276 
MR. J. LARi^rOR OK A DYXAMICAL THEORY OF 
61. It is the circumstance that the available energy A of § 51 is a function of the 
bodily configuration and constitution of the system, whose alteration by dilution is 
independent of the nature of the solvent provided the solution is sufficiently dilute, 
that makes osmotic pre.ssure independent of the solvent and therefore the same as the 
corresponding gas-pressure. This is of course different from asserting that the whole 
available energy of a dissolved substance is the same as its available energy at the 
same density in the free gaseous state. In fact the difference between these energies 
may be estimated from a knowledge of the solubility : thus the available energy per 
unit mass of the gas in the solution at its actual density p is equal to that of the 
same gas in the free space at the corresponding density p ; so that the available 
energy per molecule of the dissolved gas is equal to that of free gas of its own density 
and temperature together with E^T log p/p and also E^T for the volume occupied by 
the free gas. This makes in all for the excess of available energy, per molecule, of 
the dissolved gas E^T log ep/p, or E^T log es, where s is the solubility and E^ is a 
gas constant the same for all kinds of molecules. Like information is derivable ffiom 
the ratio of partition of any dissolved substance between any two solvents which do 
not intermix : its available energy per unit mass must in the state of equilibrium be 
the same in both solutions, 
62. The increase of available energy involved in molecules or atoms of given species 
appearing in the dilute solution during chemical change is, per molecule, a—E^T log &N 
where N is the number of such molecules already there per unit volume and a is a 
fanction of the temperature, h being a constant which depends on the standard 
temperature of reference (§51). A reaction going on in the solution involves the 
disappearing by breaking up of molecules of some of the types present, and the 
appearing of molecules of other types to an equivalent extent: when chemical equi¬ 
librium is attained, the change of available energy arising from a slight further 
transformation of this kind must vanish: that is, 
'>h ^og ?>iNi) + % («;j + ^2^2) + • • • • 
vanishes, leading .to Pv^T log ... log .. = — -b ■ • • )> ''■^iiere 
n^, n. 2 , . . . are the numbers of the molecules of the different types that take part in 
the reaction, reckoned positive when they appear, negative when they disappear; so 
that .... is equal to K, a function of the temperature, which is the law of 
chemical equilibrium originally derived by Guldberg and Waage from statistical 
considerations. Again, if A is the available energy of the whole solution, and 8Aj 
equal to SAq + E^T log IG, where K' = • • • •> denotes its variation per 
letter by Gibbs, March 18. The pressure difference is necessitated by the circumstance that the steady 
state would be brought about by interchange of individual molecules. But its amount is calculable 
a priori only "when the dissolved molecules are practically out of each others’ range : and then the 
argument in the text shows that it depends solely on the number of molecular aggregates with foreign 
nuclei that are present, ii-respective of whether these nuclei are complete molecules or parts of dis¬ 
sociated molecules. . 
