Chapter VI: Physical Chemistry

We have seen how chemistry may be regarded as having for its province the investigation of the composition of matter, and the changes in composition which matter or energy may effect on matter, while physics is concerned with the general properties of matter. A physicist, however, does more than merely quantitatively determine specific properties of matter; he endeavours to establish mathematical laws which co-ordinate his observations, and in many cases the equations expressing such laws contain functions or terms which pertain solely to the chemical composition of matter. One example will suffice here. The limiting law expressing the behaviour of gases under varying temperature and pressure assumes the form pv = RT; so stated, this law is independent of chemical composition and may be regarded as a true physical law, just as much as the law of universal gravitation is a true law of physics. But this relation is not rigorously true; in fact, it does not accurately express the behaviour of any gas. A more accurate expression (see CONDENSATION OF GASES and MOLECULE) is (p + a/v^2)(v - b) = RT, in which a and b are quantities which depend on the composition of the gas, and vary from one gas to another.

It may be surmised that the quantitative measures of most physical properties will be found to be connected with the chemical nature of substances. In the investigation of these relations the physicist and chemist meet on common ground; this union has been attended by fruitful and far-reaching results, and the correlation of physical properties and chemical composition is one of the most important ramifications of physical chemistry. This branch receives treatment below. Of considerable importance, also, are the properties of solids, liquids and gases in solution. This subject has occupied a dominant position in physico-chemical research since the investigations of van't Hoff and Arrhenius. This subject is treated in the article SOLUTION; for the properties of liquid mixtures reference should also be made to the article DISTILLATION.

Another branch of physical chemistry has for its purpose the quantitative study of chemical action, a subject which has brought out in clear detail the analogies of chemical and physical equilibrium (see CHEMICAL ACTION). Another branch, related to energetics (q.v.), is concerned with the transformation of chemical energy into other forms of energy--heat, light, electricity. Combustion is a familiar example of the transformation of chemical energy into heat and light; the quantitative measures of heat evolution or absorption (heat of combustion or combination), and the deductions therefrom, are treated in the article THERMOCHEMISTRY. Photography (q.v.) is based on chemical action induced by luminous rays; apart from this practical application there are many other cases in which actinic rays occasion chemical actions; these are treated in the article PHOTOCHEMISTRY. Transformations of electrical into chemical energy are witnessed in the processes of electrolysis (q.v.; see also ELECTROCHEMISTRY and ELECTROMETALLURGY). The converse is presented in the common electric cell.

_Physical Properties and Composition._

For the complete determination of the chemical structure of any compound, three sets of data are necessary: (1) the empirical chemical composition of the molecule; (2) the constitution, i.e. the manner in which the atoms are linked together; and (3) the configuration of the molecule, i.e. the arrangement of the atoms in space. Identity in composition, but difference in constitution, is generally known as "isomerism" (q.v.), and compounds satisfying this relation differ in many of their physical properties. If, however, two compounds only differ with regard to the spatial arrangement of the atoms, the physical properties may be (1) for the most part identical, differences, however, being apparent with regard to the action of the molecules on polarized light, as is the case when the configuration is due to the presence of an asymmetric atom (optical isomerism); or (2) both chemical and physical properties may be different when the configuration is determined by the disposition of the atoms or groups attached to a pair of doubly-linked atoms, or to two members of a ring system (geometrical isomerism or allo-isomerism). Three sets of physical properties may therefore be looked for: (1) depending on composition, (2) depending on constitution, and (3) depending on configuration. The first set provides evidence as to the molecular weight of a substance: these are termed "colligative properties." The second and third sets elucidate the actual structure of the molecule: these are known as "constitutional properties."

In any attempts to gain an insight into the relations between the physical properties and chemical composition of substances, the fact must never be ignored that a comparison can only be made when the particular property under consideration is determined under strictly comparable conditions, in other words, when the molecular states of the substances experimented upon are identical. This is readily illustrated by considering the properties of gases--the simplest state of aggregation. According to the law of Avogadro, equal volumes of different gases under the same conditions of temperature and pressure contain equal numbers of molecules; therefore, since the density depends upon the number of molecules present in unit volume, it follows that for a comparison of the densities of gases, the determinations must be made under coincident conditions, or the observations reduced or re-computed for coincident conditions. When this is done, such densities are measures of the molecular weights of the substances in question.

_Volume Relations._[17]--When dealing with colligative properties of liquids it is equally necessary to ensure comparability of conditions. In the article CONDENSATION OF GASES (see also MOLECULE) it is shown that the characteristic equation of gases and liquids is conveniently expressed in the form (p + a/v^2)(v - b) = RT. This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for. If we denote the critical volume, pressure and temperature by V_k, P_k and T_k, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv = 0, d^2p/dv^2 = 0 at the critical point, that V_k = 3b, P_k = a/27b^2, T^k = 8a/27b. Eliminating a and b between these relations, we derive P_kV_k/T_k = (3/8)R, a relation which should hold between the critical constants of any substance. Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not (3/8)R but (1/3.7)R; this means that the critical density is, as a general rule, 3.7 times the theoretical density. Deviation from this rule indicates molecular dissociation or association. By actual observations it has been shown that ether, alcohol, many esters of the normal alcohols and fatty acids, benzene, and its halogen substitution products, have critical constants agreeing with this originally empirical law, due to Sydney Young and Thomas; acetic acid behaves abnormally, pointing to associated molecules at the critical point.

Volume at critical point and at absolute zero.

The critical volume provides data which may be tested for additive
relations. Theoretically the critical volume is three times the volume
at absolute zero, i.e. the actual volume of the molecules; this is
obvious by considering the result of making T zero in the
characteristic equation. Experimentally (by extrapolation from the
"law of the rectilinear diameter") the critical volume is four times
the volume at absolute zero (see CONDENSATION or GASES). The most
direct manner in which to test any property for additive relations is
to determine the property for a number of elements, and then
investigate whether these values hold for the elements in combination.
Want of data for the elements, however, restricts this method to
narrow limits, and hence an indirect method is necessary. It is found
that isomers have nearly the same critical volume, and that equal
differences in molecular content occasion equal differences in
critical volume. For example, the difference due to an increment of
CH2 is about 56.6, as is shown in the following table:--

+--------------------+--------------+--------------+--------------+
| Name. | Formula. | Crit. Vol. | Vol. per CH2 |
+--------------------+--------------+--------------+--------------+
| Methyl formate | H.CO2CH3 | 171 | |
| Ethyl formate | H.C02C2H5 | 228 \ | 56.5 |
| Methyl acetate | CH3.CO2CH3 | 227 / 227.5 | |
| Propyl formate | H.CO2C3H7 | 284 \ | 55.8 |
| Ethyl acetate | CH3.C02C2H5 | 285 } 283.3 | |
| Methyl propionate | C2H5.CO2CH3 | 28l / | |
| Propyl acetate | CH3.CO2C3H7 | 343 \ | 57.4 |
| Ethyl propionate | C2H5.CO2C2H5 | 343 } 340.7 | |
| Methyl n-butyrate | }C3H7.CO2CH3 | 339 } | |
| Methyl isobutyrate | } | 337 / | |
+--------------------+--------------+--------------+--------------+

Since the critical volume of normal pentane C5H12 is 307.2, we have H2
= C5H12 - 5CH2 = 307.2 - 5 X 56.6 = 24.2, and C = CH2 - H2 = 32.4. The
critical volume of oxygen can be deduced from the data of the above
table, and is found to be 29, whereas the experimental value is 25.

Volume at boiling-point.

The researches of H. Kopp, begun in 1842, on the molecular volumes,
i.e. the volume occupied by one gramme molecular weight of a
substance, of liquids measured at their boiling-point under
atmospheric pressure, brought to light a series of additive relations
which, in the case of carbon compounds, render it possible to predict,
in some measure, the composition of the substance. In practice it is
generally more convenient to determine the density, the molecular
volume being then obtained by dividing the molecular weight of the
substance by the density. By the indirect method Kopp derived the
following atomic volumes: