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









Copyright, 1899, 





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- 



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. ' ' 




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. 


BATAVIA, June, 1901. 




1. Chemistry I 

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

tals I 



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 



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 




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 



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 



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 



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 



65. Colored flames 140 

66. The spectroscope 140 

67. Absorption phenomena 142 


68. Photochemical action 144 

69. Photochemical extinction 145 

70. Development and fixing of a photographic picture 146 

71. Color photography 147 



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. 


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- 

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 

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


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- 

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. HNO 9 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, + H a S0 4 = KHS0 4 + 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 

2 H, + O, = 2H a O 

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 

H a + O a = H a O * 

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

2 H, + O, = 2 H,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 H 3 and O a . 


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- 

When potassium manganate (K 2 MnO 4 ) is added to a 
considerable volume of water, potassium permanganate 
(KMnO 4 ), manganese dioxide (MnO,), and potassium hy- 
droxide (KOH) are produced. The equation expressing 
this reaction must have the following form : 

/K a MnO 4 -f ?H S O =*KMnO 4 + jMnO, + sKOH. 

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

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

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

/O 4 -{-^O = ^O 4 -|- > yO i -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 

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 

3 K,MnO 4 + 2H,O = 2KMnO 4 + 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: 

/KC1O 3 = ?KC1 + rKC!O 4 -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- 

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,MnO 4 + 2H 2 O = 2KMnO 4 -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. K a MnO 4 is a derivative of MnO s ; with water 
it gives KMnO 4 , a derivative of Mn a O 7 , and the peroxide 
MnO,. The imaginary change of the oxide is the forma- 
tion of Mn a O 7 and MnO 3 from MnO s . 

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

3 Mn0 3 = Mn,0 7 + MnO a . 

3MnO 3 requires 3K 3 MnO 4 ; Mn a O 7 assumes 2KMnO 4 ; 4K 
remains, appearing as 4KOH, and therefore 4H,O is re- 

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,Cr a O, -f H,S0 4 + H S = K a SO 4 + 2 H,CrO 4 ; 
2 H a CrO 4 = 2H a O -f 2CrO,; 

2 Cr0 9 = Cr a O, + 3 O; 
3C a H.O + 3 = 3 C a H 4 + 3 H,0; 
Cr,0 8 +- 3 H a S0 4 = Cr a (SO) 4 -f 3 H,O. 

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

K 3 Cr a O, + 4 H a S0 4 -f 3 C a H 6 

= K a S0 4 + Cr,(S0 4 ) 3 + 3 C a H 4 + 7 H a O. 

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 (HNO 3 ) 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,SO 4 ) on 
copper (Cu) gives copper sulphata (CuSO 4 ), sulphur dioxide 
(SO,), and water (H,O), 


3. Oxalic acid (C 3 H 3 O 4 ) in the presence of dilute sul- 
phuric acid (H,SO 4 ) is oxidized by potassium permanganate 
(KMnOj to carbon dioxide (CO 3 ) and water (H 3 O), while 
potassium sulphate (K 3 SO 4 ) and manganese sulphate 
(MnSOj are formed as secondary products. 

4. Potassium bichromate (K 3 Cr 3 O 7 ) on heating with con- 
centrated hydrochloric acid (HC1) is decomposed, with the 
formation of chromic chloride (Cr 3 Cl 6 ), potassium chloride 
(KCl),and water (H 3 O). 

5. Potassium iodide (KI) in neutral or alkaline solutions 
is oxidized by potassium permanganate (KMnO 4 ) 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 

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 

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 

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 


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. 


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 : 



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), 

VT = V^ (P constant), 


V t = 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 

REMARK. This law was deduced by Gay Lussac from 


investigations carried out in 1808 and f was 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. 


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 

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 

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 

1000 X gram = 5.3 grams. 

The gas density accordingly is ' - = 59. 


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- 

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 

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. 


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 a ll 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- 

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 


II. Compounds of chlorine. 

Chlorine 7 1 7 l 

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). 

1 9- 

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 

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 


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: 
N a , H a , O,, Cl a . 

Phosphorus- vapor at 1040 is P 4 , at still higher 
temperatures it breaks up partially into P a . Sulphur- 
vapor at the boiling-point of sulphur is S 8 , 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. 


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 H 2 SO 4 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 C ao . 9 H a .,O M . 4 represents the results of the 

~77 TT 

analysis. From this the formulas C 3 . m H 6>7 O s . 837 and 
CH t0ffc O,, M4 are derived. The latter may be rounded 
off to CH a O. 

The results of the analysis are accurately expressed 
by the formula CH a O ; 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,H 4 O a . 

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 CH 2 O, 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 


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 

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 

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 C 2 H,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 C 2 H 6 ONa. Sodium has no 
action on methyl ether. If to the alcohol the struc- 
tural formula (C a H 5 )OH be given, to the ether the for- 
mula (CH 3 ) 2 O, then the chemical difference mentioned 
as existing between the two bodies is expressed, and 
according to these formulae an analogy exists between 
alcohol, (C 9 H 6 )OH, and water, H a O, which explains 


the action of sodium. No such analogy is found in 
the structural formula (CH 8 ) a O. 

Acetic acid and methyl formate are isomers having 
the molecular formula C,H 4 O 2 . 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,H 3 O.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. 


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 

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 : 

C0 3 H 


C0 3 H 
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 
(CH 2 CO 3 H); malic acid is therefore optically active. 


Tartaric acid has the constitutional formula 
C0 2 H 

H C OH* 

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- 

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, R 4 , 
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 NH 4 C1. 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 NH 9 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 
CS 9 , N,0 4 , SiCl 4 , PCVPOCl,, S a Cl Q ,SOCl t , SO.C1., Ni(CO) 4 , 
C 9 H ;8 , CC1 4 , C.H.I, C a H 6 SH, (C a H ) a O, CC1.CHO, 

CH,C a H s O CH. 
HCOOCH,, ClCOOC,H t , || , || C 6 H 8 , 

^ ^ x *" COOC 2 H 6 COC1 

C 6 H 6 C1, C 6 H,NO a , 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. +2oC. iooC. i40C. 2ooC. 28oC. 

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,SO 4 ) la ; above 130 C. this breaks up into sim- 
pler complexes. 


/. 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: H 2 O, H,S. 
Trivalent are nitrogen and phosphorus: NH 3 , PH 8 . 
Tetra- or quadri-valent are carbon and silicon : CH 4 , 
SiH 4 . 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 (FeCl 3 ) it is trivalent. From the formulas of 
nitrogen dioxide (NO 3 ) and su 1 phur 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. MnCl 4 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 C 2 H 6 O, 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.CH 3 , which is the formula of methyl 

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.H a C.CH 3 , the formula of ethyl alcohol. 

Problems, i. Determine the constitutional formu- 
las of the saturated compounds the molecular formu- 
las for which are C,H 8 O. 

2. Determine the constitutional formulas of the sub- 
stances having the molecular formula C a H 4 O a , 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 C 3 H fl O 3 , 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 

4 6 

and ethyl alcohol thus : 

/ 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 

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 


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 

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.) 



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- 

At ordinary temperatures : 


At. Wt. 

Spec. Heat. 

Atomic Heat. 


o 408 




2 6 


O 12 

I 44 


O 1 7O 


At higher temperatures : 


At. Wt. 

Spec. Heat. 

Atomic Heat. 


o. 58 



O. 5 

c . e 



e . c 

Silicon at 2^2 C 


o. 203 

c .7 






Atomic Weigh 
(in round 

Specific Heat. 

Product or Atomic 



o 0408 

6 6 

Sodium . ... 


O 2Q74 

6 76 

Magnesium ... - - 

24 4 

O 24QQ 

6 oo 



o . 214 

5 80 

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



O.I74-O. IgO 

o 165 5 


6 47 



o 1690 172 

6 746 O 



O. T 57 

6 7 



o 1216 

6 "32 



o 1217 

6 69 



o 1138 

6 77 



o 1067 

6 *; 




6 44. 


6-3 6 

O.OG7 O OQ5 

5Q 6 


65 4 

O. OQ56 

6 26 


O O7Q 




o. 0814 

6 ii 


o 0746 


Bromine .... 


o 0847 

6 74 



o 0660 






0.06 I I 

6 2T 



5 08 



108 - 



6 15 





O,O565O O574 


6 426 57 




6 64 


1 20 


O O474 



o 0541 


6 86 



6 20 




6 27 

Tungsten . . . 


O. O774 

V.4 1 

6 15 



o 0326 


Platinum . . . 


O O724 

6 7i 




60 -J 

Osmium. . . . 


o 031 1 


Mercury (solid) 




O O7I4 



6 4.O 



o 0308 

6 4O 

Thorium .... 


o 0276 

6 41 



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 

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 : 


Atomic Weight. 

Atomic Heat. 

H dro en 




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 : 


Atomic Weight. 

Atomic Heat. 

8*. 4 


87 ; 

6 4 


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 : 







o 0746 

18 5 



18 7 


Cu 2 S 

o. 1070 

O 12 

I 7 .8 
IQ. I 


O. 142S 



16 e. 


o 0664 

18 ; 


o 1016 



II .9 


O . I I QQ 

iy .& 


c 125 

II .4 

ZnCl 2 





* J57 
O O5I 2 

1 1 .y 



O O73Q 

I<J Q 


o 1281 

ii 6 


o 1132 

1^ ? 




NaBr (impure). 

o. 1384 

14. q 

c_ c 

10 f\ 


o 1230 

12 .O 

Acl . . 

o 0616 





AgCl . 

O O9 I I 

J-7 . I 

Hgl . 


12 .Q 

CuCl . . 

o i--8q 






o 0521 




13 .0 



' 7 J u 

o '>- r 

1 ^' V 

Cu 2 O 

O. Ill 





H a O (solid) 



NH 4 C1 

O 'iT'? 

20 o 


O 142 

ii ^ 


o 0518 

11 2 


o 0^96 

iS 6 


O 276* 

II .O 

CaCla . 

o 1 642 



O . I K 7O 

II .1 

According to other statements 0.2439. 

Substance . 







o 1623 

12 I 

K 2 SO 4 

o 1901 

J-3 T 


o 0512 


Na 2 SO 4 

O 23 12 

32 8 



10. 1 

(NH 4 ) 2 S0 4 



A 1 O 

BaSO 4 

o. 108 

oc 2 


& c (~) 



CaSO 4 

o. 1966 

26 7 



16 6 

CuSO 4 



r>: o 

* J " J .3/4 

r>R i 

MgSO 4 


26 6 

Ff O 


MnSO 4 


27 5 

cu r\ 

r>f\ 1 

PbSO 4 




SrSO 4 

o. 1428 

26 2 


ZnSO 4 

o. 174 




SiO 2 


II 5 

SnO 2 
TiO 2 

O 1 1O1 

14 o 

CoSO 4 -f7H 3 O. 
FeS0 4 + 7H 2 O. 



MgSO 4 +7H,O. 


100. I 

K 2 C0 3 



ZnSO 4 + 7H 2 O. 



Na a CO 3 



KNO 3 

o 2^88 

Rb 3 C0 3 



NaNO 3 

24. i 


BaCO 3 

o. 1078 

21 2 

W H 4 J\U3 



CaCO 3 

o 2085 

2O 9 

BaN 2 O 6 

OT CO'? 

<JQ g 

PbCO 3 

o 0791 

21 I 

PbN 2 O 6 


?6 j 

SrCO 3 



SrN 2 O 6 



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 

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 

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 PtCl 4 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 PtCl 4 . 
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 


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 

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 

Na a ,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) = Na 3 S (solid). 


The heat of reaction is represented in the following 

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

NaOH (dissolved) + HC1 (dissolved) 

== NaCl (dissolved) + H,O . . . + 13. 7 Cal. 
Na (solid) 4 H a O (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) + H a O (liquid) . . . + 13.7 Cal., 


NaOH (dissolved) + HC1 (gaseous) 

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

C (diamond) -f O a (gaseous) 

CO 2 (gaseous) . . . -f 94.3 Cal., 

C (charcoal) -f- O a (gaseous) 

= CO 3 (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 

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 

N 2 (gas) + 3 C1 2 (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 : 

2 H (gas) + O (gas) = H 2 O (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 

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- 

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 

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 

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. 


K (solid) + HC1 (dissolved) 

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


This process may take place in two reactions: 

K (solid) + H a O* 
= KOH (dissolved) + H+( - i)H 3 O ... +48.1 Cal. 


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 

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 

*wH 3 O 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 

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) + H 3 O (liquid) + Aq* 

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

From the above law 

48.1 Cal. = K, O, H, Aq - H 2 , O (liquid). 

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

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: 

2NH 8 (gas)+ 3 0(gas) 

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

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

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, 

6 4 

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 56 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 

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

C,H 2 (gas) + 50 (gas) 

= 2CO,(gas) + H 2 (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 : 

CH 4 (vapor) + 3 (gas) 

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


C, H 4 , 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 

H t , S, O 4 , Aq = + 210.9 Cal. 
and Zn, S, O 4 , Aq = + 248.5 Cal., 

then in the reaction 

Zn (solid) + H 2 SO 4 Aq = ZnSO 4 Aq + 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 

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 

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

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

4CO, (4 liters) + 2H,O (2 liters), 

2H, (2 liters) + O a (i liter) = 2H a O (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 

6 7 

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 

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 H a S 
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. 





Heat Evolved. 





H a O 

H a S 
H a Se 
NH 9 
NH a OH 
N 3 8 
N 2 4 
N a 6 

H a S0 4 
SeO a 
H 9 Se0 4 
H a TeO 4 
H 3 PO a 
H 3 P0 3 

C0 a 

C0 a 
H 3 P0 4 
As a O, 
As,O 6 
B a O, 

H, Cl 
H, Br 
H, I 
H a , O 
H a ,0 a 
H a O, 
H a , S 
H a , Se 
H a , Te 
N, H, 
N, H s , 
H 8 , P 
H,, As 
N a , O 3 

N, 0, 
N a> 4 
N,, 5 

H, N, O 3 
4(N a . 6 , H a O) 
H a . S a , 0, 
S, O a 
S, 0, 
S, O 4 , H a 
Se, 0, 
Se, 4 , H a 
Te, O a 
Te, 3 , H a 
i(Pa, 0, 3 H 2 0) 
i(Pa, 3 , 3 H a O) 
P, 0. 
C, O a 
(C diamond) 
C, Oa 
(C amorph.) 


(C diamond) 
CO, O 
H 3 , P, 4 

Asa, 0. 

+ 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 


- 2.6 

+ I 3 .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 

THE METALLOIDS. (Continued.) 



Heat Evolved. 





Cl a O 
HC10 4 
Br a O 
HBrO s 
HI0 4 
CS a 

C1 3 I 
S a Cl a 
SOCl a 

so a ci a 

SeaCl a 
SeCl 4 
PC1 3 
PC1 6 



S a Br a 
PBr 6 
S a l a 
P a h 
PI 3 
AsI 3 

Cl a , 
H, Cl, 3 
H, Cl, 4 
Br a , O 
H, Br, O 8 
It, 5 

H, I, Oa 
H, 1.0 4 
C, S, 

(C diamond) 
Cl, I 
IC1, Cl a 

S a , Cl a 
S,0, Cl, 
S, O a , Cla 
Se, Cl a 
Se, C1 4 
Te, C1 4 
P, C1 3 
P, C1 6 

PC1 3 , Cl a 

P, C1 3 , 
As, Cla 
B, Cla 
(B amorph.) 
C, 0, Cl a 
(C diamond) 
I, Br 
S a , Br a 
P, Br, 
P, Br 5 
As, Bra 
S a , I, 
P a , U 
P, la 
As, I 8 

-I 7 .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 



+ 5.8 

+ 14-3 
-f 49-8 
+ 89.8 

+ 22.2 

+ "75" 5 

+ 146 

+ 71.5 
+ 104 


+ ' 46.2 
+ 77.4 

+ 105 
+ 29.7 

+ 52.9 

+ 2.5 

+ I 

+ 44-8 

+ 59- 1 

+ 44-9 

+ 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. 




Heat of Formation. 


Heat of Formation. 





K, H, O 

+ 103.2 

+ H6.5 


+ 131 

+ M9-5 

K 3 , 


+ 164.6 


+ 128.4 

+ J 57-7 

Na, H,0 

-f 101.9 

+ in. 8 

Ba, O 

+ 124.2 

+ 158.7 

Na a . O 

-{- IOO.2 

+ 155.2 

Ca, 3 , H 3 

+ 214.9 

+ 217-9 

Li, H, O 


f H7.4 

Sr, O 2 ,H, 

+ 214-5 

+ 226.1 

N, H,, Aq 


+ 20.3 

Ba, O 3) H 3 

+ 214.9 

+ 227.1 


+ 144 


Mg, 2 , H 3 

+ 217.3 

Al,, 0,,H 6 

+ 594 


Ca, Br 3 

+ M0.9 

+ 165.4 

Mn, O, H 3 

+ 94.8 


Ca,I 3 

+ 107.3 

+ 135 

Zn, O 

+ 85.3 


Ba, Cl a 

+ JQ4-7 

+ 196.8 

Zn, O, H 2 O 

+ 82.7 


Ba, Br 2 

+ 170 

+ 175 

Cd, O, H 2 O 

+ 65.7 



+ 184.6 

+ I95.7 

Fe, O, H a O 

+ 68.3 


Sr, Br a 

+ 157:7 

+ 173-8 

Fe a , O a , H, 

+ 396.4 


Mg, Cl a 

+ 151 

+ 186.9 

Ni, O, H 3 O 

+ 60.8 


Zn, Cl, 

+ 97.2 

+ 112. 8 

Co, 0, H a O 

+ 63.4 

. i . . 

Zn, Br a 

+ 76 

+ 91 

Pb, O 

+ 50.3 


Zn, I, 

+ 49-2 

+ 60.5 


+ 37-2 


Mn, Cl a 

+ 112 

+ 128 

Cu 3 , O 

+ 40.8 


Fe, C1 3 

+ 82.1 

+ ioo 

Ag a , 



Fe, Br 3 

+ 78.2 

Hg a , 

+ 22 


Fe, I, 


+ 46.4 

Hg, O 

+ 20.1 


Fe, C1 3 

+ 96.1 

+ 126.1 

Sn,O, H a O 

+ 68.1 


Al, Cl, 

+ 161 

+ 237.8 

Au 2 ,0,,(H 2 0) 3 



Al, Br, 

+ II9-7 

+ 205 

Pt,0,H a O 

+ 17.9 


Al, I 3 

+ 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 



+ 97-6 

+ 96-4 

Hg, Cl, 

+ 53-3 

+ 'so 

Na, Br 

+ 85.8 

+ 83.9 

Hg, Br a 

+ 40 5 

Na, I 

- 69 i 

+ 70.3 

Hg, I, 

+ 24.2 


Na, F 

f 109 

+ 108.4 

Cu, Cl 

+ 32.9 


N, H 4 , Cl 

H- 75-8 

+ 7L9 

Cu, Br 

+ -5 


N, H 4) Br 

+ 65.4 

+ 61 

Cu, I 

+ 16.3 


N, H 4 , I 

4- 49-3 

+ 45-8 

Cu, Cl, 

+ 51-6 

+ 62.7 


+ 93-8 

+ 102.2 

Cu, Br a 

+ 32.6 

+ 40.8 

Ca, Cl a 

+ 169.8 

+ 187.2 

Cd, Cl, 

+ 93-2 

+ 96-2 

Cd, Br a 

+ 75.2 

+ 75.6 

Au, Br 



Cd, I, 

+ 48.8 

+ 47-9 

Au, I 




THE METALS. (Continued). 

A. OXIDES AND HALIDES. (Continued). 

Keat of Formation. 

Heat of Formation. 







Pb, C1 2 

+ 82.8 

+ 76 

Au, Cl, 

+ 22.8 

4- 27.3 

Pb, Br 8 

-f 64.5 

+ 54-5 

Au, Br 3 



Pb, I, 

4- 39-8 

Sn, C1 2 

4- 80.8 

4- 81.1 

Ag, Cl 

H- 2 9-4 


Sn, CU 

4- 127.3 

4- 157-2 


+ 22.7 


Pt, C1 4 

- 59-8 

4- 79-4 

Ag, I 

4- 13-8 


Pt, Br 4 

4- 42.4 

4- 52.3 

Au, Cl 

4- 5-8 



K 2 , S 

4- IOI.2 

4- III. 2 

Fe,S,H 2 O 

4- 23.8 


K, H, S 

4- 62.3 

4- 63.1 

Co,S,wH 2 O 

4- 19-7 


Na 2 , S 

4- 87 

4- 102 

Ni,S,H 2 

4- 17.4 


Na, H, S 

4- 54 

4- 58.4 

Zn.S,H 2 O 

4- 39-6 


Ba, S 

4- 98.3 

Cd,S,H 3 O 

4- 32.4 


Sr, S 

4- 97-4 


Cu, S 

4- 8.1* 

. . . . 

Ca, S 

- 89.6 


Cu 2 , S 

4- 18.3 


Mg, S 

4- 77-6 


Hg, S 

- 4.8* 


A1 2 , S 3 

4- 122.4 


Ag a , S 

4- 3.3* 


Mn,S, wH,O 

4- 44-4 


Pb, S 

4- 18.4 

. . . 


Carbonates (C = diamond). 

Mn, C, O 3 

4- 210.8 

K a , C, 3 

4- 278.4 

4- 284.9 

Cd, C, 3 

4- 179-2 


Na a> C, O 3 

4- 269.9 

4- 275.4 

Ag 2 , C,0 3 

4- 120.2 


Ba, C, 3 


Pb, C, O 3 

4- 166.9 


Sr, C, 3 

4- 277.5 


K,H, C, 0, 

4- 232.9 

4- 227.6 

Ca, C, 3 

4- 267.7 

Na, H, C.Os 

4- 227 

4- 223.7 

*Not certain. 


THE METALS. (Continued.) 

C. OXY-SALTS. (Continued.) 

Heat of Formation. 

Heat of Formation. 


C K 






Ca,N a ,O 8 ,4HjO 

+ 213.8 

+ 206.6 

K 2 , S, 4 

+ 344-6 

+ 338.2 

Zn,N a ,O 6 ,6H 2 O 

+ I 3 8.I 

+ 132.3 

K, H, S, O 4 

+ 277-5 

+ 273-7 

Cu,N 3 ,O 6 ,6H a O 

+ 93 

+ 82.3 

Na a , S, O 4 

+ 328.4 

+ 329 


+ 121. 1 

+ 116.1 

Na, H, S, 4 

+ 267.8 

4- 266.6 

Pb, N a , 6 

+ I05-5 

+ 97-9 

N a , H 8 , S, 4 

f- 282.2 

+ 279-7 

Ag, N, 8 

+ 28.7 

+ 23.3 

Mg, S, 4 

+ 302.3 

+ 322.6 

Ba, S, O 4 

+ 338.I 


Other salts. 

Ca, S, 4 

+ 318.4 

+ 318.4 

Sr, S, 4 

+ 331 

K, O, Cl 

+ 88.8 

Zn, S, O 4 

+ 230 

+ 248.5 

K, Cl, O 3 

+ 95 

+ 85 

Mn, S, O 4 

+ 249.9 

+ 263.7 

K, Cl, 4 

+ "3-1 

+ 1OI 

Co, S, O 4 

+ 230.5 

K, Br, O 3 

+ 84.1 

+ 74-3 

Ni, S, 4 

i . . 

+ 229.7 

K, I, O 3 

+ 124-5 

+ "7-4 

Fe, S, O 4 


+ 235.6 

Na, 0, Cl 

+ 83.4 

Cu, S, O 4 

+ 182.8 

+ 198.4 


Na, Cl, O 3 


+ 81.2 

Cd, S, 4 

+ 221.2 

+ 231.9 

Na a S, O 3 

+ 260. 5 

+ 262.9 

Ag a , S, O 4 

+ 167.3 

+ 162.8 

Na a , S a , 6 

+ 398.9 

+ 393-5 

Pb, S, O 4 

+ 216.2 


Na a , H, P, 4 

+ 413.9 

+ 419.5 


N, H 4 , N, O 3 

+ 64.9 

+ 60.2 


K, Mn, O 4 

+ 195 

+ 184.8 

Bi, Cl, 

+ 90.6 

K, N, 3 

+ "9-5 

+ in 

Bi, O, Cl 

+ 88.2 


Na, N, 3 

-1- in- 3 

+ 106.3 

Na a ,Pt,Cl 6 6H 2 O 

+ 288.3 

+ 277-7 

N, H 4 , N, 0, 

4- 88 

+ 8i.s 

K, C, N 

+ 29.8 

+ 26.8 

Ba, N 9 , O 6 

+ 226.2 

+ 216.8 

Na, C, N 

+ 25.5 

+ 25 

Sr a , N,, 8 

+ 219.8 

+ 215.2 

Hg, C a ,N a 

- 52 


Ca, N,, 0. 

Mg,N a ,0.,6H,0 

+ 202.6 

+ 210.5 

+ 206.6 
+ 206.3 

Ag, C, N 


+ "6.5 

Sr, Ni, O,,4H a O 

+ 227.7 

+ 215.2 

K, O, C, N 

+ ' 34.3 

+ 29.1 



C diamond. 



Heat of 

Heat of 

Vol. const. 




CH 4 
C a H 9 
C 3 H 8 
(CH 3 ) 3 CH 
(CH 3 ) 4 C 
C 6 H 14 
C,H 16 


C,H 4 
C 3 H 6 
C 4 H 8 
C 6 H 10 
C 6 H 10 
C a H 3 
C 3 H 4 


CH 3 C1 

C 3 H 5 C1 
C 3 H 7 C1 
C 4 H U C1 
C,H 3 C1 
CHC1 3 
CC1 4 
CH 3 Br 
C a H 8 Br 
C 3 H 7 Br 
C b H M Br 
C 3 H 5 Br 
C,H4Br a 
CH 3 I 
C 2 H 6 I 


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

+ II37-5 

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


+ 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 












- 12.8 

- 6.0 
- 1-9 
+ 3-1 
- 58 

+ 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) 




Ethyl " 

Butyl " 

Vinyl " 

Chloroform . 

Carbon tetrachloride . . . . 

Ethyl " 

Proovl " 


Allyl " 

Ethylene bromide (gaseous) 
Methyl iodide . . 

Ethyl iodide 

7 6 




Heat of 

Heat of 
Vol. const. 



CH 3 OH 
C 2 H 5 OH 
C 3 H 7 OH 
C 4 H 9 OH 
C 5 H M OH 
C 3 H 5 OH 
C 3 H 3 OH 
CH 2 2 
C 2 H 4 2 
C 3 H 6 2 
C 10 H 20 2 
C 12 H 24 2 
C 14 H 2 ,0 2 

-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 


+ 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 









Ethyl ' 

Propvl ' 

Isoamvl ' 

Allvl ' 

Propargyl " 

'. ( Formic acid... . 

% 3 ! Acetic 

O ( Propionic " . 

Capric acid 

Palmitic ' 

Stearic ' 

C 18 H 36 2 
C 2 H 2 4 
C 3 H 4 4 
C 4 H B 4 
C 4 H 6 
(CH 3 ) 2 
(C 2 H 5 ) 2 
C 3 H 6 (OH) 3 
C 2 H 4 
(CN) 2 
CH 3 CN 
CH 3 NH 2 
(CH 3 ) 2 NH 
CO(NH 2 ) 2 
CH 3 SH 

C B H 6 

C 6 H 5 OH 
C 7 H,0 2 
C 8 H0 4 
C 7 H0 3 
C 4 H 4 S 
CH 12 6 
C )2 H 22 O n 
CH 10 6 

Oxalic ' 

4-' 196.7 

Sucdnic ' 


Dimethyl ether (gaseous) . . 

+ 42.7 
+ 565 

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

+ 42.5 

- 30.2 

- 71 


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

Mercaptan (gaseous). 


Phenol (solid) 

Phthalic " 

Salicylic " 

Thiophene (gaseous) 

- 26.2 





6 4 C 


Methyl iodide . . . . 

6 5 C 


Fthyl alcohol 

Q 8 



IO 7 

Carbon tetrachloride. . 






" bromide . 

7 e 


8 o 

" iodide . . . 

o 8 

Chloral hydrate . 

21 Q 

Ethvlen bromide. . . 

8 2 

Formic acid 

* 6 

Methyl alcohol 

8 45 

Acetic " 


IO. I 

Hydrocianic acid 

e 7 

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






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


H 2 S0 4 , Aq. 

aClH, Aq. 

2 NO,H, Aq. 

C a H 4 O a ,Aq. 

2NaOH, Aq 





2KOH, Aq 





2LiOH, Aq 



2 7 .8 


aNHs, Aq 




2 3 .8 

Ba(OH) 2 , Aq 





Si(OH) 2 , Aq 





Ca(OH) 2 , Aq 




Mg(OH) a 





Mn(OH) 2 





Ni(OH) a 




Co(OH) 2 


21. I 



Fe(OH) 2 



Zn(OH) 2 





Cd(OH) 2 



20. 6 


Cu(OH) a 













Ag a O 





f A1(OH) 3 

21 .O 




|Cr(OH) 3 

I6. 4 





II. 2 

II. 2 





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

One molecule of the acid and a equivalents of sodium hydrox- 
ide, both in dilute solution, are mixed together. 



a = i 

a = 2 

rt = 3 

a = 4 




13 . 74 

13. 74 









HNO 3 

6 84 



HC1O 3 


13. 76 

13 76 

HBrO 3 




HIO 3 

6 Q 



HC1O 4 


14 . ac 

M, qc 




H 3 PO a 




C a H 4 O 3 

13 .40 

CH 3 O a 


C 3 HO a 



I . VI 

2 77 

2. 77 

H a S0 4 
H 3 SO 


I C Q 

2Q O 



H a CrG 4 
H 3 PO 3 







H 3 P0 4 
H 3 As0 4 
H a CO 3 
(COOH) a 
C a H 4 (COOH) a 
Malic acid 



ii .0 

26. 17 


20. 6 




Tartaric acid 
Citric acid 
H a Si0 3 
H a BO 4 




II. i 







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

Substance Dissolved. 



Substance Dissolved 



in mol. 

in Cal. 

in mol 

in Cal. 



- I.I8 

NaBr4- 2H 2 O 









NH 4 C1 

- 39 




BaCl, + 2H a O 


- 4-8 

NaI4-2H 3 O 





4- 2.1 



4- 1.2 

CaCl, -f 6H a O 

- 4-34 

NaN0 3 



+ 17-4 

KN0 3 


- -5 


+ 24-5 

NH 4 N0 3 


- 6.3 



4- 27.7 

Ba(N0 8 ) a 


- 9.4 

MgCl a 4- 6H a O 


4- 2.9 

Sr(N0 3 ) a 4- 4 H 3 



MgCl 3 


4- 35-9 

Sr(N0 3 ) a 


- 4-6 

MnCl a H- 4 H a O 


4- 1.5 

Ca(N0 3 ) a 4-4H a O 


MnCl a 


-f 16.0 

Ca(N0 3 ) a 


4- 4-0 

FeCl a + 4H a O 


4- 2.7 

Mg(N0 3 ) a 4- 6H a O 



FeCl a 


4- 17-9 

Mn(NO 3 ) a -(-6H a O 


- 6.2 

FeCl 3 + i2H a O 


4- ii. 3 

Zn(NO 3 ) a 4-6H a O 


- 5-8 

FeCl 3 

< < 


Cd(N0 3 ) 3 + 4 H a O 


- 5-0 

CoCl 2 4- 6H a O 


- 2.9 

Cu(NO 3 ) a 4- 6H a O 


- 10.7 



4- 18.3 

AgN0 3 


~ 5-4 

NiCl a + 6H 3 O 



Pb(N0 3 ) a 


- 7.6 

NiCl a 

< < 

+ IQ 2 



*\j. * 
-f 15-6 

Na a SO 4 4- ioH a O 


- 18.76 

ZnBr a 



Na a SO 4 


4- 0.46 



+ "3 

K 2 SO 4 

- 6.4 

CuCl a + 2H a O 


4- 4-2 

(NH 4 ),S0 4 



CuCl a 


4- ii. i 

CaS0 4 4-2H,0 




- 3-3 

CaS0 4 

4- 4-7 



- 6.8 

MgSO 4 4- 7H 3 O 

< i 

- 3-8 

SnCl a -f 2H,O 


- 5-4 

MgS0 4 


4- 20.3 


4- 0.3 

MnSO 4 4-sH a O 

-f 004 

SnCl 4 


4- 29-9 

MnSO 4 


4- 13.8 

AuCl 3 4- 2H a O 

- i-7 

FeS0 4 4- 7H a O 


AuCl 3 


4- 4-5 

CoSO 4 4-7H a O 


- 3-6 

PtCU 4- 4H a O 


- 1.7 

NiSO 4 4-7H a O 



PtCl 4 



ZnSO 4 4-7H a O 


- 4-24 



- 5-08 

ZnSO 4 



+ 18.5 

CdSO 4 4-~ H a O 

< ( 

4- 6.0 

* Apparently weakly positive 


HEATS OF SOLUTION. (Continued.) 


Quantity of 
Water in 

Evolved in 


Quantity of 
Water in 

Evolved in 

CdSO 4 
CuSO 4 +5H 3 O 
CuSO 4 
Ag 2 S0 4 
K 2 S0 4 ,Al 2 (S0 4 ) 3 -f24H 2 
K 2 SO 4 ,Cr 2 (SO4)3-f24H 2 O 



+ 10.7 
- 2.7 

+ 15.8 
- 4-5 


Heat of solut 
pletely saturat 

NH 4 C1 
(NH 4 ) 2 S0 4 
NaN0 3 
NH 4 N0 3 
MgS0 4 +7H 9 
!CuCl 2 +2H 2 
| CaCl 2 +6H 2 O 

ion in 
ed sol 



K 2 C0 3 
K 2 C0 3 -|-3H 2 
KHC0 3 
Na 2 C0 3 
Na 2 CO 3 -f-ioH 2 O 
NaHCO 3 


:+ 6.5 

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




Problems. I. How great is the quantity of heat 
which is set free on the combination of 100 grams 
of Na 9 CO 3 with sufficient water to form the hydrate 
Na a C0 3 .ioH 2 0? 

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

Pb(N0 3 ) a Aq + H 2 S0 4 Aq = PbSO 4 + 2HNO 3 Aq. 

3. What is the heat of reaction of 
AgN0 3 Aq + HClAq = AgCl +HNO 3 Aq? 

4. What is the quantity of heat evolved on the 
combination of C 2 H 4 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 


(C 6 H 6 ) at constant pressure if the heat of combustion 
is equal to + 882.9 Cal. ? 

7. Berthelot burned C,C1 6 in the presence of water 
according to the equation 

C 2 C1. + 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,SO 4 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+H a O . . . +13.7 Cal. 

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

H 9 0(gas) + 2Cl(gas) 

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

This equation is evident from the following: 

H t , 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 

H 3 O (liquid) + 2C1 (gas) + Aq 

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



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

and H 2 , 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 

= FeCl a Aq+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- 

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 

a. Law of Simultaneously Occurring Reactions. A 

8 4 

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 

Thus the reaction 

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

H a O (liquid) + SO a Aq + 2C1 (gas) 

= H 9 SO 4 Aq + 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 + C1 2 = 2HClAq 4. O ... -f 10 Cal. 
is considerably increased by the heat of the reaction 
SO,Aq + O = H 2 SO 4 Aq . . . + 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 + H 2 O . . . + 13.7 Cal. 
The two reactions combined would then give 
2KOHAq + Cl 2 = 2KClAq-f-H 2 0+0 . . . +37-4 Cal. 

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

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

MnO 9 (solid) + H a SO 4 Aq = MnSO 4 Aq + 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 

H 9 O + 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 H a SO 4 , Na 2 S a O 3 with the forma- 
tion of Na 2 S 4 O 6 and Nal, or arsenious acid with the 
formation of As,O B . 

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 

A+B = AB . . . 0Cal., 

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

Example. Chlorine and nitrogen do not com- 
bine directly; NC1 3 = - 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. 

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 

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- 

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. 

8 9 


Formation of Potassium Hypochlorite (see p. 85). 

Formation of Nitrogen Trichloride. 

N, C1 3 = - 38 Cal. 

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

NH 4 ClAq + 6C1 = 4 HClAq + NC1 3 ; 
N, H 4 , 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- 

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 

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, NC1 3 , 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. 

9 2 

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 

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- 

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) = 2 H 3 (gas) + O, (gas) ... - 58 Cal. 
The reaction 

CaO + CO 2 = CaC0 3 

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

9 6 

is exothermic, but at higher temperatures the reaction 
CaCO 3 = 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,, 
Na 2 SO 4 ioH 2 O, CuSO 4 5H,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 

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 

9 8 

of dissociation, and the phenomenon of variable 

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- 

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- 

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 


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: 

Na a S0 4 Aq + 2HN0 3 Aq ^ 2 NaNO 3 Aq + H a SO 4 Aq 

Na,S0 4 Aq + 2HNO 3 Aq = f(H 2 SO 4 Aq + 2NaNO 9 Aq) 
+ i(Na 3 S0 4 Aq + 2HNO 3 Aq). 

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


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

CaCO 3 ^ CaO + CO,. 

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

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 

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

KC.H.O + C.H.O.) + KC,H,OC S H S O + 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 
C 2 H 6 O and C 2 H 4 O 2 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 


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; N 2 O 4 and 2NO 2 ; Na,SO 4 Aq -f- 
HNO.Aq + HNaSO 4 Aq + NaNO 3 Aq, 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 

CaCO, (solid) ^ CaO (solid) + CO a (gas), 
KNO, (solid) ^ KNO, (dissolved), 

Na a SO 4 ioH a O(sol.)^Na a SO 4 9H Q O(sol.)+H a O(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 

Na a SO 4 ioH,O (solid) ^ Na a SO 4 (sol.) + ioH a O (liq.). 


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 N 3 O 4 , and 
also if it were filled with NO a , 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 


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). 


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 


N 9 o 4 1; 2 NO,. 

The compression of this system causes an increase 
in the quantity of the N 3 O 4 . 

A special case is illustrated by the equimolecular 

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: 

CaCO 3 (solid) ^ CaO (solid) + CO a (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 

In such cases the rule also applies, that on increase 


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 

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. 


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- 

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, 


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 

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- 

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- 

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 


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 


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 


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- 

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

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 (Cl 2 ioH 2 O), 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 

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. 


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 

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 

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. 


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 

REMARK. These considerations do not apply in the 
case of hygroscopic action of a purely chemical nature, as 
for example that of P 2 O B . P 3 O B is not in equilibrium with 
water vapor at any pressure, since it forms with it a com- 
pound H 3 PO 4 . It maybe said, however, that P 2 O 6 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, CaCl a .6H a O, 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 : 

NaNO 3 + KC1 = KNO 3 + 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, 


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. 


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 

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- 



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

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 


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) 
Na a SO 4 ioH,O, but also with respect to Na,SO 4 7H a O. 
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 

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. 

I2 4 

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 


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 



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; 


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- 

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, 


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 

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). 


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 

I2 9 

or the water t 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- 


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. 


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- 



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 NO 3 ; sulphuric acid ac- 

-t- + + 

cording to the dilution into H and HSO 4 or into H, H 

and SO 4 ; potassium acetate into K and C 2 H 3 O 2 . 

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- 

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 


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 

TT o . _ I0 7*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- 


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- 

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. 


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



Na|ClAq + Ag NO 3 Aq=:AgCl(solid)+Na NO 3 Aq. 

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- 

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|C1O 3 with AglNO 3 will not form AgCl, 

since the reaction involves the ion C1O 8 , and not the atom 

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

Phenol-phthalein is a substance of very complex con- 
stitution and contains two phenol residues, the radicals 
C 6 H 4 OH. 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 


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 

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 


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- 

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 


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~O 8 ) 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 + H a O . . . + 13.7 Cal. 


According to the theory of electrolytic dissociation, 
this reaction must, however, be expressed as follows: 

H | ClAq + K | OHAq 

= K | ClAq + H 3 . . . + 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 


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 



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- 

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. 


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 


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 

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: 

H 2 + Cl t = C1.0 + H a ; 
2 H 3 + Cl,0 = H,0 -f 2HC1. 


An appreciable time would be required before a quantity 
of Cl a O would be formed sufficient to produce the second 

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 


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 


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 


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 = 3 B; 
A = B n ; 

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 



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 

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. 


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 

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. 


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. 


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 (K 2 O Mn 2 O 7 ), and in the 
same period a second series is formed from copper to 
bromine (Cu 3 O Br 2 O 7 ). 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 

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 


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 

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 

I 5 6 

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- 

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, 

c. From special considerations on the constitution of the 

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 


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 








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Rice and Johnson's Elementary Treatise on the Differential Calculus . Sm., 8vo, 3 oo 

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Sabin's Industrial and Artistic Technology of Paints and Varnish. (In press.) 
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* " " " Abridged Ed 8vo. i 50 

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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 


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Jones's Machine Design: 

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Text-book of Mechanical Drawing and Elementary Machine Design. .8vo, 

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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, 

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HydrauLcs and Hydraulic Motors. (Du Bois.) 8vo, 

Wolff's Windmill as a Prime Mover 8vo, 

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Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition, 

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Smith's Materials of Machines i2mo 

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Elements of Analytical Mechanics Svo, 3 oo 

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Carnot's Reflections on the Motive Power of Heat. (Thurston.) i2mo, t 50 

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Meyer's Modern Locomotive Construction 4to. 10 oo 

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Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 oo 

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Sinclair's Locomotive Engine Running and Management i2mo f 2 oo 

Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50 

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Barr's Kinematics of Machinery 8vo, 2 50 

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Chase's The Art of Pattern-making I2mo, 2 50 

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Hail's Car Lubrication I2mo, 

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Jones's Machine Design: 

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KBIT'S Power and Power Transmission 8vo, 2 oo 

Lanza's Applied Mechanics 8vo, 7 50 

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Maurer's Technical Mechanics 8vo, 4 oo 

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Reagan's Locomotives: Simple, Compound, and Electric I2mo, 2 50 

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Ryan, Nonris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 

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Thurston's Treatise on Friction and Lost Work in Machinery and Mill 

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Warren's Elements of Machine Construction and Drawing 8vo, 7 50 

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Principles of Elementary Mechanics i2mo, 

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The World's Columbian Exposition of 1893 4to, 


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Smith's Materials of Machines I2mo f i oo 


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Richards'. Cost of Food. A Study in Dietaries ..................... i2mo, 

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Richards and Woodman's Air, Water, and Food from a Sanitary Stand- 
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