THE LIQUID STATE If the temperature of a gas is below a certain limiting value and the pressure is gradually increased, the gas condenses to a liquid. This process involves a discontinuity in the relation be tween the pressure and the volume. On a p—v diagram, the con densation is represented by a horizontal line for which the pres sure value corresponds with the vapour pressure of the liquid. The length of the condensation line diminishes with rise of tem perature until the end-points coincide. This temperature is the highest at which a gas can be converted into a liquid and is called the critical temperature. The liquid state is non-existent above this limit. The recognition of the critical temperature is due to Thomas Andrews, who showed that this permits of the transition from the gaseous to the liquid state being carried out in a con tinuous manner. From the theoretical standpoint this is very significant, for it may be inferred that the essential features of the kinetic theory of the gaseous state may be directly applied to liquids. Since the van der Waals and other similar equations, which express generally the behaviour of gases, are derived on the implicit assumption of homogeneity of the system, it is obvious that they cannot be applicable to the ordinary condensation process. The theoretical isothermal curves must necessarily be continuous, and for temperatures at which condensation occurs in practice, the van der Waals equation yields a continuous curve with a maximum and a minimum pressure value (fig. 2). These become less pronounced as the temperature rises, and ultimately vanish. The temperature at which this occurs corresponds with that at which the three roots of the van der Waals equation, which may be shown to be a cubic in v, become equal to one another. This temperature corresponds, in other words, with the critical temperature, and in various ways it may be shown that the critical data are directly connected with the attraction and volume constants in the equation of condition. The relations in question are given by and If a and b are known, these equations may be used to derive the critical constants; conversely, if the lat ter are known the constants a and b may be calculated. In terms of the equation of conditions, the characteristic feature of the liquid state is to be found in the very large magnitude of the pressure (internal pressure) which corre sponds with the attractive force term a/ and also in the very small difference between v and b.
The kinetic condition of the molecules is nevertheless of the same kind, and the mean kinetic energy of the molecules has the same value as that of a gas at the same temperature. Properties which depend on the close associa tion of the molecules attain to greater significance, however, in the liquid state.
In view of the large magnitude and the specific character of the attractive forces in liquids and the absence of any relation which might be supposed to be analogous to the Avogadro hypothesis, it will be readily understood that the comparison of the physical properties of different liquids is attended by particular difficulties. The correlation of the physical properties of liquids with their composition and chemical constitution represented, nevertheless, one of the most important branches of physical chemistry in its earlier stages of development. It was suspected that the relations in question might possibly be made the basis of methods which could be used to supplement the information provided by the more specifically chemical methods followed in the attempts to deter mine the structure of chemical compounds. The work done in this connection has been largely empirical and fundamental questions incidental to the problem have not received that amount of con sideration to which they are justly entitled.
Considerations such as have been illustrated by reference to space-filling capacity constitute a preliminary step in the com parative study of all physical properties. For instance, internal friction may be measured in terms of viscosity or fluidity, elec trical conducting power in terms of conductivity or resistivity and the discovery of the connection between such properties and the chemical nature of substances is obviously dependent on the choice of the basis of comparison. Not infrequently, the selection involves the consideration of alternative measures which are not merely reciprocal, but bear a much more complex relation to one another. Ideal measures would in fact be those which are entirely independent of external circumstances, temperature, pressure, and even state of aggregation, but apart from mass, the physical properties of matter are not of this ideal nature and the prob lem of correlation is attended by many difficulties. In so far as the attainment of comparable temperatures is concerned, a finger-post would seem to be provided by the theory of corre sponding states. The origin of this is to be found in the circum stance that the ordinary equations of condition with specific con stants may be reduced to a general form from which the specific constants have been eliminated. The conversion is effected by measuring for each substance the pressure, volume and tempera ture in terms of the corresponding critical values, such that 7r= p/pc, 4 =v/v, and e = In these circumstances the van der Waals equation reduces to (Or+ 3/ (0 — ) =80/3 which contains no specific constants and represents, therefore, and is an equation which should be applicable to all substances, independently of their chemical nature. The reduced form of the equation is the same in type as the original and it may be shown that other equations of condition may be generalized in the same way, provided that these afford an account of the critical state and contain three constants; i.e., the same number of constants as variables. Substances for which the values of ir, and 0 are identical are said to be in corresponding states, and the general reduced equation is the analytical expression of the theory of corresponding states, according to which comparable temperatures are provided by equal values of 9. Although the experimental data of Sydney Young show that the above reduced equation is by no means an exact expression of the relation between corre sponding states, yet the deviations are such as to suggest that the fundamental idea involved in the theory is substantially correct. From this, however, it does not follow that correspondence in re spect of pressure, volume and temperature provides the conditions for correspondence in other properties ; any such assumption is necessarily of a tentative character.
In actual practice, the comparison of physical properties has been for the most part made at a fixed temperature. In such cir cumstances the actual conditions are frequently far removed from those indicated by the theory of corresponding states. The results obtained show that many properties when referred to molecular quantities of the different substances can be represented as the sum of a series of terms which depend on the nature of the constitu ent atoms and also on the manner in which the atoms are linked together within the molecule. In other words, there is evidence of additivity modified by the incidence of structural factors. At one time the principle of additivity was sought to be maintained by the assumption that the values assigned to certain atoms vary with their mode of combination. More recently the constitutive influence has been taken into account by the hypothesis that the structural peculiarities make a direct contribution to the observed value of the property in the same way as the atoms themselves. In accordance with this view the molecular value of a property of a compound can be expressed by the relation P= in which and are the atomic values of the property for carbon, hydrogen and oxygen, and is the sum of corresponding terms for the constitutional factors.
Kopp's derivation of the atomic volumes of carbon and hy drogen is based on the comparison of the molecular volumes of aliphatic compounds, e.g., C,H,,, with those of benzene com pounds, e.g., in which an increase of two in the number of carbon atoms is offset by a diminution of four in the number of hydrogen atoms. Such pairs of compounds have very nearly the same molecular volume, and from this observation it was inferred that the volume of the carbon atom is twice as great as the volume of the hydrogen atom. Since CH2= 2 2, it follows that C==ii and H=5.5. The derivation of these values obviously ignores the in fluence of ring formation on the molecular volume. More recently, a system of atomic volumes has been evolved by G. Le Bas, which is based on a comparison of aliphatic compounds with the corresponding olefines. In this, which yields C=14.7, H=3.7, no account is taken of the influence of the double bond. The relations are nevertheless very similar to those which are exhibited by the older system.
Although the use of the boiling-points for the comparison of the molecular volumes of liquids provides a temperature basis which is theoretically justified in so far as the boiling-points are approximately equally reduced temperatures, it should be rec ognized that the internal pressures resulting from the attractive forces between the molecules are not generally comparable under these conditions. In this connection, attention may be directed to a new method proposed by S. Sugden, in which the influences of temperature and of pressure are eliminated. In this it is as sumed that a measure of the magnitude of the internal pressure is afforded by the surface tension. The development of the actual procedure is based on the observation that the connection between the surface tension (•y) of a liquid, the density (D), and the density (d) of its saturated vapour can be expressed very exactly by the relation y in which C is independent of the temperature. If i4 is multiplied by the molecular weight, a quantity P is obtained, the value of which may be derived from This is termed the "parachor," and since M/(D—d) at low temperatures, where d is very small in com parison with D, represents the molecular volume of the liquid, it is obvious that the parachor affords a comparison of molecular volumes under conditions in which the surface tensions and there fore the internal pressures of the different liquids have the same value. In support of the view that the parachor really affords a measure of the volumes occupied by the actual molecules, it is found that this quantity bears a nearly constant ratio to the critical volume as expressed by P = o• 78 Vc.
For saturated substances the parachor can be expressed addi tively in terms of atomic constants. These appear to be inde pendent of the mode of combination of the atom and position isomerism is without effect. Unsaturation and ring formation produce notable changes and these vary but slightly from com pound to compound. A double bond between two carbon atoms produces the same effect as the double bond between cal bon and oxygen, or between nitrogen and oxygen in the nitroxyl group. The same structural constant can be used for the six-membered rings of benzene, cyclo-hexane, pyridine, piperidine and quinoline. The two oxygen atoms in the carboxyl group would, however, seem to require a special constant. The accompanying table shows the values of various atomic and structural parachors: Atonic and Structural Parachors C 4.8 F 25.7 = 46.6H 17.r Cl 54'3 3-ring 22.5 O 20•0 Br 68•o 4- ,, 12.0 (ester) 6o•o I 91•0 5- ,, 8.5 N 12.5 = 23.2 6- „ 6•r The results obtained in the study of the parachor are such as to suggest that this may be of real value in the elucidation of many of the structural problems which are presented by organic chemistry.
In the belief that many of the irregularities associated with molecular volumes are due to polymerization (q.v.) or the formation of molecular aggregates, J. Traube instituted a com parison of the volumes occupied by substances when dissolved in water or other solvent to form dilute solutions. The derivation of the molecular solution volumes at 25° C involves the assump tion that the volume occupied by the solvent is not affected by the presence of the dissolved substance. This is certainly not justified, but it is nevertheless noteworthy that the volume re lations exhibited by this system are very similar to those which are found by the comparison of substances in pure liquid con dition at the respective boiling-points. The fact that the sum mation of the atomic and structural constants leads to values of the molecular volume which are less than the actually measured volume by a constant quantity (12.6 cu.cm. in water at 25° C ) suggests that this may be connected with the contraction of the solvent.