352 KEYES ART. J 



water at zero degrees (vapor pressure of water 0.006 atm.), in 

 many cases the solubility may be large enough to affect the 

 vapor pressure considerably. The solubility of carbon dioxide 

 in fact is sufficient to change the thermodynamic potential of 

 the water considerably as the pressure of the carbon dioxide 

 rises. There are several other factors to be considered if the 

 case is to be treated with some degree of completeness, but for 

 this a more extensive knowledge would be required than is at 

 present available of the potentials of the components in the 

 liquid mixture, and of the gas phase. 



Nothing is very definitely known about the energy of mixtures 

 of liquids or the entropy of a liquid mixture as a function of the 

 entropies of the components. It may be assumed, however, 

 that f for a mixture of liquids is of the same general form as that 

 for the separate components. Moreover, if one or several 

 components are present in small quantity the coefficients of 

 the f equation of the mixture may be confidently assumed to be 

 linear in the masses of the soluble constituents, on the ground 

 that any continuous and differentiable function of a variable is 

 linear in the limit of small values. It is in this sense that the 

 second equation on p. 154 of the footnote should be understood 

 in its practical applications. The remaining steps lead easily 

 to the equation for the pressure of the dissolved gas as a func- 

 tion of the temperature. The values of the constants A, B, C 

 and D will be constant for an invariable composition of the 

 liquid solution. Differentiating the log (p/a) equation with re- 

 spect to temperature at constant composition, and neglecting the 

 term Dp/t which is small at low pressures, there is obtained 



f C-^) = C-BL (30) 



( d log p \ 

 \ dt J 



This quantity is proportional to the energy required to transfer 

 unit mass of the dissolved gas to the gas phase under equilibrium 

 conditions. 



It is clear from the discussion above that a basis is here 

 indicated for a theory of dilute solutions, for the treatment is by 

 no means restricted to the case of gaseous substances which 

 dissolve. Moreover, it will be observed that the latter case is 



