa, H,

+ 396.4

....

Mg, Cla

+ 151

+ 186.9

Ni, O, H3O

+ 60.8

....

Zn, Cl,

+ 97.2

+ 112. 8

Co, 0, HaO

+ 63.4

. i . .

Zn, Bra

+ 76

+ 91

Pb, O

+ 50.3

....

Zn, I,

+ 49-2

+ 60.5

Cu.O

+ 37-2

....

Mn, Cla

+ 112

+ 128

Cu3, O

+ 40.8

....

Fe, C13

+ 82.1

+ ioo

Aga, 0

5-9

....

Fe, Br3

+ 78.2

Hga, 0

+ 22

....

Fe, I,

....

+ 46.4

Hg, O

+ 20.1

....

Fe, C13

+ 96.1

+ 126.1

Sn,O, HaO

+ 68.1

....

Al, Cl,

+ 161

+ 237.8

Au2,0,,(H20)3

— 13-2

....

Al, Br,

+ II9-7

+ 205

Pt,0,HaO

+ 17.9

...

Al, I3

+ 70.4

+ 159-4

Co, Cl,

+ 76.5

+ 948

K, Cl

+ 105.6

+ JOI.2

Ni, Cl,

+ 74-5

+ 93-7

K, Br

+ 95-3

+ 90-2

Hg, Cl

+ 31-4

K, I
K, F

+ 80. 1

4- 109.5

+ 75
+ H3-I

Hg, Br
Hg, I

+ 24.1
+ M.I

....

Na,Cl

+ 97-6

+ 96-4

Hg, Cl,

+ 53-3

+ 'so

Na, Br

+ 85.8

+ 83.9

Hg, Bra

+ 40 5

Na, I

- 69 i

+ 70.3

Hg, I,

+ 24.2

....

Na, F

f 109

+ 108.4

Cu, Cl

+ 32.9

....

N, H4, Cl

H- 75-8

+ 7L9

Cu, Br

+ -5

....

N, H4) Br

+ 65.4

+ 61

Cu, I

+ 16.3

....

N, H4, I

4- 49-3

+ 45-8

Cu, Cl,

+ 51-6

+ 62.7

Li,Cl

+ 93-8

+ 102.2

Cu, Bra

+ 32.6

+ 40.8

Ca, Cla

+ 169.8

+ 187.2

Cd, Cl,

+ 93-2

+ 96-2

Cd, Bra

+ 75.2

+ 75.6

Au, Br

— O.I

....

Cd, I,

+ 48.8

+ 47-9

Au, I

— 5-5

....

HEATS OF FORMATION OF CERTAIN COMPOUNDS OF
THE METALS.— (Continued).

A. OXIDES AND HALIDES. — (Continued).

Keat of Formation.

Heat of Formation.

Substance.

Solid.

Dissolved.

Substance.

Solid.

Dissolved.

Pb, C12

+ 82.8

+ 76

Au, Cl,

+ 22.8

4- 27.3

Pb, Br8

-f 64.5

+ 54-5

Au, Br3

....

5-1

Pb, I,

4- 39-8

Sn, C12

4- 80.8

4- 81.1

Ag, Cl

H- 29-4

....

Sn, CU

4- 127.3

4- 157-2

Ag,Br

+ 22.7

....

Pt, C14

- 59-8

4- 79-4

Ag, I

4- 13-8

....

Pt, Br4

4- 42.4

4- 52.3

Au, Cl

4- 5-8

....

B. SULPHIDES.

K2, S

4- IOI.2

4- III. 2

Fe,S,«H2O

4- 23.8

....

K, H, S

4- 62.3

4- 63.1

Co,S,wH2O

4- 19-7

....

Na2, S

4- 87

4- 102

Ni,S,H20

4- 17.4

....

Na, H, S

4- 54

4- 58.4

Zn.S,«H2O

4- 39-6

....

Ba, S

4- 98.3

Cd,S,«H3O

4- 32.4

....

Sr, S

4- 97-4

....

Cu, S

4- 8.1*

. . . .

Ca, S

- 89.6

....

Cu2, S

4- 18.3

....

Mg, S

4- 77-6

....

Hg, S

- 4.8*

....

A12, S3

4- 122.4

....

Aga, S

4- 3.3*

....

Mn,S, wH,O

4- 44-4

....

Pb, S

4- 18.4

. • . .

C. OXY-SALTS.

Carbonates (C = diamond).

Mn, C, O3

4- 210.8

Ka, C, 03

4- 278.4

4- 284.9

Cd, C, 03

4- 179-2

....

Naa> C, O3

4- 269.9

4- 275.4

Ag2, C,03

4- 120.2

....

Ba, C, 03

4-280.5

Pb, C, O3

4- 166.9

....

Sr, C, 03

4- 277.5

....

K,H, C, 0,

4- 232.9

4- 227.6

Ca, C, 03

4- 267.7

—

Na, H, C.Os

4- 227

4- 223.7

*Not certain.

HEATS OF FORMATION OF CERTAIN COMPOUNDS OF
THE METALS.— (Continued.)

C. OXY-SALTS. — (Continued.)

Heat of Formation.

Substance

C K »

Solid.

Dissolved.

Solid.

Dissolved

Sulphates.

Ca,Na,O8,4HjO

+ 213.8

+ 206.6

K2, S, 04

+ 344-6

+ 338.2

Zn,Na,O6,6H2O

+ I38.I

+ 132.3

K, H, S, O4

+ 277-5

+ 273-7

Cu,N3,O6,6HaO

+ 93

+ 82.3

Naa, S, O4

+ 328.4

+ 329

Cd,N,,O.,4H,O

+ 121. 1

+ 116.1

Na, H, S, 04

+ 267.8

4- 266.6

Pb, Na, 06

+ I05-5

+ 97-9

Na, H8, S, 04

•f- 282.2

+ 279-7

Ag, N, 08

+ 28.7

+ 23.3

Mg, S, 04

+ 302.3

+ 322.6

Ba, S, O4

+ 338.I

....

Other salts.

Ca, S, 04

+ 318.4

Sr, S, 04

+ 331

K, O, Cl

+ 88.8

Zn, S, O4

+ 230

+ 248.5

K, Cl, O3

+ 95

+ 85

Mn, S, O4

+ 249.9

+ 263.7

K, Cl, 04

+ "3-1

+ 1OI

Co, S, O4

+ 230.5

K, Br, O3

+ 84.1

+ 74-3

Ni, S, 04

i • . .

+ 229.7

K, I, O3

+ 124-5

+ "7-4

Fe, S, O4

....

+ 235.6

Na, 0, Cl

+ 83.4

Cu, S, O4

+ 182.8

+ 198.4

Na, Cl, O3

+"86.8

+ 81.2

Cd, S, 04

+ 221.2

+ 231.9

Naa S, O3

+ 260. 5

+ 262.9

Aga, S, O4

+ 167.3

+ 162.8

Naa, Sa, 06

+ 398.9

+ 393-5

Pb, S, O4

+ 216.2

....

Naa, H, P, 04

+ 413.9

+ 419.5

N, H4, N, O3

+ 64.9

+ 60.2

Nitrates.

K, Mn, O4

+ 195

+ 184.8

Bi, Cl,

+ 90.6

K, N, 03

+ "9-5

+ in

Bi, O, Cl

+ 88.2

«...

Na, N, 03

-1- in- 3

+ 106.3

Naa,Pt,Cl66H2O

+ 288.3

+ 277-7

N, H4, N, 0,

4- 88

+ 8i.s

K, C, N

+ 29.8

+ 26.8

Ba, N9, O6

+ 226.2

+ 216.8

Na, C, N

+ 25.5

+ 25

Sra, N,, 08

+ 219.8

+ 215.2

Hg, Ca,Na

- 52

— 55

Ca, N,, 0.

Mg,Na,0.,6H,0

+ 202.6

+ 210.5

+ 206.6
+ 206.3

Ag, C, N
AgCN,KCNAq

— 31-2

+ "6.5

Sr, Ni, O,,4HaO

+ 227.7

+ 215.2

K, O, C, N

+ ' 34.3

+ 29.1

HEATS OF COMBUSTION AND HEATS OF FORMATION
OF SOME ORGANIC COMPOUNDS.

C — diamond.

Substance.

Formula.

Heat of
Comb.

Heat of

Formation.
Vol. const.

Observer.

SATUR/

LTED HYDR<

CH4
CaH9
C3H8
(CH3)3CH
(CH3)4C
C6H14
(normal)
C,H16
(normal)

ATED HVDl

C,H4
C3H6
C4H8
C6H10
C6H10
CaH3
C3H4

>GEN DERIV

CH3C1

C3H5C1
C3H7C1
C4HUC1
C,H3C1
CHC13
CC14
CH3Br
CaH8Br
C3H7Br
CbHMBr
C3H5Br
C,H4Bra
CH3I
C2H6I

>CARBONS.

+213.8
+ 370.5
+ 529.2
+ 687.2
+ 847.1
+ 989-2

+ II37-5
IOCARBON

+ 333-4
+ 4Q2-7
+ 650.6
-f 807.6
+ 932.8
+ 3i5.o
+ 467-6

ATIVES.

+ 164.8

+ 32L9
+ 480.2

+ 637.9
+ 286.2

+ 70-5

+ 184.7
+ 341.8

+ 499-3
+ 462.1

+ 201.5
+ 359-2

+ I6.5
+ 22.1
+ 25-4
+ 29.1
+ 3L5

+ 53-2

Thomsen
«

Stohmann

Lougui-
nine

Thomsen
if

Berthelot
Thomsen

Thomsen

Berthelot
Thomsen
Berthelot

Thomsen
«

Propane • •

UNSATUB

- 12.8

- 6.0
- 1-9
+ 3-1
-27.8
- 58
— 48.9

+ 19-2
+ 24-2
+ 27.8
+ 32.2
- 7-9
+ 20.9
+ 18.4
+ ii. 6
+ 16.6

+ 21. 1

+ 27.1
- 9-6

+ 15
- 4-7
- 0.6

Amylene (gaseous)

Diallyl

Allylene

HALC

Ethyl "

Butyl "

Vinyl "

Chloroform • • . •

Carbon tetrachloride . . . .

Ethyl "

Proovl "

Amyl

Allyl "

Ethylene bromide (gaseous)
Methyl iodide . .

Ethyl iodide

HEATS OF COMBUSTION AND HEATS OF FORMATION
OF SOME ORGANIC COMPOUNDS.— (Continued.}

Substance.

Formula.

Heat of
Comb.

Heat of
Formation.
Vol. const.

Observer.

ALC

:OHOLS (Ga
CH3OH
C2H5OH
C3H7OH
C4H9OH
C5HMOH
C3H5OH
C3H3OH
ACIDS.
CH202
C2H402
C3H602
C10H2002
C12H2402
C14H2,02

seous).
-f 182.2
+ 340-5
-f 498.6
+ 658 5
-h 820.1
+ 464.8
+ 43I-I

+ 69.4
+ 225.4
+ 386.5
f- 1455.6
f 1747-6
+ 2052 9
+ 2361.9
+ 2677.8
4- 60.2
+ 207.3
+ 356.8
4- 261.8

INCES.

+ 349-4
+ 659.6
+ 396.8
-f 281.9

4- 158.6
+ 259.6
+ 312.1
+ 258.3
+ 420.5
+ 152.2
4- 298.8

• + 787.8

+ 73L9
+ 770.5
+ 771-9
+ 729-5
+ 610 6

+ 1352.7
4- 678.0
4- 677.5

+ 47-9
+ 51-5
+ 56
+ 57-5
+ 58
+ 21.6

- 12.7

+ 92-S
+ 98.6

+ 99-i

Thomsen

Thomsen
Stohmann

Thomsen

Stohmann
Thomsen

Stohmann

Thomsen
Stohmann

Ethyl '

Propvl '

Isoamvl '

Allvl '

Propargyl "

„'. ( Formic acid... .

% 3 •! Acetic

O ( Propionic " .

Capric acid

Palmitic '

Stearic '

C18H3602
C2H204
C3H404
C4HB04
C4H60«
HER SUBSTV
(CH3)20
(C2H5)20
C3H6(OH)3
C2H40
CNH
(CN)2
CH3CN
CH3NH2
(CH3)2NH
CO(NH2)2
CH3SH

CBH6

C6H5OH
C7H,02
C8H«04
C7H«03
C4H4S
C«H1206
C)2H22On
CaH.oO.
C«H1006

Oxalic '

4-' 196.7

Sucdnic '

Or
Dimethyl ether (gaseous) . .
Diethyl
Glycerine

+ 42.7
+ 565

Acetaldehyde (gaseous)... .
Hydrocyanic acid ' ....
Cyanogen ' ....
Acetomtrile ' ....
Methvlamine ' ....
Dimethylamine ' ....
Urea

+ 42.5

- 30.2

- 71

— 21.6

+ 5-7
+ 5-6
+ 77-5
+ 5-4
( - 17 i
J (gas.)
| - 9.1

Mercaptan (gaseous).

Benzol

Phenol (solid)

Phthalic "

Salicylic "

Thiophene (gaseous)
Dextrose

- 26.2

Cane-sugar

Starch

MOLECULAR HEAT OF VAPORIZATION OF SOME ORGANIC
COMPOUNDS.

6 4 C

Methyl iodide . . . .

6 5 C

Fthyl alcohol •

Q 8

Chloroform.

7.q

IO 7

Carbon tetrachloride. .

7.2

Aldehyde

6.0

6.45

" bromide . • •

7 e

Chloral

8 o

" iodide . . .

o 8

Chloral hydrate .

21 Q

Ethvlen bromide. . • .

8 2

Formic acid • •

* 6

Methyl alcohol

8 45

Acetic "

7.2^

IO. I

Hydrocianic acid

e 7

Valeric acid .... ......

10.6

7.2

Ether

6.7

HEAT OF NEUTRALIZATION OF BASES.

The solutions contain two equivalents of base or acid dissolved
in 400 mols. of water. Many bases, however, are not soluble.

Bases.

H2S04, Aq.

aClH, Aq.

2NO,H, Aq.

CaH4Oa,Aq.

2NaOH, Aq

31-4

27-5

27.4

26.8

2KOH, Aq

31-3

27-5

26.6

2LiOH, Aq

31.3

27.7

27.8

....

aNHs, Aq

28.2

24.4

24.6

23.8

Ba(OH)2, Aq

(36.9)

27.8

28.2

26.8

Si(OH)2, Aq

30.7

27.6

27.8

26.6

Ca(OH)2, Aq

SI-*

27.6

26.8

Mg(OH)a

3I-I

27.7

27.6

....

Mn(OH)2

26.5

23.0

22.6

Ni(OH)a

26.3

22.6

....

Co(OH)2

24.7

21. I

....

...»

Fe(OH)2

24.9

21.4

Zn(OH)2

23-5

19.9

18.0

Cd(OH)2

23.8

2O.3

20. 6

....

Cu(OH)a

18.4

14.9

12.8

PbO

(23-4)

(16.8)

17.8

15.5

HgO

18.9

6.4

AgaO

14-5

(42.5)

10.9

....

f A1(OH)3

21 .O

18.6

....

|Cr(OH)3

I6.4

13.7

....

IFe(OH),

II. 2

11.3

8.0

SnO

2.8

The numbers in parenthesis denote the formation of insoluble
salts. In these cases
Heat evolved = Heat of neutralization -}- Heat of precipitation.

NEUTRALIZATION OF ACIDS BY SODIUM HYDROXIDE.
One molecule of the acid and a equivalents of sodium hydrox-
ide, both in dilute solution, are mixed together.

Acids.

««i

a = i

a = 2

rt = 3

a = 4

a-6

HC1

6.8?

13 . 74

13. 74

HBr

5.87

13.75

6.84

13.68

HNO3

6 84

13.68

n.68

HC1O3

6.88

13. 76

13 • 76

HBrO3

6.80

13.78

HIO3

6 Q

13.81

1^.81

HC1O4

7.18

14 . ac

M, qc

16.27

H3POa

7.60

15.20

15.40

CaH4O3

13 .40

CH3Oa

13.41;

C3H«Oa

10.48

HCN

I . VI

2 77

2. 77

HaS04
H3SO»

14.6

I C Q

31.0
2Q O

3LO

....

HaCrG4
H3PO3

7.47

13.13
14.8

24-7

28.4

28.0

25.2

H3P04
H3As04
HaCO3
(COOH)a
CaH4(COOH)a
Malic acid

7-3
7.36

6*.g*

14.8
15.0
ii .0
13.8
12.4
13.0

27.1
27.6
20.2
28.3
24.0
26. 17

34-0

35.9
20. 6

24.1

28^5

....

Tartaric acid
Citric acid
HaSi03
HaBO4

3-2

6.4

12.4
12.67

4-3
II. i

25.3
25.4
5-2
20.0

25.8
38.9

5-4

41.7
20.6

HEATS OF SOLUTION.

When one gram molecule of the substance dissolves in the given
quantity of water at 18°, then the number of calories stated are set
free.

Substance Dissolved.

Quant.
Water

Heat
Evolved

Substance Dissolved

Ouant
Water

Heat
Evolved

in mol.

in Cal.

in mol

in Cal.

NaCl

200

- I.I8

NaBr4- 2H2O

2OO

— 4.7

KC1

— 4-4

NaBr

— 0.19

NH4C1

- 39

— 5-1

BaCl, + 2HaO

4OO

- 4-8

NaI4-2H3O

— 4.0

Bad,

4- 2.1

Nal

«(

4- 1.2

CaCl, -f 6HaO

••

- 4-34

NaN03

««

— 5.0

CaCl,

+ 17-4

KN03

(«

- «-5

CaBr,

+ 24-5

NH4N03

«C

- 6.3

Cal,

« <

4- 27.7

Ba(N08)a

400

- 9.4

MgCla 4- 6HaO

4- 2.9

Sr(N03)a4-4H30

— 12.5

MgCl3

4- 35-9

Sr(N03)a

- 4-6

MnClaH-4HaO

4- 1.5

Ca(N03)a4-4HaO

•

— 7.2

MnCla

-f 16.0

Ca(N03)a

4- 4-0

FeCla + 4HaO

4- 2.7

Mg(N03)a 4- 6HaO

(

— 4.2

FeCla

4- 17-9

Mn(NO3)a-(-6HaO

(

- 6.2

FeCl3+ i2HaO

4- ii. 3

Zn(NO3)a4-6HaO

- 5-8

FeCl3

< <

4-63.3

Cd(N03)3+4HaO

«(

- 5-0

CoCl2 4- 6HaO

- 2.9

Cu(NO3)a 4- 6HaO

- 10.7

Cod,

4- 18.3

AgN03

200

~ 5-4

NiCla + 6H3O

— i.i

Pb(N03)a

4OO

- 7.6

NiCla

< <

+ IQ 2

ZnCl,

< «

*\j. *
-f 15-6

NaaSO4 4- ioHaO

400

- 18.76

ZnBra

4-is

NaaSO4

4- 0.46

Znl,

+ "•3

K2SO4

««

- 6.4

CuCla + 2HaO

4- 4-2

(NH4),S04

«i

— 2.4

CuCla

4- ii. i

CaS044-2H,0

0.0*

HgCl,

- 3-3

CaS04

4- 4-7

PbCl,

- 6.8

MgSO4 4- 7H3O

< i

- 3-8

SnCla -f 2H,O

- 5-4

MgS04

•'

4- 20.3

SnCl,

4- 0.3

MnSO44-sHaO

-f 004

SnCl4

300

4- 29-9

MnSO4

4- 13.8

AuCl3 4- 2HaO

- i-7

FeS04 4- 7HaO

•«

— 4-5

AuCl3

4- 4-5

CoSO44-7HaO

- 3-6

PtCU 4- 4HaO

- 1.7

NiSO44-7HaO

— 4-3

PtCl4

4-19-6

ZnSO44-7HaO

< «

- 4-24

KBr

200

- 5-08

ZnSO4

+ 18.5

CdSO44-~ HaO

< (

4- 6.0

* Apparently weakly positive

HEATS OF SOLUTION. (Continued.)

Substance
Dissolved.

Quantity of
Water in
Molecules.

Heat
Evolved in
Calories.

Substance
Dissolved.

Quantity of
Water in
Molecules.

Heat
Evolved in
Calories.

CdSO4
CuSO4+5H3O
CuSO4
Ag2S04
K2S04,Al2(S04)3-f24H20
K2SO4,Cr2(SO4)3-f24H2O

400

2400
1600

+ 10.7
- 2.7

+ 15.8
- 4-5

— 20.2
-22.3

Heat of solut
pletely saturat

NH4C1
KC1
NaCl
(NH4)2S04
NaN03
NH4N03
MgS04+7H90
!CuCl2+2H20
| CaCl2+6H2O

ion in
ed sol

com-
4tion.

-3.88
-3-5
— O.2

K2C03
K2C03-|-3H20
KHC03
Na2C03
Na2CO3-f-ioH2O
NaHCO3

400

:+ 6.5

- 3-8
- 5-3
+ 5.6
-16.1
- 4-3

1.4

-2.5
-3-5
—4.4
-3-0

-8.4

Problems. I. How great is the quantity of heat
which is set free on the combination of 100 grams
of Na9CO3 with sufficient water to form the hydrate
NaaC03.ioH20?

2. Calculate the heat of the reaction represented by
the equation

Pb(N03)aAq + H2S04Aq = PbSO4 + 2HNO3Aq.

3. What is the heat of reaction of
AgN03Aq + HClAq = AgCl +HNO3Aq?

4. What is the quantity of heat evolved on the
combination of C2H4 with gaseous bromine, the
volume being kept constant ?

5. Calculate the quantity of heat set free when
10 grams of zinc is dissolved in dilute sulphuric acid.

6. What is the heat of formation of dipropargyl

(C6H6) at constant pressure if the heat of combustion
is equal to + 882.9 Cal. ?

7. Berthelot burned C,C16 in the presence of water
according to the equation

C2C1. + O + Aq = 2CO, + 6HClAq

and found that the quantity of heat set free was equal
to -f- 131.2 Cal. What is the heat of formation of
C.C1.? *

8. 20 cc of a lO-per-cent solution of cupric chloride
are treated with an excess of iron-filings until the
copper is completely precipitated. Calculate approxi-
mately the increase in temperature of the water, con-
sidering the specific gravity, as well as the specific
heat of the liquid, to be equal to I, and neglecting the
value of the heat of the iron and the copper.

9. A calorimeter contains 350 cc of a tenth-normal
solution of HC1. With this is mixed 250 cc of a
solution of NaOH containing sufficient NaOH to
exactly neutralize the HC1 in the first solution.
Before mixing the temperature of the two solutions
is the same. What will be the increase in tempera-
ture ?

10. 350 cc of a tenth-normal H,SO4 solution are
mixed with 250 cc of a fifth-normal NaOH solution at
the same temperature. What is the increase in tem-
perature ?

§ 33. Principle of Greatest Work. Substances
which enter into chemical reaction with one another
when brought together under normal conditions tend
to produce those systems which are formed with the
maximum evolution of heat.

Differently formulated. Of the possible reactions
in which a system of substances can take part, that
one results in which the greatest quantity of heat is
set free.

Examples. In a system composed of potassium,
chlorine and iodine, KC1 and not KI, is formed, since

K+ I = KI . . . 80. 1 Cal.,
while K + Cl = KC1 . . . 105.6 Cal.

The system (KI -f- Cl) would change to the system
(KC1 + I), since

KI + C1 = KC1 + I . . . 25.5 Cal.

Acids and bases act on one another because the
formation of salts is attended by the evolution of
heat ; for example,

KOHAq+HClAqnr KClAq+HaO . . . +13.7 Cal.

Gaseous chlorine does not decompose water-vapor,
since at 100° the reaction would be

H90(gas) + 2Cl(gas)

= 2HC1 (gas) + O (gas) ... - 14 Cal.

This equation is evident from the following:

Ht, O (gas) at 100° = + 58 Cal.
and H, Cl (gas) = + 22 Cal.

At ordinary temperatures, however, liquid water is
decomposed, though very slowly, by chlorine, for

H3O (liquid) + 2C1 (gas) + Aq

= 2HClAq + O (gas) . , . + 10 Cal.,

since

H, Cl (gas) = +22 Cal., HC1, Aq = + 17.2 Cal.,

and H2, O (liquid) = + 68.4 Cal.

Copper does not replace iron in a solution of ferrous
chloride, the reverse substitution taking place, how-
ever, since

Fe (solid) + CuCl,Aq

= FeClaAq+Cu (solid) . . . +37.3 Cal.

REMARK. This principle was first enunciated by J. Thorn-
sen, but soon after renounced. It was later taken up by Ber-
thelot, who defended it for thirty years. Its application is
extremely wide-reaching and important, notwithstanding the
appreciable errors which it often involves. The fundamen-
tal idea of this principle is that chemical action takes place
only when the change through which the system passes is
accompanied by the evolution of heat. This principle of
course holds only for reactions which take place at low
temperatures; and Van't Hoff has in fact shown that its
validity is greater the nearer the absolute zero is ap-
proached.

The enunciation of this principle involves a difficulty
since it is conditionally assumed that the substances, of
their own free reciprocal action, shall react without the in-
fluence of an external influence, an external energy. Un-
der ordinary conditions, however, external influences do
exist, namely, the temperature and the pressure of the sur-
roundings. It should be stated here that the universal
application of this principle was very recently renounced
by Berthelot himself.

§ 34. Application of the Principle of Greatest
Work.

a. Law of Simultaneously Occurring Reactions. A

reaction takes place the more readily if its ^roaucts
can immediately enter into another reaction.

REMARK. This law covers the action of elements in the
so-called nascent state, as well as the phenomena which
were originally attributed to predisposed affinities. The
law may be deduced from the principle of greatest work,
since the second reaction involves a certain evolution
of heat, which is added to that of the first. As a result
the heat of reaction is raised ; from a negative heat it
may increase to a positive one, from one of low positive
value to one of higher value, so that finally the total heat
of reaction may be equal to a large number of calories.

First Example. As already stated, chlorine
has no action on water-vapor, but does react with liquid
water. In the latter case the HC1 formed can dissolve
immediately in water, which process considerably in-
creases the quantity of heat evolved.

This action takes place slowly. If, however, the
conditions are such that the HC1 or the oxygen may
immediately on their formation enter into a chemical
reaction, the, decomposition of the water is much more
rapid.

Thus the reaction

H2O (Hquid)+2Cl+Aq=2HClAq+O . . . +10 Cal.
proceeds slowly, while the reaction

HaO (liquid) + SOaAq + 2C1 (gas)

= H9SO4Aq + 2HClAq . . . + 73.7 Cal.

quickly takes place.

The latter reaction is an example of the action of
oxygen in the nascent state, and may perhaps be ex-
plained by the assumption that this element is set

free in the form of atoms, and these act immediately,
before combining to form molecules. This explana-
tion may be the correct one, but it is nevertheless
certain that the small heat of reaction of the change

H,O + C12 = 2HClAq 4. O ... -f 10 Cal.
is considerably increased by the heat of the reaction
SO,Aq + O = H2SO4Aq . . . + 63.7 Cal.

In the above case the second reaction is produced
by the oxygen; under proper conditions, however, the
hydrochloric acid may take part in this second action.
Thus, when KOH is dissolved in the solution, the fok
lowing reaction takes place:

KOHAq+ HClAq = KClAq + H2O . . . + 13.7 Cal.
The two reactions combined would then give
2KOHAq + Cl2 = 2KClAq-f-H20+0 . . . +37-4 Cal.

This equation is, however, not yet complete, since
the oxygen combines with KC1, with the formation of
KC10:

KClAq + O = KClOAq ... - 12 Cal.,
making the total reaction
2KOHAq + Cl2 (gas)

= KClAq + KClOAq + H,O . . . +25. 4 Cal.

The formation of KC1O causes a decrease in the
heat of reaction. In fact this decrease is considerably
greater than the heat resulting from the action of
chlorine on water; nevertheless the fact that a second-
ary reaction like the formation of KC1O can take
place must be considered as a defect in logic existing
in the principle itself, since with these exceptions

reactions of this nature may be included under one
general rule.

Second Example. Manganese dioxide and
dilute sulphuric acid do not react with one another
according to the scheme

MnO9 (solid) + HaSO4Aq = MnSO4Aq + H,O + O.

If, however, oxalic acid be added, the reaction
takes place immediately, the oxalic acid being oxi-
dized to carbon dioxide and water. The first reaction
is presumably attended by a negative heat of reaction ;
the second increases this by the high heat of com-
bustion of oxalic acid.

In a similar manner the action of sulphuric acid on
potassium permanganate is made possible by the
presence of oxalic acid.

Third Example. In the reaction

H9O + Aq + 2l = 2HIAq + O

a quantity of heat equal to 42 calories is absorbed.
As a result of this water is not decomposed by
iodine according to the above equation. The decom-
position, however, takes place immediately if the
conditions are such that the oxygen can oxidize SO,
with the formation of HaSO4, Na2SaO3 with the forma-
tion of Na2S4O6 and Nal, or arsenious acid with the
formation of As,OB.

b. The Prediction of Reactions. The following rules
are often confirmed:

I. A and B will combine if A, B = + q Cal. For if

A, B = + q Cal.,
then A+B = AB . . . + q Cal.,

and the system (A + B) will tend to change to the
form AB, and the form (A + B) will be unstable.

Example. KC1 is formed directly from K and
Cl; and K, Cl = + 105.6 Cal.

2. A and B will not combine without the action of
some external energy if A, B = — q Cal., for in this
case

A+B = AB . . . — 0Cal.,

and the system (A + B) will remain in this form.

Example. Chlorine and nitrogen do not com-
bine directly; NC13 = - 38.5 Cal.

3. A will displace B from its compounds with C if
(A, C — B, C) = + ^ Cal., since in this case

A + BC = AC + B . . . + q Cal.,

and the system (A -f- B + C) tends to pass to the
form (AC + B), the form (A + BC) being unstable.
Example.

KI (solid) + Cl (gas)

= KC1 (solid) + I (solid) . . . + 25.5 Cal. ;

K, Cl = + 105 Cal., K, I = + 80. i Cal.

The reverse reaction takes place only under special
conditions.

4. AB and CD enter into a double decomposition:

AB + CD = AC + BD,
if (A, C+B, D)>(A, B + C, D);

that is, if

(A, C + B, D) - (A, B + C, D) = + q Cal.,

since in this case the form (AC + BD) is the more
stable form of the system (A + B + C + D).

c. Experimental Proof of the Above Rules. If only
those reactions are considered which take place at
ordinary temperatures or at temperatures approaching
these, the above rules will be fairly well confirmed
in practice. The heat of formation of chlorides is
greater than that of the corresponding bromides and
iodides, and bromine and iodine are in fact generally
displaced from their compounds by chlorine. The
heats of formation of compounds of the metals with
halogens follow the rule that these are greatest in
the cases of the strongly positive metals, and decrease
with the positive properties of the metals; practical
experience agrees with the rule, the weakly positive
metals being displaced from their compounds by those
which are more strongly positive. The formation of
salts from acids and bases is a double decomposition,
in which the sums of the heats of formation of the
products are greater than those of the substances in
the initial states, and as a matter of fact the forma-
tion of salts of this nature takes place without diffi-
culty.

d. Formation of Compounds with Negative Heats of
Formation. The formation of such compounds is ren-
dered possible by their appearance as secondary
products in a reaction in which the other products
have high heats of formation. In such cases, to be
sure, the heat of reaction need not be relatively great;
still it can be positive and would be greater if the
secondary products were not formed.

Examples.

Formation of Potassium Hypochlorite (see p. 85).

Formation of Nitrogen Trichloride.

N, C13 = - 38 Cal.

This substance is formed when chlorine is led into
a solution of ammonium chloride:

NH4ClAq + 6C1 = 4HClAq + NC13 ;
N, H4, Cl, Aq = + 7i.9CaL;
4C1, H, Aq = + 156.8 Cal.

The heat of reaction is therefore -|- 46.9 Cal.

e. Explosive Substances and Mixtures. Systems
whose heat of reaction is great will generally undergo
alteration. Generally, also, if in such a system
the reaction is started at any one point, sufficient
heat will be there developed to raise the material in
the immediate neighborhood to the temperature at
which the reaction takes place; as a result of this the
reaction is propagated throughout the entire mass.
When this propagation takes place with great velocity
and is accompanied by a great increase in pressure,
the result is known as an explosion. It is often possi-
ble to start the reaction at one point by a strong
pressure or shock.

Explosive substances (compounds) are substances
the formation of which is accompanied by the ab-
sorption of much heat, and which produce gaseous
products on their explosion. This is the case with
nitrogen trichloride, nitroglycerine, and acetylene.

These substances decompose when subjected to pres-
sure at any one point, since the pressure starts the
reaction at this point and it is then communicated to
the entire mass. The pressure which induces the
explosion is not the same for all substances. Ni-
trogen chloride and nitroglycerine decompose when
subjected to a very slight shock; acetylene, on the
contrary, requires a very strong one.

Explosive mixtures contain components the reac-
tion between which develops much heat, gaseous
products being at the same time formed. Examples
of such mixtures are gunpowder and oxyhydrogen-
gas.

The force of an explosion depends upon the velocity
of propagation of the reaction, upon the heat evolved,
and upon the nature of the products formed. The ex-
plosion is, moreover, the more violent when the ex-
ploding substance is a liquid or a solid and the products
are gaseous, since in this case the increase in pressure
is due not only to the increase in temperature, but
also, and in fact chiefly, to the change from the solid
or liquid to the gaseous state : a given weight of the
substance occupying a given space, before the reaction
as a liquid or solid and immediately after as a gas.
This alteration in condition alone causes a pressure
the magnitude of which is not far from a thousand
atmospheres, and this value is further increased by
the high temperature. These statements are true for
nitrogen trichloride, nitroglycerine, and gunpowder.

The values of the pressure and temperature of an

explosion when calculated from the theory give
larger numbers than are found by actual experiment.
The reasons for this are that the reactions are not com-
plete, and that the values for the heats of reaction and
specific heats of the products used in the calculation
are determined at temperatures and pressures entirely
different from those at which the explosion takes
place.

§ 35. Causes for the Starting of Reactions. Sub-
stances which enter into reaction with one another
can often remain mixed together for a long period
without any reaction taking place, the starting of the
reaction requiring certain special conditions. This is
especially true in the case of substances having nega-
tive heats of formation; without special provocation
they do not undergo any alteration.

Examples. Oxyhydrogen-gas at ordinary tem-
peratures, gunpowder, acetylene, a mixture of metallic
iron and sulphur.

The causes which induce the reaction are not always
the same: sometimes it is a shock, as in the case of
fulminate of mercury, NC13, and nitroglycerine;
sometimes the application of fire, as with gunpowder
and oxyhydrogen-gas; and again the action of light
is sufficient, as in the case of a mixture of hydrogen
and chlorine.

Occasionally the entire mass of the substance or
mixture must be heated, and then the reaction, hav-
ing once started, continues without the application of
further heat. A case of this sort is the formation of
chloroform from chloride of lime, calcium hydroxide,
alcohol, and water.

§ 36. Criticism of the Principle of Greatest Work.
This principle may be very extensively applied to
reactions which take place under normal conditions
of temperature and pressure, and especially to the
cases of the reactions of such substances as show great
stability on increase of temperature.

One difficulty, however, has already been men-
tioned: the appearance of endothermic reactions as
results of complicated actions which, taken as a
whole, are exothermic (comp. § 34, a and d}.

The general applicability of this principle is very
much impaired by numerous other important consid-
erations, which will now be mentioned.

§ 37. Endothermic Reactions which take place
at Normal Temperatures. The following chemical
reaction is endothermic :

NaFAq+HClAq = NaClAq+HFAq . . . -2.3 Cal.

Also in many other cases heat is absorbed if the
solution of an acid be mixed with the solution of a
salt. It is not necessary, however, to consider only
the strictly chemical change, since the distinction
between chemical and physical processes is not always
clear, and, what is of still more importance, the
theory upon which the principle of greatest work is
based holds equally good for alterations in the
physical condition. The existence of many endother-
mic physical processes which take place spontane-
ously may be readily demonstrated.

Freezing- mixtures. Snow and sodium chloride
mixed together at o° give a liquid, a salt solution, the
temperature of which lies a number of degrees

below o°. Crystallized sodium sulphate (Glauber's
salt) and concentrated hydrochloric acid when mixed
absorb an appreciable quantity of heat.

In both these cases the action is spontaneous and
strongly endothermic.

The Solution of Salts in Water. Most salts dissolve
in water with the absorption of heat. However, this
action is self-inducing, i.e., takes place of its own
accord.

REMARK. Salts which form crystalline compounds with
water usually dissolve in water with the absorption of heat
only when they are introduced in the form of the com-
pounds containing the same number of molecules of water
with which they crystallize at ordinary temperatures.

The Evaporation of Liquids. Many liquids evap-
orate at normal temperatures, absorbing at the same
time an appreciable quantity of heat, known as the
heat of vaporization. Water, alcohol, and ether are
such liquids. This process is endothermic and takes
place spontaneously.

§ 38. Mass Action. Very often an element C can
cause the decomposition of a compound AB — although
A, B > A, C — if the quantity of C is very great in
proportion to the quantity of AB. This is true in the
case of double decompositions.

Examples, i. A small quantity of potassium
chloride is decomposed by a large quantity of bro-
mine, with the formation of potassium bromide, not-
withstanding the fact that

K, Cl = 105.5 Cal., while K, Br = + 95 Cal

2. Ethyl alcohol and acetic acid mixed in molecular
proportion form ethyl acetate, but only two-thirds of
the alcohol and acid enter into this reaction, the other
third remaining in the form of the unaltered materials.
If, however, more alcohol or acid be added, the
quantity of the ethyl acetate is increased. The heat
of reaction in this case is nearly equal to zero.

3. Dilute hydrochloric acid mixed with a dilute
solution of sodium sulphate partially decomposes the
salt, an endothermic reaction taking place, and this
reaction proceeds further if more acid is added.

§ 39. Dissociation. Compounds which are formed
at ordinary temperatures by an exothermic reaction
are generally decomposed at very much higher tem-
peratures (comp. § 32). This decomposition, how-
ever, is an endothermic reaction.

REMARK. Investigations of the phenomena of dissocia-
tion were first carried out by Georges Aime (1837) and
later by Henri Sainte Claire DeVille (1857).

Examples. Water, hydrogen chloride, and
carbon dioxide are partially decomposed at high tem-
peratures. Ammonium chloride and many other am-
monium salts decompose into acid and ammonia-gas.
Calcium carbonate gives off carbon dioxide on heat-
ing. The so-called efflorescence, the spontaneous loss
of water from hydrated salts, may be considered as a
dissociation phenomenon.

§ 40. The Principle of Variable Equilibrium.
This principle includes many of the exceptions to the
principle of greatest work which have been mentioned.

If a chemical system of a certain form changes to
another form by a reversible process, then at every

temperature each of the two forms will be present in
a fixed concentration.*

If the transformation of the form A into the form B
takes place with the evolution of heat, then an increase
of temperature will cause an increase in the quantity of
matter in the form A.

If A changes to B with the absorption of heat, then
an increase of temperature will cause an increase in the
quantity of matter in the form B.

If the transformation of A into B takes place with-
out any caloric ejfect, then an increase in temperature
will in no way alter the distribution of the system be-
tween the two forms as they exist at normal tempera-
tures.

REMARK. This principle was introduced into chemistry
in 1884 by Van't Hoff.

Examples. Dissociation Phenomena. The phe-
nomena of dissociation mentioned above are examples
of exothermic reactions, into which, however, at
higher temperatures endothermic considerations also
enter. Water is formed from hydrogen and oxygen
with the evolution of a large quantity of heat; at high
temperatures, however, a part of the water dissociates
according to the equation

2H,0 (vapor) = 2H3 (gas) + O, (gas) ... - 58 Cal.
The reaction

CaO + CO2 = CaC03

* Another rule applies to condensed equilibrium (see § 45, c).

is exothermic, but at higher temperatures the reaction
CaCO3 = CaO + CO,

takes place, and this is endothermic: — 30.8 Cal.

Salt Solutions. Good examples are also
found in the phenomena accompanying the dissolving
of salts.

When a saturated solution of a salt (comp. § 52) is
in contact with the salt, the system (salt + water)
exists in two forms: solid salt and salt solution.

On heating, the concentration of the solution
changes: it either increases or decreases, only in
special cases does it remain constant.

In most cases the concentration increases with the
temperature — for example, in the case of KNO,,
Na2SO4ioH2O, CuSO45H,O. The salts dissolve with
the absorption of heat, an endothermic reaction takes
place, and as a result of this reaction that form of the
system results in which on an increase of temperature
an increased quantity of the reacting substance ap-
pears (comp. § 53, Rem. i).

The concentration decreases in the case of ethyl
acetate and calcium sulphate. These substances,
whose solution in water is an exothermic process,
separate from the solvent on an increase in tempera-
ture; that form of the system which results from an
exothermic action decreases in quantity when the
temperature is raised.

The concentration of a saturated solution of sodium
chloride is but very slightly affected by the tempera-
ture; the heat of solution of this salt is in fact very
nearly equal to zero.

Formation of Esters. The formation of
ethyl acetate and water from ethyl alcohol and acetic
acid is a strictly chemical example of a reaction which
proceeds without caloric effect. At normal tempera-
ture only two-thirds of the molecular quantities of the
mixed substances are converted into the second form;
at high temperatures this reaction takes place very
rapidly, but the quantities of the original substances
which take part in it are neither greater nor less than
at the normal temperature.

REMARK. The principle of greatest work, if viewed from
the standpoint of the principle of variable equilibrium, may,
according to Van't Hoff, be briefly summed up as follows:
the principle of greatest work is the more correct the nearer
the temperature of the reaction approaches the absolute
zero; at the absolute zero it is of universal validity. The
frequent confirmation of the principle at normal tempera-
ture is due to the fact that this temperature, in comparison
with the highest attainable temperature, is not far removed
from the absolute zero.

It may also be said that at the absolute zero no disso-
ciation takes place.

§ 41. Chemical Equilibrium. The principle of
greatest work prescribes the complete transformation
of reacting substances, and requires the existence of
a single form for every chemical system — namely, that
form which is produced with the greatest evolution of
heat.

As already mentioned, this condition is contradicted
by a number of circumstances, including the endo-
thermic reactions which take place at normal tempera-
tures, the action of the chemical mass, the phenomenon

of dissociation, and the phenomenon of variable
equilibrium.

All of these different facts may be summed up in
one general theory, called the theory of chemical
equilibrium. The elements of this theory may be
stated as follows:

Reacting substances do not enter completely into a
transformation, the quantity of unaltered material
depending upon the relative quantities of the reacting
substances, upon the pressure, and upon the tempera-
ture.

The elements of this theory may, however, be
differently stated. A chemical system can exist in
more than a single form; generally the different forms
exist side by side, and the system is distributed
between them in quantities which depend upon the
mass of the substances, the pressure, and the tem-
perature.

The expression equilibrium of the forms is derived
from the fact that the final state of the system is
to be considered, not as a state of rest, but as a state
of motion ; a continual transformation and re-formation
of the different forms taking place, but the actual
quantity of each of the forms existing at any one
moment being always the same. When this condition
arises, then the quantities of the forms stand to one
another in a fixed relation.

§ 42. Graphic Representation. If AB and CD
enter into a double decomposition, then in the final
state of the system, besides a fixed quantity of AC
and BD, a certain quantity of AB and CD will also be

present. The final state of the system can be repre-
sented by the equation

AB + CD = x(AC + BD) + (i - *)(AB + CD).

In this manner both the qualitative and quantitative
relations may be shown. If also the formation and
re-formation is to be expressed, then the equation is
written

CDAC

It is evident that both simple decompositions and
substitutions can be represented in this manner:

AB t; A + B ; AB + C ^ AC + B.

Examples. I. The elements hydrogen and
oxygen combine to form water, but may also exist in
the form (hydrogen -f- oxygen). At high tempera-
tures both forms can exist side by side, and the state
of the system may be thus represented :

2H, + O, = 2xU,0 + (i - *X2H.+ O,).

2. Action of nitric acid on sodium sulphate:

NaaS04Aq + 2HN03Aq ^ 2NaNO3Aq + HaSO4Aq
and

Na,S04Aq + 2HNO3Aq = f(H2SO4Aq + 2NaNO9Aq)
+ i(Na3S04Aq + 2HNO3Aq).

3. The colorless nitrogen tetroxide decomposes on
increase in temperature and decrease in pressure,
forming the colored modification:

100

4. Calcium carbonate on heating is decomposed
into calcium oxide and carbon dioxide:

CaCO3 ^ CaO + CO,.

§ 43. Proof of the Existence of Equilibrium
between Simultaneous Reactions. That a final
state of equilibrium must exist between the two re-
actions.

Form A = Form B and Form B = Form A

follows from the fact — which is indeed the character-
istic of equilibrium reactions — that the final state of
the system is independent of the form in the initial
condition.

When ethyl alcohol is mixed with acetic acid in
molecular quantities, the final state attained is the
following:

KC.H.O + C.H.O.) + KC,H,OCSHSO + H,O).

The same result is obtained, however, when ethyl
acetate and water are mixed in molecular quantities.

From this it is evident that not only the molecules
C2H6O and C2H4O2 but also the molecules of the ester
and the water act on one another. And there is no
reason for believing that this action ceases when the
permanent, final state is reached.

With relation to these facts equilibrium reactions
are also often called reciprocal reactions in contradis-
tinction to reactions which proceed only in one direc-
tion. Although it is possible that all reactions are
under certain conditions reciprocal, nevertheless these
conditions have not been observed in all cases. It is

101

also a fact that in many cases the existence of a recip-
rocal reaction at all temperatures is assumed from the
observation of the existence of such a reaction at
certain definite temperatures. A very evident disso-
ciation of water-vapor can be observed at high tem-
peratures; at lower temperatures, however, a dissocia-
tion cannot be detected. It is nevertheless assumed
that it exists, although the quantity of the dissociation-
products is infinitely small.

§ 44. The Three Kinds of Chemical Equilibrium.

a. Homogeneous Equilibrium. This term is applied
to equilibrium between substances which form physi-
cally homogeneous mixtures, viz., water- vapor and
oxyhydrogen-gas; N2O4 and 2NO2; Na,SO4Aq -f-
HNO.Aq + HNaSO4Aq + NaNO3Aq, etc.

b. Heterogeneous Equilibrium. This expression is
used in the case of equilibrium between substances
which are not in the same states of aggregation; for
example,

CaCO, (solid) ^ CaO (solid) + COa (gas),
KNO, (solid) ^ KNO, (dissolved),

NaaSO4ioHaO(sol.)^NaaSO49HQO(sol.)+HaO(vapor).

c. Condensed Equilibrium. This denotes: equilib-
rium between substances which are all solid or all
liquid, but are not mixed; or part solid and part
liquid, but not mixed.

Examples. Monoclinic sulphur <""* Qrthorhombic
sulphur.

NaaSO4ioH,O (solid) ^ NaaSO4 (sol.) + ioHaO (liq.).

IO2

§ 45- Effect of Temperature on Equilibrium.

a. On Homogeneous Equilibrium. The state of a
system of two substances which are in equilibrium
with one another, at a certain temperature and at a
certain pressure, is determined by the relative quanti-
ties of both forms present.

The relation of the two substances to one another
is further dependent upon the temperature of the sys-
tem and stands in a direct relation to the heat-toning*
which accompanies the transformation of the one form
into the other.

The laws which govern the relation between the
quantities of the substances entering into the trans-
formation and the temperature and heat of transfor-
mation are the same as the rules given under the
principle of variable equilibrium in §40.

REMARK. In the case of homogeneous equilibrium the
relative quantities of both forms can generally be deter-
mined from the specific gravity of the system. If the
weight of one liter of nitrogen tetroxide at a certain tem-
perature and pressure be determined, — it being known what
this value would be if the space were filled with N3O4, and
also if it were filled with NOa, — then the composition of a
mixture which would correspond to the observed weight
can be calculated.

In the case of reactions between solutions of acids and
salts the quantities which enter into the transformations,
and also the equilibrium relations, can be calculated from
the results of calorimetric, volumetric, and optical investiga-
tions. J. Thomsen determined the heat evolved on mixing
solutions of salts and acids, and, by comparing this heat-

* Heat-toning is the thermal effect measured in calorimetric
units.

103

toning with that which would appear if the decompositions
were complete, was able to calculate the quantities of sub-
stances which had actually undergone decomposition. W.
Ostwald determined the specific gravities and indices of
refraction of mixed solutions, as well as the corresponding
values for the separate solutions of the salts, acids, and
products of the reactions, and used these values for calcu-
lating the extent of the decomposition.

There are also other special methods.

b. Effect of Temperature on Heterogeneous Equilib-
rium. When a condensed form is in contact with a
dilute form, — a solid or liquid body in contact with a
gas, vapor, or solution, — the equilibrium of the system
is not determined by a certain distribution of the sys-
tem between two forms, but by a fixed concentration of
the dilute form. If the latter is a gas or a vapor, then
this fixed concentration is manifested through a certain
pressure, known as the dissociation-pressure, which is
independent of the quantity of the substance existing
in the condensed form.

The concentration increases with the temperature if
the heat-toning of the transformation of the condensed
into the dilute form is negative; if the latter is positive,
then the condensation decreases in accordance with the
principle of variable equilibrium (§ 40) .

An example is furnished by the decomposition of cal-
cium carbonate, which, if heated in an inclosed space,
dissociates into calcium oxide and carbon dioxide until
the gas reaches a certain pressure. Other examples are
furnished by hydrated salts, which have a certain vapor-
tension, depending on the temperature; and also by
saturated solutions of salts (§ 40).

104

c. Effect of Temperature on Condensed Equilibrium.
At a fixed pressure this type of equilibrium occurs at
only a single temperature, and the quantities of the
substances appearing in the coexistent forms are indefi-
nite; at 96° rhombohedral and monoclinic sulphur
exist side by side in arbitrary quantities. On an in-
crease in temperature the equilibrium vanishes, and the
change of one form into the other takes place in ac-
cordance with the rule given in § 40 ; that form appear-
ing which is produced from the other with the absorption
of heat.

In the case of condensed systems the conditions are
such that the two forms can only coexist at a single
temperature, above which one form, and below which
the other form, is stable. The temperature at which
both forms appear is called the temperature of trans-
formation or the transformation-point.

§ 46. Effect of Pressure on Equilibrium.

a. Effect on Homogeneous Equilibrium. When a
gaseous homogeneous mixture of reacting substances
has attained a state of equilibrium and the tempera-
ture remains constant, an increase in the pressure
causes a change of the transformed quantities, and
that form results which is produced from the other by
a decrease in the number of molecules.

Briefly stated, the system, oh an increase in pres-
sure, tends to pass over into the more condensed
form.

Example.

N9o4 1; 2 NO,.

The compression of this system causes an increase
in the quantity of the N3O4.

A special case is illustrated by the equimolecular
reaction

In such a reaction the condition of equilibrium is
not affected by the pressure, if this is not too great.

b. Effect of Pressure on Heterogeneous Equilibrium.
When the dilute form is a gas, an increase in the
pressure at constant temperature does not have a
permanent effect on the equilibrium:

CaCO3 (solid) ^ CaO (solid) + COa (gas).

At constant temperature an increase in the pressure
of the carbon dioxide — corresponding to an increase
in the concentration of the carbon dioxide — causes
the formation of CaCO,, which continues until the
pressure has attained its original value.

The same behavior has been observed in the case
of hydrated salts: compression of the vapor causes the
recombination of the vapor with the dehydrated salt.

For salts which are in contact with their saturated
solutions the rule applies that an increase in pres-
sure increases the quantity of dissolved material, if
the total volume of the salt and the water required
for its solution is greater than the volume of the solu-
tion, or, what amounts to the same thing, if the
process o( solution is accompanied by a contraction in
volume.

In such cases the rule also applies, that on increase

io6

in pressure the system tends to pass into the more
condensed form.

c. Effect of Pressure on Condensed Equilibrium.
In cases of equilibrium of this nature the relation
between the quantities of the two forms is not directly
dependent on the pressure, if the temperature is con-
stant, since at the temperature of transformation the
two forms exist side by side in arbitrary quantities.
The temperature of transformation, however, is altered
by an increase in pressure, and is in most cases
lowered.

§ 47. Effect of Chemical Mass on Equilibrium.
The influence of this factor is evident only in the case
of homogeneous equilibrium. An increase in the
quantity of one of the reacting substances increases
the products of that reaction which is promoted by
the presence of the substance added.

In the reaction

Alcohol -f- acid <"""* Ester -|- water

the formation of the ester is promoted by an increase
in the quantity of the acid and also by an increase in
the quantity of the alcohol. The addition of water,
on the contrary, retards the formation of the ester.

REMARK i. If the action of one of the substances is
impeded, this is equivalent to a decrease in its mass. For
example: In the formation of esters the reaction is pro-
moted by leading a current of hydrogen chloride through
the mixture of acid and alcohol. The hydrogen chloride
combines with the water, and the action of the latter on the
ester is thus checked.

REMARK 2. The idea of mass action was brought for-
ward by Berthollet in the beginning of the present century.

107

In later chemistry the first important application of this
idea was made by Guldberg and Waage (1867).

§ 48. Analogy between Changes in Physical and
Chemical State. An insight into the laws of chemical
equilibrium is obtained by a consideration of the condi-
tions under which a substance changes its physical state.

Water can be solid, liquid and vaporous, and the
transformation of one of these forms into the others is
accompanied by certain thermal effects. These trans-
formations are influenced by temperature and pressure,
and they are reversible; a change in condition, caused
by an alteration in pressure or temperature, is repro-
duced when the temperature and pressure are again re-
established.

A state of equilibrium exists in the case of the physi-
cal forms: at o° ice is in equilibrium with water, below
o° ice is in equilibrium with vapor, above o° water is in
equilibrium with vapor.

Increase in temperature leads to the appearance of
that physical form the production of which is accompa-
nied by the absorption of heat (principle of variable
equilibrium, § 40). Ice on heating is converted into
water. In this transformation a considerable quantity
of heat, called the latent heat of fusion, is absorbed.

Water on heating forms vapor of increasing density
and pressure; this vapor is formed with the absorption
of heat, the latent heat of vaporization.

The system

Water -f- Vapor

is in equilibrium according to the equation
Water ^~> Vapor,

io8

and furnishes a case analogous to that of heteroge-
neous equilibrium. The state of equilibrium is such
that at a certain temperature the density and pressure
of the vapor have a fixed and definite value. Com-
pression does not permanently affect these values,
since when this occurs the vapor changes to liquid
water, and the original pressure is again established.
A condensed equilibrium exists at o° in the case of

Ice ^ Water.

By an increase in pressure the temperature of trans-
formation (corresponding in this case to the freezing
point) is lowered.

§ 49. Berthollet's Law.

Principle. I. When two substances A and B, each
of which can enter into a reaction with a third sub-
stance, C, are present in a homogeneous mixture
together with C, then there will exist in the final state
neither AC only nor BC only, but AC and BC will
occur in a state of equilibrium, their relative quantities
depending on the mutual affinities, as well as on the
chemical masses, of A and B.

2. If the substances AC and BC are either insoluble
or only very slightly soluble in the liquid, then they
will separate out, and the substances which remain
dissolved in the liquid will tend to establish a new
state of equilibrium, thereby causing the formation of
fresh quantities of AC or BC.

BertJiollef s First Laiv. When dissolved substances
by their mutual action bring about the formation of
an insoluble substance, then the reaction will proceed
until the reacting substances are entirely decomposed.

Example. Silver nitrate and hydrochloric acid
are completely converted into silver chloride and nitric
acid.

Bertholle? s Second Law. When the reacting sub-
stances form a volatile compound, then the reaction
proceeds, until the Original substances have undergone
complete transformation, the volatile substance being
continuously eliminated.

Example. Calcium carbonate is completely de-
composed by dilute hydrochloric acid, carbon dioxide
being formed; sodium chloride is completely decom-
posed by sulphuric acid, with the formation of
hydrogen chloride.

REMARK. These laws were published in " Essai de sia-
tique chimique " (1804).

Explanation. Berthollet's laws correspond
with modern theory, since they state the existence of
an equilibrium between two forms, and since they in-
troduce the idea of mass action into the consideration.
The influence of temperature and pressure, however,
are not taken into account, and in addition to this the
thermal effect of the alteration in form is entirely neg-
lected.

Nevertheless these laws are of great practical value,
since they include many reactions which take place
under normal conditions and since they in most cases
apply to the reactions, which are met with in the ordi-
nary course of laboratory work. They are lacking,
however, in logical rigor, since the conditions of in-
solubility and volatility with respect to the liquid are
not sharply defined. From the first law it cannot be
predicted that AgCN will dissolve in KCN, nor that

AgCl will be decomposed by KCN. The second law
does not explain why sulphide of iron, but not sul-
phide of copper, is decomposed by hydrochloric acid;
the first law furnishes no explanation as to why, in a
mixture of ferrous chloride and cupric chloride dis-
solved in acidified water, sulphide of copper and not
sulphide of iron is precipitated by hydrogen sulphide.
Problems of this sort, however, can often be solved
with the help of the principle of greatest work.

§ 50. Watt's Principle. When a space, in which
at two points different but constant temperatures are
maintained, contains a liquid at these points, then the
vapor of the liquid moves to the point of lower tempera-
ture ; at this point it condenses, and in the end the
liquid will be found only at this point of lower tem-
perature, the space then being filled with vapor,
the pressure of A\hich is equal to the maximum
vapor pressure of the liquid at the lower tempera-
ture.

Example. If water be heated to boiling, in a
still which is connected with a receiver cooled to o°,
the vapor passes over into the . receiver; there it will
be transformed almost completely into liquid, and
finally all the water will have passed into the receiver,
and the space within the still will be filled with vapor
at a pressure of 4 mm.

Explanation. Water at 100° is in equilib-
rium with water vapor having a pressure equal to I
atmosphere; water at o° is in equilibrium with vapor
the density of which corresponds to a pressure of
4 mm.

In A the vapor pressure has a constant value equal

Ill

to I atmosphere, in B, however, this value cannot
exceed 4 mm. Since the tendency of the vapor from
both vessels is to fill the space offered to it, the cool
vapor is forced back by the hot vapor, since the
pressure of the latter is much greater than that of the
former. The hot vapor therefore passes into B, where
it is mostly converted into liquid, since in B only
vapor having a pressure of 4 mm can exist. It is

1 Athm

100?-

evident that this transfer will cease only when all
liquid has disappeared from A, and when a pressure
of 4 mm exists at all points in the enclosed space.

Application .

Distillation, A liquid is separated from a non-
volatile substance with which it is mixed, by heating
the mixture in a vessel, and connecting this vessel
with a cooled receiver. The vapor of the volatile
liquid passes over into the receiver and there con-
denses, while the non-volatile substance remains in
the distilling vessel.

In this manner water can be separated from dis-
solved salts. — Thus also nitric acid is separated from
the mixture which results on adding sulphuric acid to
sodium nitrate, this operation, causing the complete

112

decomposition of the mixed materials; since the
equilibrium existing in the mixture first formed is
destroyed by the removal of nitric acid, and the ten-
dency towards the formation of a new state of equilib-
rium results in the formation of fresh quantities of
nitric acid.

Fractional Distillation. A mixture of liquids, when
heated in a distillation apparatus, produces vapor,
which at first consists chiefly of the vapor of the most
volatile liquid. As a result this substance is present
in the distillate in a purer state than in the original
mixture. If the vapor which has condensed to a
liquid be again distilled, then the first portion of this
distillate will be a purer product than the liquid
obtained in the previous operation. By fractional
distillation, however, an absolutely pure product can-
not be obtained ; first, because by each distillation
the quantity of admixed substance becomes indeed
smaller, but does not entirely disappear; secondly,
since in many cases a mixture is finally formed, which
without alteration in composition may be converted
into vapor and again condensed. This takes place
because the boiling-point of this mixture is both lower
than the boiling-point of its components and also
lower than that of a mixture of different composition.
The result is that on distillation first the mixture
having the lowest boiling-point and later the other
mixtures pass over into the distillate. The same
behavior is observed in cases where a certain mixture
has a boiling-point which is higher than that of its
components and than that of a mixture of different
composition. In such cases the more volatile mix-

tures first pass over, and the least volatile remain
behind in the distilling vessel.

The occurrence of such mixtures of constant com-
position as are mentioned above is the explanation of
why ethyl alcohol cannot be separated from water by
fractional distillation, a mixture containing 94 per cent
of alcohol and 6 per cent of water distilling over.
It is also impossible to concentrate aqueous hydro-
chloric acid beyond a certain point, the concentration
of the vapor continually approaching that of the liquid
remaining in the retort, until finally the vapor and
liquid have the same composition, this composition
remaining unaltered on further distillation.

The composition of the unaltered mixture passing
over is dependent on the pressure, and therefore such
a mixture can not be considered a chemical com-
pound.

A very important instance of fractional distillation
is found in the purification of mineral oils by distilla-
tion.

Liquefaction of Gases under their own Pressure. If
one arm of a closed tube bent at an angle in the middle
contains crystals of chlorine hydrate (Cl2ioH2O), and
the other arm be placed in a cooling mixture, then, if the
arm containing the chlorine hydrate be cautiously
heated, chlorine will be evolved and will pass over into
the cooler end. If an excess of the gas is present, a
point will be reached where the pressure of the gaseous
chlorine slightly exceeds its maximum pressure at the
temperature of the cooling mixture, and the chlorine
will therefore liquefy in that end of the tube. From

this point distillation will continue, in accordance with
Watt's principle.

Ammonia-gas can also be liquefied by a similar
process, the solid compound, ammonium silver chlo-
ride, being heated in a closed tube, one end of which
dips into a freezing-mixture.

The temperature of the freezing-mixture must, of
course, be lower than the critical temperature of the
gas.

Applications of the Theory of Points of Transforma-
tion. As has been already stated, a substance which
is in contact with its vapor in an inclosed space in
which more than one temperature exists, tends to
pass to that form of the system in which the vapor
has the lowest pressure. Further, when more than
one form can exist at the lowest temperature, the
system tends to assume that form the vapor pressure
of which is the lowest. Liquid water can, under cer-
tain conditions, exist below o°, in contact with vapor
having a definite temperature and pressure. But ice
also is in equilibrium with vapor below o°. For every
temperature below o°, however, the vapor pressure of
water is greater than that of ice. Therefore, when
ice and liquid water coexist at any temperature
below o°, the vapor will distill from the water to the
ice, and will be transformed into ice. Also above o°
ice and water cannot form a stable system (comp.

§48).

At o°, however, the vapor of both water and ice
has the same density and the same pressure; therefore
at this temperature the coexistence of both forms is

possible, while at higher temperatures only one form
is stable.

The freezing-point of water is therefore the trans-
formation-point of the condensed equilibrium:

Ice (+ vapor) ~^_ Water (+ vapor).

By a similar course of reasoning the conclusion may
be reached that at a certain temperature rhombo-
hedral and monoclinic sulphur can exist side by side,
since above this temperature the one only, below
this temperature the other only, of the two forms is
stable.

§51. Watt's Principle applied to Matter at Nor-
mal Temperature. The soundness of Watt's law is
established by two facts. First: A condensed sub-
stance constitutes with its vapor a stable system, since
a certain pressure and density correspond to every
definite temperature. Secondly: No equilibrium exists
if two systems of different density and different pressure
are present in the same inclosed space; the vapor,
under such conditions, passing from the region of
higher pressure to the region of lower pressure.

In the previous paragraph those cases were consid-
ered where the differences in density and pressure were
caused by differences in temperature. It is evident,
however, that the transfer of matter in the form of
vapor can also occur when the differences of vapor pres-
sure are due to other causes. The principle of Watt
may be still further expanded, and may be stated as
follows:

When in any given space there are two centres,
characterized by a difference in pressure of the vapor

of one and the same substance in contact with a con-
densed form of this substance, the vapor of the sub-
stance will pass from the centre of higher to the centre
of lower pressure.

A tendency to establish an equality of pressure exists
in the system comprising the two centres.

Example. If pure water and a salt solution are
contained in an inclosed space, water vapor will pass
from the pure water to the solution.

Application.

Hygroscopic Salts and Acids. By hygroscopic salts
and acids are meant such substances as are strongly
soluble in water; their saturated solution is in equi-
librium with vapor the pressure of which is much
lower than that of pure water at the same tempera-
ture. When water is contained in an inclosed space
in which a substance of this nature is also present,
vapor passes from the water to the substance, since a
small quantity of water brought into contact with this
substance forms on its surface a very concentrated
solution; this solution has a very low vapor pressure
and constitutes a centre of low pressure, to which the
vapor of the pure water continually passes, i.e., dis-
tills over at normal temperature.

Since the vapor pressure of all salt solutions is lower
than that of pure water, such solutions will therefore
attract to them the vapor of pure water. The vapor
pressures of solutions of difficultly soluble substances
are only very slightly lower than that of water; the dis-
tillation will therefore take place very slowly.

The atmosphere always contains water vapor, the

density and pressure of which vary greatly with
different localities and at different times. If a salt
solution be exposed to the air it absorbs water vapor
if its own vapor pressure be lower than that of the
water vapor in the atmosphere : in such cases the solu-
tion is said to exert a hygroscopic action. The
hygroscopic action of very soluble salts is consider-
able. On the surface of such substances the moist air
forms a film, consisting of a very concentrated, satu-
rated solution, which produces a centre of low vapor
pressure. As soon as this centre is created, the water
vapor of the atmosphere, the pressure of which ordi-
narily exceeds that of the salt solution, passes to this
centre. Fresh quantities of the solution are formed,
and this remains saturated and has a very low vapor
pressure, so long as an excess of the undissolved salt
remain^. When the salt has completely dissolved,
then the solution continues to absorb water vapor
until the dilution reaches the point where the vapor
pressure of the solution is equal to that of the
atmosphere.

REMARK. These considerations do not apply in the
case of hygroscopic action of a purely chemical nature, as
for example that of P2OB. P3OB is not in equilibrium with
water vapor at any pressure, since it forms with it a com-
pound H3PO4. It maybe said, however, that P2O6 repre-
sents a centre the vapor pressure of which is equal to zero.
The same is true for anhydrous calcium chloride; the first
hygroscopic action of this salt being confined to the forma-
tion of the hydrated salt, CaCla.6HaO, the salt in the mean-
time constituting a centre with the vapor pressure zero;
later a saturated solution is formed.

The saturated solutions of slightly soluble sub-

stances do not exert any hygroscopic action, their
vapor pressures being greater than the pressure of the
water vapor of the atmosphere. Such solutions lose
water vapor until no more water remains.

The Deliquescence of Solid Substances in the Air. It
is now not difficult to determine what substances de-
liquesce in the air. They are those substances the sat-
urated solutions of which at normal temperatures have
a vapor pressure less than the pressure of the atmos-
pheric water vapor; if their vapor pressure is greater
than the vapor pressure of the atmospheric water, then
the substances do not deliquesce, but, on the contrary,
when they are moist they dry in the air.

In general, therefore, deliquescence is a property of
readily soluble substances.

Potassium carbonate deliquesces, because a trace of
water forms with it a small quantity of a saturated and
very concentrated solution having a very low vapor pres-
sure, more water vapor being continually absorbed by
this solution. Potassium sulphate, on the contrary,
does not deliquesce, since, although it may perhaps be
already moist, it can form only a very dilute solution
the vapor pressure of which is greater than the tension
of the atmospheric water vapor, and therefore the sul-
phate will lose water vapor in the air.

Pure sodium chloride is but slightly soluble and
does not deliquesce. Commercial sodium chloride,
however, generally contains small quantities of very
soluble magnesium chloride, and since this latter sub-
stance deliquesces, the sodium chloride itself appears
to be hygroscopic.

Sodium nitrate (Chili saltpeter) is, at normal tern-

peratures, very readily soluble in water, potassium
nitrate (potassium saltpeter) but very slightly. The
Chili saltpeter is so hygroscopic that it cannot be used
in the manufacture of gunpowder, while potassium
saltpeter is very well suited to this purpose. The
difference in solubility of the two salts is the basis of
the method for preparing potassium nitrate from
sodium nitrate according to the reaction :

NaNO3 + KC1 = KNO3 + NaCl.

Hot solutions of NaNO, and KC1 are mixed and
boiled, the potassium nitrate remaining dissolved in
the hot water. On cooling it crystallizes out, since it
is only slightly soluble in cold water. The solubility
of sodium chloride in hot and cold water is, however,
about the same; the sodium chloride therefore remains
in solution. The same conditions that make potassium
saltpeter suitable for the manufacture of gunpowder
also make it possible to prepare this saltpeter from
sodium nitrate and potassium chloride.

The Efflorescence of Hydrated Salts. As already
stated, a hydrated salt is at a given temperature in
equilibrium with water vapor of a definite density and
pressure. For every salt, as for pure water, there is
a certain characteristic table of vapor pressures. A
hydrated salt at a certain temperature therefore repre-
sents a centre of definite vapor tension.

When at normal temperature the vapor tension of
the salt exceeds that of the atmospheric water vapor,
then the crystals will lose water in the air and will
effloresce. If, however, the vapor tension of the
crystals is exceeded by that of the atmospheric vapor,

120

then the crystals will lose no water, or, as it may be
more correctly stated, the water lost will be imme-
diately replaced by the atmospheric vapor, and the
crystals will not effloresce.

Example. Sodium sulphate (Glauber's salt) efflo-
resces, calcium sulphate (gypsum) does not effloresce.
If fresh crystals of both salts are exposed to the air,
their identity can, after a short time, be readily
determined, since the first will, but the second will
not, have effloresced.

REMARK 2. In the above considerations it is assumed
that the relative amount of water in the air is nearly con-
stant. It is clear, however, that when the amount of water
is small many substances will not deliquesce, but will efflo-
resce, while when the amount of water is large the same sub-
stances will deliquesce and not effloresce.

CHAPTER V.
SOLUTIONS.

§52. Definitions. Many substances can form with
water a homogeneous liquid mixture; a mixture of
this sort is called a solution.

REMARK. Water is not the only liquid which can dis-
solve substances ; in this book, however, chiefly aqueous
solutions will be considered.

A solution is saturated at a certain temperature if,
when brought in contact with the substance a quan-
tity of which it already contains, no further quantities
of the substance pass into the solution. If the solu-
tion contains more of the substance than is required to
form a saturated solution, then the solution is super-
saturated. Supersaturation can only occur when the
solution is not in contact with solid particles of the dis-
solved substance; since this would immediately cause
the separation of a part of the substance contained in
the solution, and the strength of the solution would be
reduced.

A saturated solution of a substance in contact with
the same substance in the undissolved state represents,
at a constant temperature, a system of stable equilib-
rium. With most substances the quantity of material
which can be dissolved is greater the higher the tem-

121

122

perature. There are other substances, however, the
solubilities of which decrease with an increase in tem-
perature.

Examples. Potassium nitrate, sodium nitrate,
sodium sulphate, and many other salts are more solu-
ble in warm water than in cold. Calcium sulphate
and ethyl acetate, on the contrary, are least soluble
in hot solutions. Sodium chloride is about equally
soluble in cold and warm water.

§ 53. General Laws of Solubility. The coefficient
of solubility of a substance is the number of grams of
the substance which at a given temperature will dis-
solve in 100 grams of water.

For the relation between solubility, temperature,
and heat of solution see § 40.

REMARK i. It should be noted that the expression * heat
of solution ' mentioned in paragraph 40 denotes the quantity
of heat which is evolved when a substance dissolves to
form an almost saturated solution, corresponding therefore
to the heat of solution in nearly saturated solution.

The solubility of solids and liquids is only very
slightly affected even by very great pressures. Com-
pare § 46.

REMARK 2. The relations between solubility and pres-
sure, and between solubility and temperature, only hold
when the water and the dissolved substance do not mix in
all proportions. Alcohol, for example, has no coefficient of
solubility, since it mixes with water in all proportions.

Gases, which are but slightly soluble in water, fol-
low the law of Henry; their solubility at a fixed tem-
perature is proportional to the pressure.

§ 54. Solubility of Hydrates. Salts containing

133

water of crystallization conform to the rule that each
hydrate has its particular solubility. It is therefore
possible for a solution to be saturated with respect to
several different substances, namely, to different
hydrates. A concentrated solution of sodium sulphate,
prepared at 40°, and afterwards cooled to the tempera-
ture of the room, is not only saturated with respect
to (i.e., deposits crystals not only on contact with)
NaaSO4ioH,O, but also with respect to Na,SO47HaO.
This fact makes it difficult to determine in what
state a dissolved salt is present in a solution. This,
however, is certain : that one hydrate in contact with
the solution represents a system of stable equilibrium.

REMARK. The relation between the solubility of a salt
and the temperature is generally represented by a diagram,
in which the temperatures appear as abscissas and the solu-
bilities as ordinates. In such a diagram the solubilities are
not those of hydrates, but of quantities of anhydrous salts
present in 100 parts of water. The solubility is often taken
as the quantity of anhydrous salt which is present in 100
parts of solution. In the diagram on page 124 the coefficient
of solubility is, however, the one first mentioned.

§ 55. Osmosis. If a solution is contained in a
vessel, through the walls of which water, but not the
dissolved substance, can pass, and the vessel is placed
in water, then water will pass from the outside
through the walls of the vessel into the solution
(osmosis).

The property of partial permeability is possessed
by many vegetable and animal membranes; but
osmosis has been most accurately studied by the use
pf artificially prepared semipermeable membranes.

I24

The passage of water through the walls of the ves-
sel can be prevented by applying a pressure to the
solution. Such a pressure, in equilibrium with the

40 50 60

TEMPERATURE

force exerted by the water in passing into the solution,
is equal to the osmotic pressure.

The osmotic pressure increases with the concentra-
tion and temperature of the solution.

§ 56. Osmotic Phenomena in Dilute Solutions.
If a solution is contained in a cylinder into one end
of which a piston is fitted, the other end being closed

100

125

by a semipermeable membrane and surrounded by
water, the solution may be compared to a gas which
is contained in a cylinder closed at one end, and kept
in equilibrium with the atmosphere by a frictionless
piston at the other. If the piston be raised, then the
dissolved substance expands, — that is, water passes in
through the membrane from the outside, — the volume
of the solution increases, and the osmotic pressure
falls. If the piston be now pressed into the cylinder,
then water passes out through the membrane, the
volume of the solution diminishes, and the osmotic
pressure becomes greater. If the system be heated,
and the piston be held at one position, then the
pressure on the piston must be increased, and the
osmotic pressure becomes correspondingly higher.

Both concentrated and dilute solutions are in this
respect analogous to gases. Dilute solutions, more-
over, show a complete quantitative agreement with
gases, as has been shown by Van't Hoff (1886).
When a dilute solution is contained in a cell with a
semipermeable membrane, and the cell is placed in
water, then the solution follows the laivs of Boyle and
Gay-Lussac and the law of Avogadro.

Further, for solutions of one and the same substance:

At constant temperature the osmotic pressure is
proportional to the concentration;

At constant volume the osmotic pressure is propor-
tional to the absolute temperature.

For solutions of different substances:

Under conditions of equal temperature and equal
concentration the osmotic pressure is inversely pro-
portional to the molecular weight; or;

126

Solutions of the same molecular concentration *
have at the same temperature an equal osmotic pres
sure. And lastly:

The osmotic pressure of a dissolved substance at a
certain temperature and concentration is equal to the
gas pressure which the same substance in a gaseous
state would exert at the same temperature and con-
centration.

Example. The following osmotic pressures
have been observed in solutions of cane-sugar at
14° C:

Per Cent Solution. Osmotic Pressure.

i 535 mm

2 I0l6 "

4 2082 "

6 3075 "

If cane-sugar could exist as a gas, then at a con-
centration of 10 grams per liter and at a temperature
of 14° its pressure would be

760 X22.32 X -ffff X ffj mm = 521 mm.

REMARK. It is evident that the molecular quantity of the
dissolved substance can be calculated from the osmotic
pressure of a solution of known concentration (compare
§ 21, Rem. i).

§ 57. Experimental Basis. This is partly found
in measurements of the osmotic pressure. Such
measurements, however, involve considerable diffi-
culty, and it is found almost impossible to prepare

*The molecular concentration is the number of molecular
quantities of the substance in one liter of the solution,

127

membranes which are absolutely impervious to the
dissolved substances.

Important data are, however, found in the phe-
nomena which stand in close relation to the osmotic
pressure, as has been pointed out by Van't Hoff.
These phenomena are the lowering of the freezing-
point, the elevation of the boiling-point, and the decrease
in the vapor pressure.

a. Lowering of the Freezing-point. It has long
been known that the freezing-point of water is low-
ered by the addition of a soluble compound. This
lowering is, within certain limits, proportional to the
concentration of the solution. According to the
theory of osmotic pressure, this pressure is propor-
tional to the number of molecules dissolved in a liter,
and also for one and the same substance the lowering
of the freezing-point is proportional to the concen-
tration, while for the solutions of different substances,
but of equal concentration, the lowering is inversely
proportional to the molecular weights of the dissolved
substances.

REMARK i. If the depression of the freezing-point fora
one-per-cent solution of any substance in a given solvent
be determined, then the depression produced by dissolving
a molecular quantity of the same substance in TOO grams of
the given solvent can be calculated, it being assumed that
such a solution would be possible and that it would obey
the law for dilute solutions. The value of the result ob-
tained is purely fictitious, but is of great assistance in ex-
perimental work and is known as the molecular depression
for the given solvent. The molecular depression of the
freezing-point depends upon the nature of the liquid, and
is the same for all dissolved substances (compare § 58).

128

REMARK 2. The constant for the molecular depression
of the freezing-point has a different value for every solvent.
Van't Hoff has pointed out the fact that a direct quantita-
tive relation exists between this constant and the latent
heat of fusion of the solvent, so that either one of the two
quantities can be calculated from the other.

b. Elevation of the Boiling-point. For the same dis-
solved substance the elevation of the boiling-point is
proportional to the concentration.

For equally concentrated solutions of different sub-
stances the elevation of the boiling-point is inversely
proportional to the molecular weights of the substances.

c. Decrease in the Vapor Pressure. Similar rules
apply to the lowering of the vapor pressure of solvents.

REMARK 3. The above rules may be summed up as fol-
lows : the osmotic pressure, depression of the freezing-point,
elevation of the boiling-point and decrease in vapor pres-
sure are equally great for solutions which contain an equal
number of molecules dissolved per liter in the same solvent.

REMARK 4. The molecular quantity of the dissolved
substance can be determined from any one of the three
rules given. The depression of the freezing-point method
is, however, the one most generally used.

Many substances the molecular weights of which had
been previously determined have given similar values when
examined by the more recent methods. Nevertheless
the molecular weight is to a certain extent dependent on
the nature of the solvent.

REMARK 5. Important osmotic phenomena may be ob-
served in the case of living organic cells.

If a plant-cell be brought into a salt solution osmosis
takes place. The protoplasm which surrounds the liquid,
the sap of the cell, under normal conditions adheres to the
cell-wall, and acts as a semipermeable membrane, permit-
ting only water, but not the substances dissolved in the sap

I29

or the watert to pass through. According as the salt solu-
tion used is more or less concentrated, the sap of the cell
will absorb water or send out water through the protoplasm.
A certain concentration of the salt solution must naturally
exist which is in equilibrium with the sap, so that the solu-
tion does not remove water from the sap, nor does the sap
remove water from the solution. At this concentration the
sap and the solution have an equal osmotic pressure; they
are isosmotic or isotonic. The solutions of different salts are
isotonic and of e.qual osmotic pressure when they are in
equilibrium with the sap of the same cell. Stronger solu-
tions withdraw all water from the cell. The elastic pro-
toplasm contracts and breaks loose from the rigid wall of
the cell. This phenomenon, known as plasmolysis, is ob-
served by the use of a microscope.

The isotonic coefficient of a substance is the osmotic
pressure of its aqueous solution when this has the same
molecular concentration as a potassium nitrate solution, the
osmotic pressure of which is arbitrarily chosen as 3. The
isotonic coefficient of cane-sugar is 1.88; therefore a solu-
tion of cane-sugar is isotonic with a sodium nitrate solution
when the molecular concentration of the former stands to
the concentration of the latter in the proportion 3 : 1.88
(H. de Vries).

Equal osmotic pressures are observed in the cases of
equiniolecular solutions of various neutral organic com-
pounds and organic acids. The behavior of blood-cor-
puscles is very similar to that of plant-cells, and was first
investigated by Bonders and Hamburger. The latter
worked out a method for the determination of molecular
weights which was based upon phenomena observed in the
course of the investigation.

§ 58. Exceptions. The methods for the determi-
nation of the molecular weight described in this
chapter lead in the case of a large number of sub-

130

stances to results which are not in accord with the
general osmotic theory. These substances comprise
the strong acids, the strong bases and salts. Atten-
tion was called by Arrhenius (1887) to the rule that
exceptions occur in the cases of all substances which
are electrolytes.

CHAPTER VI.
ELECTROCHEMISTRY.

§ 59. Definitions. A chemical compound which
in the dissolved or melted condition conducts the elec-
tric current is called an electrolyte.

If an electric current is passed through the aqueous
solution of an electrolyte, certain chemical changes are
produced. The processes called electrolysis.

The point at which the positive electricity enters the
solution is called the anode; the point at which it leaves,
the cathode. Both anode and cathode are known as
the electrodes.

The little particles charged with electricity which
collectively constitute a molecule of the electrolyte are
called the ions of the latter.

The ions which during electrolysis move to the
anode are called the anions; those which move toward
the cathode, the cathions.

§ 60. Electrolytic Dissociation. When an elec-
trolyte dissolves in water a part of its molecules split
up into ions. This process is called electrolytic dis-
sociation.

131

133

If the solution takes place in a large volume of
water, i.e., if the solution is very dilute, all of the
molecules are split up into ions. In such a solution
the electrolyte is present only in the form of ions.

Examples. Potassium chloride in aqueous

solutions is partly split up into the ions K and Cl;

4- | -

potassium nitrate into K and NO3; sulphuric acid ac-

-t- + +

cording to the dilution into H and HSO4 or into H, H

and SO4; potassium acetate into K and C2H3O2.

REMARK. Clausius was the first to put forward the hy-
pothesis that electrolytes on passing into solution in water
partly split up into their ions. If such a solution is elec-
trolyzed, then the ions, which at first move in all directions
through the solution, will be guided by the current, the
cathions to the cathode and the anions to the anode.

The action of the current on the electrolyte is therefore
not the decomposition — since the electrolyte is already de-
composed into its ions in the solution — but the transporta-
tion of the ions to the electrodes.

Later (1887) Arrhenius chose this hypothesis as a starting-
point and founded upon it his theory of electrolytic dis-
sociation.

Since the ions are charged with electricity they can exist
in water without action on it. A normal potassium atom
would instantly decompose water ; a charged potassium
atom (potassium ion), however, is neutral in its action to-
wards water until the electric charge which it bears has
been removed from it, as occurs when it comes in contact
with the cathode.

§61. Faraday's Law. This can be stated as
follows: The movement of electricity in electrolytes

133

takes place only with the simultaneous movement of
the ions.

Chemically equivalent quantities of different ions
move with equal quantities of electricity.

If equal quantities of electricity pass through solu-
tions of different electrolytes, for example, silver nitrate
and copper sulphate, then, according to Faraday, the
weights of silver and copper ions which move through
these solutions with this quantity of electricity will
stand to each other in the ratio of the chemical equi-
valent weights of silver and copper; i.e., — : — — .

During electrolysis, when the transported ions are
discharged at the electrodes and the silver and copper
ions pass into the neutral condition, the weights of the
metals deposited will stand in the ratios of their chem-
ical equivalent weights.

REMARKS. Experiment has demonstrated that when in
one second the unit quantity of electricity (one coulomb)
passes through a solution of a silver salt, in this time there
will be deposited 1.118 milligrams of metallic silver. This
quantity is called the electrochemical equivalent of silver.

From these data, by applying Faraday's law, the electro-
chemical equivalent of every other ion can be calculated.

Thus, for example, the electrochemical equivalent of lead
(x) is obtained from the equation

TTo . _ I07*93 . 206.9 .

A • A 1 O • «^v — —

I 2

x = 1.071.

§62. Conductivity of Organic and Inorganic
Compounds. In general, organic compounds in aque-

134

ous solutions are poor conductors and similar solutions
of inorganic compounds are good conductors. Solu-
tions of strong acids in water conduct better than solu-
tions of weak acids; organic acids in solutions conduct
to a perceptible extent only when greatly diluted.
Organic salts are good conductors.

The exceptions mentioned in § 58 are not observed,
or at most the variations from the general law are only
slight, when solvents other than water are used.

§ 63. Some Laws Governing Electrolytic Dis-
sociation.

a. This dissociation increases with the dilution, and
with increasing dilution approaches a maximum value.

Example. Potassium chloride in fairly con-
centrated solutions is partially dissociated into the
ions K and Cl. The state of the system is therefore

The degree of dissociation, at a certain temperature
and concentration, has a fixed value. With increas-
ing dilution x decreases and (i — x) increases, until
finally when infinite dilution is reached all the mole-
cules of KC1 have dissociated into ions.

b. In the case of strong acids and bases and their
salts, in general in the cases of substances which
enter into strong reactions, the dissociation is nearly
complete in fairly concentrated solutions.

The reactions of analytical chemistry are chiefly
reactions between ions.

135

Example. The formation of silver chloride
from silver nitrate and sodium chloride takes place
according to the equation:

Na|ClAq + Ag NO3Aq=:AgCl(solid)+Na NO3Aq.

REMARK i. At first thought it might appear remarkable
that such bodies as HC1, NaOH, and KC1 exist in solution
chiefly in the form of ions. It must be remembered, how-
ever, that these substances enter most readily into reactions,
and the ability to enter into reaction depends upon the
readiness with which the substances interchange their con-
stituents.

REMARK 2. The existence of electrolytic dissociation
explains why, for example, chlorine does not always show
the same reactions. According to the theory of Arrhenius
the reactions are not reactions between atoms, but between

+ | - Al-

iens. Therefore K|C1O3 with AglNO3 will not form AgCl,

since the reaction involves the ion C1O8, and not the atom
Cl.

REMARK 3. The part played by phenol-phthaline in
volumetric-analysis titrations is explained by the theory of
Arrhenius.

Phenol-phthalein is a substance of very complex con-
stitution and contains two phenol residues, the radicals
C6H4OH. These groups impart to the substance to a cer-
tain degree the properties of an acid, so that phenol-phtha-
lein may be considered as an organic acid of the character
RH. Like all organic acids, this substance in aqueous
solutions is but very slightly dissociated, a condition which
is quite different in the case of its salts. On neutralization
with a base a salt RK is formed, and this salt is dissociated

136

into the ions R and K. The red color observed when phe-
nol-phthalein is used as an indicator, is therefore due to the
formations of the ions R from the non-dissociated substance
RH.

That this explanation is correct is proved, first, by the
fact that all soluble bases produce with phenol-phthalein
the same red coloration, and, secondly, by the fact that the
red coloration is extremely weak in alcoholic solutions — alcohol
almost completely retarding electrolytic dissociation (§ 58),
— but becomes much more intense when the alcoholic solu-
tion is diluted with water.

c. With respect to the osmotic pressure and the
corresponding phenomena each ion has the value of a
molecule, since each ion moves about in the liquid as
an independent unit.

This rule explains the appearance of exceptions to
the theory of osmotic pressure as enunciated by Van't
Hoff. An example illustrating this will be given :

As previously stated, the condition of potassium
chloride in an aqueous solution is the following:

If n molecules of KC1 were originally introduced into
the solution, then the above equation would become

The number of separate particles existing in the
solution is therefore not n, but is equal to

n(i — x) + 2x = n(\ + x).

Since the osmotic pressure is proportional to the
number of dissolved molecules, and since each ion

137

acts as a separate individual particle, the value of the
osmotic pressure is a result of the action of, not n
molecules, but n(i 4- x) particles.

The value of x increases with increasing dilution
and approaches the maximum value i. Therefore at
extreme dilution the value of the osmotic pressure is
twice as great as that prescribed by theory.

These considerations also apply to the phenomena
of the depression of the freezing-point, etc,

If the depression of the freezing-point is determined
for a solution of potassium chloride of certain concen-
tration, the value thus obtained may be compared
with that which would be obtained if no dissociation
took place, and the value of x may be calculated.
This follows since the relation between the observed
value and the theoretical number is, according to the
above explanation, (i + x].

§ 64. Proof of the Theory of Electrolytic Disso-
ciation.

a. The exceptions to the general law of osmotic
pressure appear in the case of electrolytes.

This fact has already been mentioned,

b. The variation is greater with greater dilution.

c. The degree of dissociation, calculated from the
depression of the freezing-point, is equal to that
determined from the conductivity of the solution.

According to the theory of Arrhenius the ions con-
duct the electricity in a solution, the undissociated
molecules taking no part in this process. To deter-
mine the degree of dissociation, at a certain concen-
tration, the conductivity of the solution at this con-
centration is compared with the conductivity of a

138

solution of the same substance at infinite dilution ; in
the latter case the conductivity reaches its maximum
value. From these data the number of free ions and
the degree of dissociation at the given concentration
can be calculated.

REMARK. The conductivity must always be reduced to
a fixed concentration of the solution ; since although the
dissociation increases with the dilution, the concentration
of the dissolved substance decreases at the same time.

The degree of dissociation, as determined from the
conductivity of the solution, is the same as that cal-
culated from the depression of the freezing-point.

d. The law of thermoneutrality (compare § 32).
The mixing of dilute salt solutions produces no

thermal effect. This fact is readily explained by the
theory of dissociation; since in dilute solutions the
salts are almost completely dissociated, and when they
are mixed no alteration in their condition takes place.

Na | ClAq + K | NO.Aq,
both before and after mixing, is a solution of the ions

(Na, Cl, K, N~O8) in water.

e. The neutralization of a strong base by a strong
acid always gives the same heat-toning.

Hydrochloric acid, nitric acid, hydrobromic acid,
and hydriodic acid, when in dilute solution, give for
molecular quantities nearly the same quantity of heat,
-(-13.7 Cal. For example,

HClAq + KOHAq = KClAq + HaO . . . + 13.7 Cal.

139

According to the theory of electrolytic dissociation,
this reaction must, however, be expressed as follows:

H | ClAq + K | OHAq

= K | ClAq + H30 . . . + 13-7 Cal.

Therefore the thermal effect of mixing" the two solu-
tions is due solely to the formation of water from its
ions. The heat of formation of water from its ions is
accordingly equal to -f- 13.7 Cal.

Since the strong bases and the strong acids are all-
most entirely dissociated into their ions by water, the
only action on mixing the solutions is in all cases the
formation of water from its ions, and therefore the
thermal effect is in all cases the same

CHAPTER VII.
PHENOMENA OF LIGHT.

§ 65. Colored Flames. Many salts introduced
into a nonluminous gas-flame impart to the flame a
coloration which is characteristic of the metal of the
salt. Sodium salts color the flame yellow, potassium
salts violet, barium salts green. In analytical chem-
istry this coloration is used to identify many metals.

Often, however, the color effect is not sufficient for
the identification of an element, since the characteris-
tic color of one element may be masked by that of
another, and indeed the intense yellow color of
sodium is almost never absent. It is therefore neces-
sary to analyze the effect, and to separate the light
into its components. A rough method for accomplish-
ing this is by the use of cobalt glass or an indigo
prism; these allow the potassium light, but not the
sodium light, to pass through them, and it is thus
possible to identify the color of potassium in a mix-
ture of it with sodium.

§ 66. The Spectroscope. The analysis of the light
by means of the spectroscope is, however, much more
accurate. In this apparatus a ray of light from the
flame passes through a narrow slit and falls on a glass
prism. The action of the prism on the ray of complex

140

141

light passing through it is such that this ray is broken
up into a series of other rays, each of which consists of
light of a single wave-length (i.e., of a single simple
color), and these simple rays issue from the prism at
different angles. It is therefore possible to observe the
separate components of the original complex light, and
in the spectroscope this is done by placing a small tele-
scope in the path of the simple rays. The action of
the prism on the ray of complex light depends upon
the fact that lights of different wave-lengths have
different coefficients of refraction.

Every coloration imparted to the flame by a metal
in the vaporous condition consists of a definite num-
ber of different kinds of light of certain wave-lengths.
The observation of these different kinds of light and
the determination of their wave-lengths furnishes an
accurate means for determining the presence of metals
in the flame.

REMARK i. While the light emitted by luminous vapors
consists of but relatively few simple components, the spec-
trum (i.e., the collection of simple rays) of glowing solid or
liquid bodies consists of a continuous series of different
kinds of light.

Generally the spectrum of only the free metal is
observed when a salt is introduced into the flame, the
constituents of the flame decomposing and reducing
the compounds of the metal. When salts and oxides
vaporize in the flame without decomposition, then
other spectra are obtained.

REMARK 2. According to an investigation made by
Pringsheim, the luminosity of the metals is not dependent
on the temperature, but on the chemical action of the

flame on the salt or the oxide, therefore on the reduc-
tion.

For many metals the temperature of the gas-flame
is not sufficiently high to convert them into luminous
vapor. In such cases electrodes are prepared from
these metals, and electric sparks are allowed to pass
between them. By the action of the spark small
quantities of the metals are removed from the poles
and converted into vapor.

The spectrum of a gaseous substance is obtained by
introducing the gas into a tube under diminished
pressure and passing through it the current from an
induction-coil; the gas is heated to glowing and the
color is analyzed by the spectroscope.

Since the light of every vaporous element is com-
posed of a series of rays of definite wave-length, cer-
tain lines in the spectrum are characteristic of certain
elements, and the discovery of new lines may lead to
the identification of a new element. As a matter of
fact a number of elements have been discovered in
this manner by the use of the spectroscope, — namely;
caesium, indium, gallium, and germanium.

REMARK 3. Characteristic phenomena appear in the
spectroscopic investigation of salts of the so-called rare
earths— earths of the didymium group, of the erbium group,
and of the yttrium group. On the basis of a well-founded
theory on the nature of these earths it does not necessarily
follow, but it is nevertheless possible, that these substances
are mixtures of different oxides, and do not consist of a
single oxide only.

§ 67. Absorption Phenomena. The light which
we call white is in reality very complex and consists of

rays of all possible wave-lengths. White light gives a
continuous spectrum, that is, a spectrum which is not
broken up into lines of especial brilliancy or intensity,
but which, on the contrary, shades off uniformly from
infra-red to ultra-violet. When white light is allowed
to pass through the luminous vapor of an element, the
vapor absorbs from the white light those components
which the vapor itself is able to emit^ and as a result the
spectrum of the white light is found to contain a series
of dark lines which correspond to the bright lines in
the spectrum of the vaporous element. Also non-
luminous vapors show a similar property of absorption.
These facts play an important part in the explana-
tion of the dark lines which appear in the solar spec-
trum. Many of the dark lines in the solar spectrum
correspond to the bright lines of certain luminous
elements. From these facts Kirchoff deduced the
following hypothesis: The sun consists of a solid
or liquid nucleus which is surrounded by an atmos-
phere of luminous vapor. The nucleus emits
white light, and when this light reaches the earth
it is destitute of those rays which have been ab-
sorbed by the solar atmosphere. The dark lines of
the solar spectrum correspond to elements which exist
in the solar atmosphere, but which must be present
in the nucleus also. Since, however, many of the
dark lines of the solar spectrum correspond to the
bright lines in the spectrum of the light emitted by
the luminous vapor of terrestrial elements, it may
safely be assumed that the earth and sun are largely
composed of the same elements. The fixed stars
also give a spectrum containing dark lines.

144

§ 68. Photochemical Action. In the phenomena
of light which have been described the substances
which absorb the light undergo no chemical alteration.
There are, however, a large number of cases known
where the action of the light on the illuminated body
produces an alteration which is of a purely chemical
nature. A consideration of these cases leads to the
following general laws:

a. All kinds of light from infra-red to ultra-violet
are capable of exerting a photochemical action.

REMARK i. The assumption that only violet light can
produce chemical action is incorrect. The most evident
photochemical action in nature, the decomposition of the
atmospheric carbon dioxide under the influence of the
green chlorophyll of plants, is due chiefly to the yellow con-
stituents of sunlight. It is also incorrect to speak of certain
kinds of light as being especially active from a chemical
standpoint, since every kinds of light can produce certain,
characteristic chemical action.

b. Photochemical action is exerted only by those
rays which are absorbed by the illuminated substance.

REMARK 2. The reverse of this law, that absorption is
necessarily associated with chemical action, is not true.

c. The nature of the illuminated substance deter-
mines the nature of the chemical action. Red light,
however, exerts chiefly an oxidizing, violet light
chiefly a reducing, action on compounds of the metals.
The reciprocal action of metalloids is generally pro-
moted by violet light.

d. The readiness with which a substance is affected
by rays of a certain wave-length is increased by the
admixture of other substances which absorb these
rays.

145

e. A substance is usually more readily decomposed
by light if it be mixed with other substances which
can combine with the products of the decomposition.

REMARK 3. The explanation of this fact is that the
removal of the decomposition-products prevents the re-
formation of the original substance.

§ 69. Photochemical Extinction. Photochemical
extinction is that phenomenon which is exhibited when
rays which pass through a medium which is sensitive
to light are weaker in their chemical action when they
pass through a second layer of the same medium, this
weakening not being assignable to a purely optical
absorption.

Example. Light which has passed through a
mixture of equal parts of chlorine and hydrogen in a
layer of given thickness has a much more feeble chem-
ical action than that which has passed through a layer of
chlorine of half the thickness, although the optical
absorption is in both cases the same.

When the chemical action of light reaches its great-
est intensity, not immediately after absorption, but
after a certain time has elapsed, the phenomenon is
called photochemical induction.

REMARK. The combination of hydrogen with chlorine
is explained by assuming that these gases do not act directly
upon one another, but combine through the agency of
water-vapor, with which an intermediate compound is first
formed. It is possible that the reactions are the following:

H20 + Clt = C1.0 + Ha;
2H3 + Cl,0 = H,0 -f 2HC1.

146

An appreciable time would be required before a quantity
of ClaO would be formed sufficient to produce the second
reaction.

This hypothesis is founded on the fact that a mixture of
moist chlorine and hydrogen is much more sensitive to light
than a dry mixture of the same gases.

§ 70. Development and Fixing of a Photo-
graphic Image. In all the various photographic
methods the light acts for only a short time on the
sensitive plate, and in this time no visible image is pro-
duced. After the exposure, when the plate is treated
with a so-called developer, the image gradually ap-
pears. In the modern methods of photography the de-
veloper is a reducing substance which reduces the silver
salt of the sensitive plate, this reduction occurring only
at those points where the light has acted and has pro-
duced a latent image.

REMARK. The explanation of the process of develop-
ment is purely hypothetical, and depends upon the process
of daguerreotyping, which has not been practised for many
years. Daguerre (1838) exposed a silver plate, weakly
iodized on the surface, for several seconds to the action of
light. In this period no visible picture was produced, and
Daguerre then brought the surface of the plate into contact
with the vapor of mercury. This vapor was precipitated
most rapidly on those points of the plate where the light
had caused the decomposition of the silver iodide with the
formation of slight traces of silver, and as a result the sur-
face of the plate became rougher at those points.

On the basis of these facts, it may be assumed that in
the modern methods of development the developer first
attacks the sensitive surface of the plate at those points
where partial decomposition has already taken place. The
silver bromide of the silver-bromide gelatine plates, partially

147

decomposed by light, concentrates the action of the de-
veloper at those points where the decomposition has already
begun, and at those points a more rapid reduction, and
accordingly a more rapid separation of silver, takes place.

It must be clearly understood that this explanation is of
a very hypothetical nature.

When the image is developed, it is made perma-
nent or fixed. The plate is immersed in a solution of
some substance v/hich dissolves the undecomposed
portion of the sensitive material and thus removes it.

By this process, however, only a so-called negative
is obtained : the high lights of the object photographed
have sent out many rays, have caused a strong sep-
aration of silver, and have produced a dark image; the
shadows, on the contrary, have produced a lighter
image. A positive is obtained by placing the nega-
tive plate on a piece of sensitive paper and exposing
this to the light; the relations of light and shadow are
now exactly reversed.

§ 71. Color Photography. Lippmann in 1891
succeeded in photographing the solar spectrum in its
natural colors. The sensitive film which he exposed
to the light was backed by a layer of mercury. The
light-waves passed through the film and were reflected
back by the surface of the mercury; the reflected
waves interfered with the direct waves and formed
standing waves. The wave-lengths of these waves is
extremely small, and accordingly a large number of
crests and nodes were formed in the sensitive film,
the decomposition of the silver salts reaching a maxi-
mum at the crests and being equal to zero at the nodes.
The films were developed and fixed in the usual

148

manner, and layers of reduced silver were formed in
the sensitive film. The distances between the layers
of silver were equal to one-half the wave-length of the
color which produced them. When the film was
viewed by white light, the layers of silver caused inter-
ference phenomena, and therefore reflected light of a
color corresponding to that by which they had been
produced.

CHAPTER VIII.
THE PERIODIC SYSTEM.

§ 72. Definition. The periodic system is a group-
ing of the elements which depends upon the law
that the properties of the elements, so far as these
may be expressed by numbers, are periodic functions
of their atomic weights.

REMARK i. The quantity A is a function of the quan-
tity B, if they alter simultaneously, and if to every value of
B there corresponds one or more values of A. Thus A is a
function of B in the following equations :

A = 3B;
A = Bn;

A = arc sin B.

A is aperiodic function of B if on a continuous increase
in the value of B the value of A is the same at regular in-
tervals. Thus in the equation

A = sin B

A is a periodic function of B, since for every value of B A
has a certain value; A will, however, have the same value
if B is 360° or 720° or n times 360° greater, and accordingly
for every interval of 360° A again receives the same value.
This interval is called a period, and the series of values

149

150

which A receives while B is passing through an interval is
also called a period.

REMARK 2. The basis of the periodic system is the
periodic function. Nevertheless the periodicity is not as-
sociated with mathematical exactitude with a period of
definite interval. The theory may therefore be brought
into closer agreement with the facts if it be stated that when
the elements are arranged in the order of their increasing
atomic weights they may be separated into definite groups,
and the properties of any one group can be found recurring
in the others at certain stated positions.

REMARK 3. A relation between the properties of the
elements and their atomic weights has long been sought, it
having been observed that a mathematical relation exists
between the atomic weights of those elements which, from
their general properties, form a natural group or family.
Thus the atomic weight of strontium is approximately the
mean of the atomic weight of calcium and the atomic
weight of barium; the atomic weight of sodium is approxi-
mately the mean of the atomic weights of lithium and
potassium. Zeuner (1857) divided the elements known at
that time into triads.

In the years 1862 and 1863 de Chancourtois and New-
lands attempted to carry out a classification of the elements
according to their atomic weights; the latter pointed out
that similar properties appeared in the case of every
eighth element in the series. This was known as the law of
octaves.

In the year 1869 attention was first called, by Mendelejeff
and Lothar Meyer, to the periodicity of the properties with
respect to the atomic weights, and by them a system was
established in which the idea of periodicity was rigidly
applied. This system is the one at present in use.

§ 73. Graphic Representation. If in a plane
points are so determined with respect to two axes that

the abscissas are proportional to the atomic weights
and the ordinates are proportional to some property
of the elements which may be expressed by numbers,
and the points thus determined are connected by
straight lines, a broken curve is obtained which rises
and falls in a series of waves. The characteristics of
the particular property under consideration in one
wave recur in the other waves at corresponding posi-
tions. The periodic variation of the physical proper-
ties of the elements is most strikingly shown in the
graphic representation of the atomic volume.

An undulating curve of this nature is therefore a
graphic representation of the periodic system.

§ 74. Tabular Representation. If the groups of
kindred elements in a horizontal row are arranged
one below the other, then the periodic system is
obtained in the form of a table. Passing from left to
right, the elements follow their atomic weights, and
the properties which appear in one of the horizontal
rows will be found to occur again in other rows in
analogous positions. As a result the elements having
similar properties are found in the same vertical row.*

§ 75. Small and Large Periods. In the case of
the first two periods, each of which contains 7 ele-
ments, the agreement of the corresponding members
is very great. The third period begins with potas-
sium, which corresponds with sodium; but between
potassium and rubidium, with which the fourth period

* In the back of this book there is given a table of the elements
arranged chiefly according to the scheme proposed by Lothar
Meyer, from which, however, the table given by Mendelejeff does
not materially differ.

152

begins, there are 16 elements, and after rubidium
1 6* elements must be passed before caesium, an ele-
ment showing great analogy to potassium and rubid-
ium, is reached. In this case two periods of 17
elements each must be assumed, and as a matter of
fact these groups of 17 may, with respect to most of
their properties, be considered as independent periods.
They are therefore called large periods, in contradis-
tinction to the small periods which are formed by the
groups Li — Fl and Na — Cl.

The large periods fall with respect to certain prop-
erties into two groups of seven elements, in which a
slight analogy to the small periods can be observed;
the remaining three elements show no analogy and are
therefore placed in a separate column. In Lothar
Meyer's table the first large period is formed by the
third and fourth horizontal rows; the first seven ele-
ments of the first row form the first, the seven ele-
ments of the second row form the second, group. The
chief analogy with the small periods is shown when
the large periods are considered entire; the secondary
analogy, that of valence, appears in each of the
groups.

§ 76. Variation of Physical Properties in Periods.
Not only does there exist the mentioned regularity
in the recurrence of the properties of the elements,
but also the variation of the properties of the elements
in one and the same period may often be included un-
der a general rule. In general the physical properties,

* The existence of an element having an atomic weight of about
loc is here assumed.

153

when these can be expressed by numbers, attain a
maximum or a minimum in the middle of a period.

The specific gravity (in the solid state) increases
until the middle of the period is reached, there attains
a maximum, and then decreases.

The atomic volume (the quotient of the atomic
weight and the specific gravity in the solid state)
decreases to the middle of the period, there reaches
a minimum, and then increases.

If the relation between the atomic volume and the
atomic weight is graphically represented by means of
a curve (compare § 73), a series of waves are obtained
which very clearly express the idea of periodicity of
the properties. Other properties are also represented
by the position of elements on this curve. The rising
portions of the waves, including the lowest points,
contain the difficultly fusible and nonvolatile elements ;
the descending portions contain those elements which
are readily fusible and volatile.

The atomic heat, which for most elements is a nearly
constant quantity (§ 24), can also be considered as
one of the magnitudes included under the periodic
law, in so much as its variation is nearly zero in the
case of all the periods. If, as in the case of the
atomic volume, the relation between the atomic heat
and the atomic weight be represented graphically, a
straight line is obtained.

The elements which do not correspond to the law
of Dulong and Petit are found in the first and second
periods, a certain regularity being observable in their
variations ; the atomic heat becomes lower to the middle
of the peripd and then increases.

154

The valence increases in the first and second hori-
zontal rows from I to 4, and then falls again to i.
(The valence is here determined from the hydrogen
and hydrocarbon compounds and, in case such com-
pounds are not formed by the element, is deduced
from the chlorine compounds.) On the right-hand
side of the system are found those elements which
have more than one valence, and while the lowest falls
from 4 to I the highest rises from 4 to 7, as is seen
in the case of the oxygen compounds.

In the large periods the existence of a double
periodicity with respect to the valence may be ob-
served. From potassium to manganese the valence
increases from I to 7, as may be seen in the case of
the salt-forming oxides (K2O — Mn2O7), and in the
same period a second series is formed from copper to
bromine (Cu3O — Br2O7). Each two rows show a
secondary analogy with the small periods, and upon
this fact is based the arrangement of the large periods
in Lothar Meyer's table, in which the three elements
which in their valence show no analogy to the ele-
ments in the small periods are placed in a separate
column.

Still other properties of the elements are more or
less accurately expressed in the periodic system, but
the most important cases have been mentioned.

§ 77. Application of the Periodic System.

a. Correction of the Atomic Weights. Since the
general properties of an element are related to its
atomic weight, these properties may, like the atomic ,
weight, be used for determining the position of the
element in the periodic system. The introduction of

155

the natural system has therefore resulted in the case
of a number of elements in an alteration of their
atomic weights. Indium, for which the atomic
weight 75.6 was adopted, must from its general prop-
erties occupy a position between tin and cadmium;
therefore the atomic weight of this element has been
doubled and increased to 113.4. Also the metals of
the platinum group have been reinvestigated, and the
values of their atomic weights have been found to
agree with the position which had been assigned to
them from a consideration of their properties.

REMARK i. For nickel and cobalt, however, as well as
for tellurium, the atomic weights most recently determined
do not correspond to the positions of these elements in the
natural system.

b. Predicting the Existence of Undiscovered Elements.
Many vacancies may be noticed in the table ; it is to
be expected that these should be occupied by elements
which are still undiscovered and which from their
atomic weights and general properties are entitled to
these positions. It is therefore possible to predict in
advance the atomic weight and properties of such
elements. Expectations of this sort have already
been realized in the case of gallium, scandium, and
germanium.

c. Determination of the Atomic Weights. As was
explained in a, the determination of the position of
an element in the system leads to the fixing of the
magnitude of its atomic weight, and this quantity can
then be corrected with the help of analytical data.

d. The Unit of the Elements. The fact that many
properties of the elements are so closely related to a

I56

purely mathematical property, the atomic weight, has
given much encouragement to the idea, which has
already been the subject of considerable speculation,
that the elements may be considered as formed by the
condensation of a single primordial substance. Prout
suggested (1817) that all the atomic weights were mul-
tiples of the atomic weight of hydrogen. The more
accurate analyses of later investigators have shown
that the atomic weights are in no way equal multiples
of this unit, and that no simple least-common-divisor
can be discovered for the atomic weights.

It is nevertheless noteworthy that the atomic
weights of many elements are very near whole num-
bers.

REMARK 2. The methods for determining atomic weight
are therefore:

1. The analysis of molecular quantities of the compounds
of the element.

The molecular quantity, or the magnitude of the gram
molecule, is determined:

a. From the gas density and Avogadro's hypothesis.

b. From the osmotic pressure of solutions of the com-
pounds and the corresponding magnitudes — i.e., the depres-
sion of the freezing-point, the elevation of the boiling-point,
etc.

c. From special considerations on the constitution of the
compounds.

NOTE: The method a is the most important.

2. Application of the law of Dulong and Petit and the
law of Joule.

3. Application of the periodic system.

Each of the three methods gives the value of the atomic
weight with only relative accuracy; its exact value must be

is;

determined by the analysis of compounds of the particular
element under consideration,

§ 78. Closing Remarks on the Periodic System.

The elements helium, neon, argon, krypton, and xenon,
discovered by Rayleigh and Ramsay, judging from
the determinations thus far made, have the atomic
weights 4, 20, 39.9, 81.8, and 128, respectively.

The position of these elements in the periodic system
has not yet been satisfactorily determined and a discus-
sion of their significance cannot be entered into at this
point.

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Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and

Suspension Bridges , 8vo, 3 50

Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 oo

Foster's Treatise on Wooden Trestle Bridges 4to, 5 oo

Fowler's Coffer-dam Process for Piers 8vo, 2 50

Greene's Roof Trusses 8vo, i 25

Bridge Trusses 8vo, 2 50

Arches in Wood, Iron, and Stone 8vo, 2 50

Howe's Treatise on Arches 8vo, 4 oo

Design of Simple Roof-trusses in Wood and Steel 8vo, 2 oo

Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of

Modern Framed Structures Small 4to, 10 oo

Merriman and Jacoby's Text-book on Roofs and Bridges:

Part I. — Stresses in Simple Trusses 8vo, 2 50

Part IL— Graphic Statics 8vo, 2 50

Part HI.— Bridge Design. 4th Edition, Rewritten 8vo, 2 50

Part IV.— Higher Structures 8vo, 2 50

Morison's Memphis Bridge 4to, 10 oo

Waddell's De Pontibus, a Pocket-book for Bridge Engineers. . . i6mo, morocco, 3 oo

Specifications for Steel Bridges i2tno, i 25

Wood's Treatise on the Theory of the Construction of Bridges and Roofs.Svo, 2 oo
Wright's Designing of Draw-spans:

Part I. —Plate-girder Draws 8vo, 2 50

Part II. — Rive ted- truss and Pin-connected Long-span Draws 8vo, 2 50

Two parts in one volume 8vo, 3 50

HYDRAULICS.

Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from an

Orifice. (Trautwine.) 8vo, 2 oo

Bovey's Treatise on Hydraulics 8vo, 5 oo

Church's Mechanics of Engineering 8vo, 6 oo

Diagrams of Mean Velocity of Water in Open Channels paper, i 50

Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50

Flather's Dynamometers, and the Measurement of Power 12 mo, 3 oo

FolwelTs Water-supply Engineering 8vo, 4 oo

Frizell's Water-power 8vo, 5 oo

Fuertes's Water and Public Health lamo, i 50

Water-filtration Works i2mo, 2 50

Ganguillet and Kutter's General Formula for the Uniform Flow of Water in

Rivers and Other Channels. (Hering and Trautwine.) 8vo, 4 oo

Hazen's Filtration of Public Water-supply .8vo, 3 oo

Hazlehurst's Towers and Tanks for Water- works 8vo, 2 50

Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal

Conduits 8vo, 2 oo

Mason's Water-supply. (Considered Principally from a Sanitary Stand-
point.) 3d Edition, Rewritten 8vo, 4 oo

Merriman's Treatise on Hydraulics, gth Edition, Rewritten 8vo, 5 oo

* Michie's Elements of Analytical Mechanics 8vo, 4 oo

Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water-
supply Large 8vo, 5 oo

** Thomas and Watt's Improvement of Riyers. (Post., 44 c. additional), 4to, 6 oo

Turneaure and Russell's Public Water-supplies 8vo, 5 oo

Wegmann's Desien and Construction of Dams. . 4to, 5 oo

Water-supply of the City of New York from 1658 to'iSgs 4to, 10 oo

Weisbach's Hydraulics and Hydraulic Motors. (Du Bois.) 8vo, 5 oo

Wilson's Manual of Irrigation Engineering Small 8vo, 4 oo

Wolff's Windmill as a Prime Mover 8vo, 3 oo

Wood's Turbines 8vo, 2 50

Elements of Analytical Mechanics 8vo, 3 oo

MATERIALS OF ENGINEERING.

Baker's Treatise on Masonry Construction 8vo, 5 oo

Roads and Pavements 8vo, 5 oo

Black's United States Public Works Oblong 4to, 5 oo

Bovey's Strength of Materials and Theory of Structures 8vo, 7 50

Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edi-
tion, Rewritten 8vo, 7 50

Byrne's Highway Construction 8vo, 5 oo

Inspection of the Materials and Workmanship Employed in Construction.

i6mo, 3 oo

Church's Mechanics of Engineering 8vo, 6 oo

Du Bois's Mechanics of Engineering. VoL I Small 4to, 7 50

Johnson's Materials of Construction Large 8vo, 6 oo

Keep's Cast Iron 8vo, 2 50

Lanza's Applied Mechanics 8vo, 7 '50

Martens's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 750

Merrill's Stones for Building and Decoration 8vo, 3 oo

Merriman's Text-book on the Mechanics of Materials 8vo, 4 oo

Strength of Materials i2mo, i oo

Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo

Patton's Practical Treatise on Foundations 8vo, 5 oo

Rockwell's Roads and Pavements in France i2mo, * ar.

Smith's Materials of Machines i2mo, i oo

Snow's Principal Species of Wood 8vo, 3 50

Spalding's Hydraulic Cement i2mo, 2 oo

Text-book on Roads and Pavements i2mo, 2 oo

Thurston's Materials of Engineering. 3 Parts 8vo, 8 oo

art I. — Non-metallic Materials of Engineering and Metallurgy 8vo, 2 oo

Part n. — Iron and Steel 8vo, 3 50

Part III. — A Treatise on Brasses, Bronzes, and Other Alloys and their

Constituents 8vo, 2 50

Thurston's Text-book of the Materials of Construction 8vo, 5 oo

Tillson's Street Pavements and Paving Materials 8vo, 4 oo

Waddell's De Pontibus. (A Pocket-book for Bridge Engineers.) . . i6mo, mor., 3 oo

Specifications for Steel Bridges i2mo, i 25

Wood's Treatise on the Resistance of Materials, and an Appendix on the Pres-
ervation of Timber 8vo, 2 oo

Elements of Analytical Mechanics 8vo, 3 oo

Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. . .8vo, 4 oo

RAILWAY ENGINEERING.

Andrews's Handbook for Street Railway Engineers. 3X5 inches, morocco, i 25

Berg's Buildings and Structures of American Railroads 4to, 5 oo

Brooks's Handbook of Street Railroad Location i6mo. morocco, i 50

Butts's Civil Engineer's Field-book i6mo, morocco, 2 50

Crandall's Transition Curve i6mo, morocco, i 50

Railway and Other Earthwork Tables 8vo, i 50

Dawson's "Engineering" and Electric Traction Pocket-book. i6mo, morocco, 5 oo

Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 oo

* Drinker's Tunneling, Explosive Compounds, and Rock Drills, 4to, half mor., 25 oo

Fisher's Table of Cubic Yards Cardboard, 25

Godwin's Railroad Engineers' Field-book and Explorers' Guide i6mo, mor., 2 50

Howard's Transition Curve Field-book i6mo, morocco, i 50

Hudson's Tables for Calculating the Cubic Contents of Excavations and Em-
bankments 8vo, i oo

Molitor and Beard's Manual for Resident Engineers i6mo, i oo

Nagle's Field Manual for Railroad Engineers i6mo morocco. 3 oo

Philbrick's Field Manual for Engineers i6mo, morocco, 3 oo

Searles's Field Engineering i6mo, morocco, 3 oo

Railroad Spiral. i6mo, morocco, i 50

Taylor's Prismoidal Formulae and Earthwork 8vo, i 50

* Trautwine's Method of Calculating the Cubic Contents of Excavations and

Embankments by the Aid of Diagrams 8vo, 2 oo

The Field Practice of {Laying Out Circular Curves for Railroads.

izrno, morocco, 2 50

Cross-section Sheet Paper, 25

Webb's Railroad Construction. 2d Edition, Rewritten i6mo. morocco, 5 oo

Wellington's Economic Theory of the Location of Railways Small 8vo, 5 oo

DRAWING.

Barr's Kinematics of Machinery 8vo, 2 50

* Bartlett's Mechanical Drawing. . . 8vo, 3 oc

* •• ' " Abridged Ed 8vo, 150

Coolidge's Manual of Drawing 8vo, paper, i oo

Coolidge and Freeman's Elements of General Drafting for Mechanical Engi-
neers. (In press.')

Durley's Kinematics of Machines 8vo, 4 oo

Hill's Text-book on Shades and Shadows, and Perspective 8vo, 2 oo

Jamison's Elements of Mechanical Drawing. (In press.)

Jones's Machine Design:

Part I. — Kinematics of Machinery 8vo, i 50

Part II. — Form, Strength, and Proportions of Parts 8vo, 3 oo

Mac Cord's Elements of Descriptive Geometr> 8vo, 3 oo

Kinematics; or, Practical Mechanism , 8vo, 5 oo

Mechanical Drawing , . . . > 4to, 4 oo

Velocity Diagrams 8vo, i 50

* Mahan's Descriptive Geometry and Stone-cutting , , 8vo, i 50

Industrial Drawing. (Thompson.) 8vo, 3 50

Reed's Topographical Drawing and Sketching 4to, 5 oo

Reid's Course in Mechanical Drawing 8vo, 2 oo

Text-book of Mechanical Drawing and Elementary Machine Design . . 8vo, 3 oo

Robinson's Principles of Mechanism 8vo, 3 oo

Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 50

Warren's Elements of Plane and Solid Free-hand Geometrical Drawing. . i2mo, oo

Drafting Instruments and Operations i2mo,

Manual of Elementary Projection Drawing i2mo,

Manual of Elementary Problems in the Linear Perspective of Form and

Shadow i2nio, oo

Plane Problems in Elementary Geometry i2mo, 25

Primary Geometry I2mo, 75

Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50

General Problems of Shades and Shadows 8vo. 3 oo

Elements of Machine Construction and Drawing 8vo, 7 50

Problems. Theorems, and Examples in Descriptive Geometry 8vo, 2 50

Weisbach's Kinematics and the Power of Transmission. (Hermann and

Klein.) 8vo. 5 oo

Whelpley's Practical Instruction in the Art of Letter Engraving i2mo, 2 oo

Wilson's Topographic Surveying 8vo, 3 50

Free-hand Perspective , 8vo, 2 50

Free-hand Lettering 8vo, i oo

Woolf's Elementary Course in Descriptive Geometry Large 8vo, 3 oo

'ELECTRICITY AND PHYSICS.

Anthony and Brackett's Text-book of Physics. (Magie.) Small 8vo, 3 oo

Anthony's Lecture-notes on the Theory of Electrical Measurements I2mo, i oo

Benjamin's History of Electricity 8vo, 3 oo

Voltaic CelL 8vo, 3 oo

Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.). .8vo, 3 oo

Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 oo

Dawson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 oo
Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von

Ende.) i2mo,**2 50

Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 oo

Flather's Dvnamometers, and the Measurement of Power I2mo, 3 oo

Gilbert's De Magnete. (Mottelay.) 8vo, 2 50

Hanchett's Alternating Currents Explained I2mo, i oo

Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50

Holman's Precision of Measurements 8vo, 2 oo

Telescopic Mirror-scale Method, Adjustments, and Tests Large 8vo, 75

Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo

Le Chatelier's High-temperature Measurements. (Boudouard — Burgess. )i2mo, 3 oo

Lob's Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz.) i2mo. i oo

* Lyons's Treatise on Electro magnetic Phenomena. Vols. I. and II. 8vo, each, 6 oo

* Michie. Elements of Wave Motion Relating to Sound and Light 8vo, 4 oo

Niaudet's Elementary Treatise on Electric Batteries. (Fishoack. ) jaino, 2 50

• Rosenberg's Electrical Engineering. (Haldane Gee — Kinzbrunner.). . . .8vo, 50

Ryan, Norris, and Hoxie's Electrical Machinery. VoL 1 8vo, 50

Thurston's Stationary Steam-engines 8vo, 50

* Tillman's Elementary Lessons in Heat 8vo, 50

Tory and Pitcher's Manual of Laboratory Physics Small 8vo, oo

Ulke's Modern Electrolytic Copper Refining 8vo, 3 oo

LAW.

* Davis's Elements of Law 8vo, 2 50

* Treatise on the Military Law of United States 8vo, 7 oo

Sheep, 7 50

Manual for Courts-martial i6mo, morocco, i 50

Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo

Sheep, 6 50

Law of Operations Preliminary to Construction in Engineering and Archi-
tecture 8vo, 5 oo

Sheep, 5 50

Law of Contracts 8vo, 3 oo

Winthrop's Abridgment of Military Law I2mo, 2 50

MANUFACTURES.

Bernadou's Smokeless Powder — Kitro-cellulose and Theory of the Cellulose

Molecule i2mo, 2 50

Boliand's Iron Founder i2mo, 2 50

" The Iron Founder," Supplement. . . . i2mo, 2 50

Encyclopedia of Founding and Dictionary of Foundry Terms Used in the

Practice of Moulding i2mo, 3 oo

Eissler's Modern High Explosives 8vo, 4 oo

Eff rent's Enzymes and their Applications. (Prescott.) 8vo, 3 oo

Fitzgerald's Boston Machinist i8mo, i oo

Ford's Boiler Making for Boiler Makers i8mo, i oo

Hopkins's Oil-chemists' Handbook 8vo, 3 oo

Keep's Cast Iron 8vo, a 50

Leach's The Inspection and Analysis of Food with Special Reference to State

Control. (In preparation.)

Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo

Metcalfe's Cost of Manufactures — And the Administration of Workshops,

Public and Private 8vo, 5 oo

Meyer's Modern Locomotive Construction 4to, 10 oo

Morse's Calculations used in Cane-sugar Factories i6mo, morocco, i 50

* Reisig's Guide to Piece-dyeing 8vo, 25 oo

Smith's Press-working of Metals 8vo, 3 oo

Spalding's Hydraulic Cement i2mof 2 oo

Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 oo

Handbook tor sugar Manuiacmrers ana their Chemists.. . i6mo, morocco, 2 oo
Thurston's Manual of Steam-boilers, their Designs, Construction and Opera-
tion 8vo, 5 oo

* Walke's Lectures on Explosives 8vo, 4 oo

West's American Foundry Practice i2mo, 2 50

Moulder's Text-book i2mo, 2 50

Wiechmann's Sugar Analysis Small 8vo, 2 50

Wolff's Windmill as a Prime Mover 8vo, 3 oo

Woodbury's Fire Protection of Mills 8vo, 2 50

Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. . .8vo, 4 oo

MATHEMATICS.

Baker's Elliptic Functions 8vo, i 50

* Bass's Elements of Differential Calculus I2mo, 4 oo

Briggs's Elements of Plane Analytic Geometry i2mo,

Compton's Manual of Logarithmic Computations i2mo,

Daris's Introduction to the Logic of Algebra 8vo,

* Dickson's College Algebra Large i2mo,

* Answers to Dickson's College Algebra 8vo, paper,

* Introduction to the Theory of Algebraic Equations Large I2mo,

Ualsted's Elements of Geometry 8vo,

Elementary Synthetic Geometry 8vo,

oo
50
So
50

25
25
75
50
Rational Geometry i2mo, 75

* Johnson's Three-place Logarithmic Tables: Vest-pocket size paper, 15

100 copies for 5 oo

* Mounted on heavy cardboard, 8 X 10 inches, 25

10 copies for 2 oo

Elementary Treatise on the Integral Calculus Small 8vo, i 50

Curve Tracing in Cartesian Co-ordinates _ . I2mo, i oo

Treatise on Ordinary and Partial Differential Equations Small 8vo, 3 50

Theory of Errors and the Method of Least Squares i2mo, i 50

* Theoretical Mechanics . . I2mo, 3 oo

Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) i2mo, 2 oo

* Ludlow and Bass. Elements of Trigonometry and Logarithmic and Other

Tables 8vo, 3 oo

Trigonometry and Tables published separately Each, 2 oo

* Ludlow's Logarithmic and Trigonometric Tables 8vo, i oo

Maurer's Technical Mechanics 8vo, 4 oo

Merriman and Woodward's Higher Mathematics 8vo, 5 oo

Merriman's Method of Least Squares 8vo, 2 oo

Rice and Johnson's Elementary Treatise on the Differential Calculus . Sm., 8vo, 3 oo

Differential and Integral Calculus. 2 vols. in one Small 8vo, 2 50

Sabin's Industrial and Artistic Technology of Paints and Varnish. (In press.)
Wood's Elements of Co-ordinate Geometry 8vo, 2 oo

Trigonometry: Analytical, Plane, and Spherical i2mo, i oo

MECHANICAL ENGmEERING.
MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS.

Baldwin's Steam Heating for Buildings I2mo, 2 50

Barr's Kinematics of Machinery 8vo, 2 50

* Bartlett's Mechanical Drawing 8vo, 3 oo

* " " " Abridged Ed 8vo. i 50

Benjamin's Wrinkles and Recipes *2mo, 2 oo

Carpenter's Experimental Engineering 8vo, 6 oo

Heating and Ventilating Buildings 8vo, 4 oo

Gary's Smoke Suppression in Plants using Bituminous CoaL (In prep-
aration.)

Clerk's Gas and Oil Engine Small 8vo, 4 oo

Coolidge's Manual of Drawing 8vo, paper, i oo

Coolidge and Freeman's Elements of General Drafting for Mechanical En-
gineers. (In press.)

Cromwell's Treatise on Toothed Gearing i2mo, i 50

Treatise on Belts and Pulleys i2mo, i 50

Durley's Kinematics of Machines 8vo, 4 oo

Flather's Dynamometers and the Measurement of Power i2mo, 3 oo

Rope Driving , i2mo, 2 oo

Gill's Gas and Fuel Analysis for Engineers v , , i2mo, i 25

Hall's Car Lubrication i2mo, i oo

Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50

Button's The Gas Engine 8vo, 5 oo

Jones's Machine Design:

Part I. — Kinematics of Machinery 8vo,

Part II. — Form, Strength, and Proportions of Parts 8vo,

Kent's Mechanical Engineer's Pocket-book i6mo, morocco,

Kerr's Power and Power Transmission 8vo,

MacCord's Kinematics; or, Practical Mechanism 8vo,

Mechanical Drawing 4to,

Velocity Diagrams 8vo,

Mahan's Industrial Drawing. (Thompson.) 8vo,

Poole's Calorific Power of Fuels 8vo,

Reid's Course in Mechanical Drawing „ 8vo.

Text-book of Mechanical Drawing and Elementary Machine Design. .8vo,

Richards's Compressed Air I2mo,

Robinson's Principles of Mechanism 8vo,

Smith's Press-working of Metals 8vo,

Thurston's Treatise on Friction and Lost Work in Machinery and Mill

Work 8vo,

Animal as a Machine and Prime Motor, and the Laws of Energetics . izmo,

Warren's Elements of Machine Construction and Drawing Svo,

Weisbach's Kinematics and the Power of Transmission. Herrmann —

Klein.) 8vo,

Machinery of Transmission and Governors. (Herrmann — Klein.). .8vo,

HydrauLcs and Hydraulic Motors. (Du Bois.) 8vo,

Wolff's Windmill as a Prime Mover 8vo,

Wood's Turbines i 8vo,

MATERIALS OF ENGINEERING.

Bovey's Strength of Materials and Theory of Structures 8vo, 7 50

Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition,

Reset Svo, 7 50

Church's Mechanics of Engineering 8vo, 6 oo

Johnson'? Materials of Construction Large 8vo, 6 oo

Keep's Cast Iron 8vo, 2 50

Lanza's Applied Mechanics 8vo, 7 50

Martens's Handbook on Testing Materials. (Henning.) 8vo, 7 50

Merriman's Text-book on the Mechanic* of Materials 8vo, 4 oo

Strength of Materials i2mo,

Metcalf's Steel. A Manual for Steel-users i2mo.

Smith's Materials of Machines i2mo

Ihurston's Materials of Engineering 3 vols. , Svo,

Part H.— Iron and Steel Svo,

Part HI. — A Treatise on Brasses, Bronzes, and Other Alloys and their

Constituents Svo 2 50

Text-book of the Materials of Construction Svo, 5 oo

Wood's Treatise on the Resistance of Materials and an Appendix on the

Preservation of Timber 8vo, 2 oo

Elements of Analytical Mechanics Svo, 3 oo

Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. . .Svo, 4 oo

STEAM-ENGINES AND BOILERS.

Carnot's Reflections on the Motive Power of Heat. (Thurston.) i2mo, t 50

Dawson's "Engineering" and Electric Traction Pocket-book. .i6mo, mor., 5 co

Ford's Boiler Making for Boiler Makers i8mo, i oo

Goss's Locomotive Sparks 8vo, 2 oo

Hemenway's Indicator Practice and Steam-engine Economy 12 mo, a oo

Button's Mechanical Engineering of Power Plants 8vo, 5 oo

Heat and Heat-engines 8vo, 5 oo

Kent's Steam-boiler Economy 8vo, oo

Kneass's Practice and Theory of the Injector 8vo 50

MacCord's Slide-valves 8vo, oo

Meyer's Modern Locomotive Construction 4to. 10 oo

Peabody's Manual of the Steam-engine Indicator i2mo, 50

Tables of the Properties of Saturated Steam and Other Vapors 8vo, oo

Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 oo

Valve-gears for Steam-engines 8vo, 2 50

Peabody and Miller's Steam-boilers 8vo, 4 oo

Pray'a Twenty Years with the Indicator. Large 8vo, 2 50

Pupln's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors.

(Osterberg.) i2mo. i 25

Reagan's Locomotives : Simple, Compound, and Electric i2mo, 2 50

Rontgen's Principles of Thermodynamics. (Du Bois.) 8vo, 5 oo

Sinclair's Locomotive Engine Running and Management i2mof 2 oo

Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50

Snow's Steam-boiler Practice * 8vo, 3 oo

Spangler's Valve-gears 8vo, 2 50

Notes on Thermodynamics I2mo, i oo

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo

Thurston's Handy Tables 8vo, i 50

Manual of the Steam-engine 2 vols., 8vo, 10 oo

Part I. — History, Structuce, and Theory 8vo, 6 oo

Part II. — Design, Construction, and Operation 8vo, 6 oo

Handbook of Engine and Boiler Trials, and the Use of the Indicator and

the Prony Brake 8vo 5 oo

Stationary Steam-engines 8vo, 2 50

Steam-boiler Explosions in Theory and in Practice i2mo i 50

Manual of Steam-boilers , Their Designs, Construction, and Operation . 8vo, 5 oo

Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo, 5 oo

Whitham's Steam-engine Design 8vo, 5 oo

Wilson's Treatise on Steam-boilers. (Flather.) i6mo, 2 50

Wood's Thermodynamics Heat Motors, and Refrigerating Machines. . . .8vo, 4 oo

MECHANICS AND MACHINERY.

Barr's Kinematics of Machinery • 8vo, 2 50

Bovey's Strength of Materials and Theory of Structures 8vo, 7 50

Chase's The Art of Pattern-making I2mo, 2 50

Chordal. — Extracts from Letters I2mo, 2 oo

Church's Mechanics of Engineering 8vo, 6 oo

Notes and Examples in Mechanics 8vo, oo

Compton's First Lessons in Metal-working ' 1 12mo, 50

Compton and De Groodt's The Speed Lathe I2mo, 50

Cromwell's Treatise on Toothed Gearing I2mo, 50

Treatise on Belts and Pulleys i2mo, 50

Dana's Text-book of Elementary Mechanics for the Use of Colleges and

Schools I2mo, i 50

Dingey's Machinery Pattern Making i2mo, 2 oo

Dredge's Record of the Transportation Exhibits Building of the World's

Columbian Exposition of 180,3 4to, half morocco, 5 oo

Du Bo s's Elementary Principles of Mechanics:

Vol. I.— Kinematics 8vo, 3 50

Vol II. — Statics 8vo, 4 oo

Vol. III. — Kinetics 8vo, 3 50

Mechanics of Engineering. Vol. I Small 4to, 7 50

VoL II Small 4to, 10 oo

Durley's Kinematics of Machines 8vo, 4 oo

Fitzgerald's Boston Machinist i6mo, i oo

Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo

Rope Driving I2mo,

Goss's Locomotive Sparks 8vo

Hail's Car Lubrication I2mo,

Holly's Art of Saw Filing i8mo,

* Johnson's Theoretical Mechanics I2mo,

Statics by Graphic and Algebraic Methods 8vo,

Jones's Machine Design:

Part I. — Kinematics of Machinery 8vo, i 50

Part n. — Form, Strength, and Proportions of Parts 8vo, 3 oo

KBIT'S Power and Power Transmission 8vo, 2 oo

Lanza's Applied Mechanics 8vo, 7 50

MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo

Velocity Diagrams 8vo, i 50

Maurer's Technical Mechanics 8vo, 4 oo

Merriman's Text- book on the Mechanics of Materials 8?o, 4 oo

* Michie's Elements of Analytical Mechanics 8vo, 4 oo

Reagan's Locomotives: Simple, Compound, and Electric I2mo, 2 50

Reid's Course in Mechanical Drawing 8vo, 2 oo

Text-book of Mechanical Drawing and Elementary Machine Design. .8vo, 3 oo

Richards's Compressed Air izmo, x 50

Robinson's Principles of Mechanism 8vo, 3 oo

Ryan, Nonris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50

Sinclair's Locomotive-engine Running and Management I2mo, 2 oo

Smith's Press-working of Metals 8vo, 3 oo

Materials of Machines i2mo, x oo

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo

Thurston's Treatise on Friction and Lost Work in Machinery and Mill

Work 8vo, 3 oo

Animal as a Machine and Prime Motor, and the Laws of Energetics, izmo, i oo

Warren's Elements of Machine Construction and Drawing 8vo, 7 50

Weisbach's Kinematics and the Power of Transmission. (Herrmann —
Klein.) 8vo,

Machinery of Transmission and Governors. (Herrmann — Klein.). 8vo,
Wood's Elements of Analytical Mechanics 8vo,

Principles of Elementary Mechanics i2mo,

Turbines « 8vo,

The World's Columbian Exposition of 1893 4to,

METALLURGY.

Egleston's Metallurgy of Silver, Gold, and Mercury:

VoL I.— Silver 8vo, 7 5<>

VoL II.— Gold and Mercury 8vo, 7 So

** Iles's Lead-smelting. (Postage 9 cents additional.) I2mo, 2 50

Keep's Cast Iron 8vo, 2 50

Kunhardt's Practice of Ore Dressing in Europe 8vo, i 50

Le Chatelier's High-temperature Measurements. (Boudouard — Burgess.) . i2tno, 3 oo

Metcalf's SteeL A Manual for Steel-users i2mo, 2 oo

Smith's Materials of Machines I2mof i oo

Thurston's Materials of Engineering. In Three Parts 8vo, 8 oo

Part II. — Iron and Steel 8vo, 3 So

Part III. — A Treatise on Brasses, Bronzes, and Other Alloys and their

Constituents 8vo, 2 50

Hike's Modern Electrolytic Copper Refining 8vo, 3 oo

MINERALOGY.

Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 50

Boyd's Resources of Southwest Virginia 8vo, 3 oo

Map of Southwest Virginia Pocket-book form, 2 oo

Brush's Manual of Determinative Mineralogy. (Penfield.) 8vo, 4 oo

Chester's Catalogue of Minerals 8vo, paper, i oo

Cloth, i 25

Dictionary of the Names of Minerals «• 8vo, 3 50

Dana's System of Mineralogy Large 8vo, half leather, 12 50

First Appendix to Dana's New "System of Mineralogy." Large 8vo, i oo

Text-book of Mineralogy 8vo, 4 oo

Minerals and How to Study Them. . . s i2mo, i 50

Catalogue of American Localities of Minerals Large 8vo, i oo

Manual of Mineralogy and Petrography i2mo, 2 oo

Eakle's Mineral Tables 8vo, i 25

Egleston's Catalogue of Minerals and Synonyms 8vo, 2 50

Hussak's The Determination of Rock-forming Minerals. (Smith.) Small 8vo, 2 oo

Merrill's Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 oo

* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests.

8vo, paper, o 50
Rosenbusch's Microscopical Physiography of the Rock-making Minerals.

(Iddings.) 8vo, 5 oo

* Tillman's Text-book of Important Minerals and Docks 8vo, 2 oo

Williams's Manual of Lithology 8vo, 3 oo

MINING.

Beard's Ventilation of Mines I2mo, 2 50

Boyd's Resources of Southwest Virginia 8vo, 3 oo

Map of Southwest Virginia Pocket-book form, 2 oo

» Drinker's Tunneling, Explosive Compounds, and Rock Drills.

4to, half morocco, 25 oo

Eissler's Modern High Explosives 8vo, 4 oo

Fowler's Sewage Works Analyses i2mo, 2 oo

Goodyear 's Coal-mines of the Western Coast of the United States 12 mo, 2 50

Ihlseng's Manual of Mining 8vo, 4 oo

** Iles's Lead-smelting. (Postage gc. additionaL) I2mo, 50

Kunhardt's Practice of Ore Dressing in Europe 8vo, 50

O'DriscolTs Notes on the Treatment of Gold Ores 8vo, oo

* Walke's Lectures on Explosives 8vo, oo

Wilson's Cyanide Processes I2mo, 50

Chlorination Process X2mo, 50

Hydraulic and Placer Mining Z2mo, oo

Treatise on Practical and Theoretical Mine Ventilation I2mo 25

SANITARY SCIENCE.

Copeland's Manual of Bacteriology. (In preparation.)

Folwell's Sewerage. (Designing, Construction and Maintenance, ) 8vo, 3 oo

Water-supply Engineering 8vo, 4 oo

Fuertes's Water and Public Health jarno, i 50

Water-filtration Works xamo, 2 50

Gerhard's Guide to Sanitary House-inspection ...................... i6mo, i oo

Goodrich's Economical Disposal of Town's Refuse .............. Demy 8vo, 3 50

Hazen's Filtration of Public Water-supplies .......................... 8vo, 3 oo

Kiersted's Sewage Disposal ..................................... i2mo, i 25

Leach's The Inspection and Analysis of Food with Special Reference to State

Control. (In preparation.)
Mason's Water-supply. (Considered Principally from a Sanitary Stand-

point.) 3d Edition, Rewritten ............................ 8vo, 4 oo

Examination of Water. (Chemical and Bacteriological.) ........ i2mo, i 25

Merriman's Elements of Sanitary Engineering ...... ................ 8vo, 2 oo

Nichols's Water-supply. (Considered Mainly from a Chemical and Sanitary

Standpoint) (1883.) .................................... 8vo, 2 50

Ogden's Sewer Design ........................................... i2mo, 2 oo

Prescott and Winslow's Elements of Water Bacteriology .with Special Reference

to Sanitary Water Analysis. . ........................... I2mo5

* Price's Handbook on Sanitation ................................ i2mo,

Richards'. Cost of Food. A Study in Dietaries ..................... i2mo,

Cost of Living au Modified by Sanitary Science .................. i2mo,

Richards and Woodman's Air, Water, and Food from a Sanitary Stand-
point ................................................... 8vo,

* Richards and Williams's The Dietary Computer ..................... 8vo,

Rideal's Sewage and Bacterial Purification of Sewage .................. 8vo,

Turneaure and Russell's Public Water-supplies ....................... 8vo,

Whipple's Microscopy of Drinking-water ............................ 8vo,

Woodhull's Notes and Military Hygiene ........................... i6mo,

MISCELLANEOUS.

Barker's Deep-sea Soundings ..................................... 8vo, 2

Emmons's Geological Guide-book of the Rocky Mountain Excursion of the
International Congress of Geologists .......... , ...... Large 8vc

Ferrel's Popular Treatise on the Winds .............................. 8vo

Haines's American Railway Management .......................... 12010,

Mott's Composition, Digestibility . and Nutritive Value of Food. Mounted chart.
Fallacy of the Present Theory of Sound ..................... . . i6mo

Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894. Small 8vo,
Rotherham's Emphasized New Testament ..................... Large 8vo,

Steel's Treatise on the Diseases of the Dog ........................... 8vo,

Totten's Important Question in Metrology ........................... 8vo 2

The World's Columbian Exposition ot 1893 ........................... 4to, i

Worcester and Atkinson. Small Hospitals, Establishment and Maintenance,
and Suggestions for Hospital Architecture, with Plans for a Small
Hospital ............................................... I2mo, r

HEBREW AND CHALDEE TEXT-BOOKS.

Green's Grammar of the Hebrew Language .......................... 8vo, 3

Elementary Hebrew Grammar ................................ i2mo, i

Hebrew Chrestomathy ........................................ 8vo, 2

Gesenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures.

(Tregelles.) ........................... Small 4to, half morocco, 5

Lett* ris't Hebrew Bible ............................................ »v°. 2

14 DAY USE

RETURN TO DESK FROM WHICH BORROWED

LOAN DEPT.

This book is due on the last date stamped below, or

on the date to which renewed.
Renewed books are subject to immediate recall.

-*3 UD

DEC 4

p\. •'

*r»r

6£ -2- PIT

25N»v'64M

-L6097

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