EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 161 



Now if the gas is an ideal gas-mixture, 



7 a* t j dp* , , aJL , dp* 

 d^ = - 1 - dp 1 = -f*i and a/z 2 = -^ dp 2 = ^ , 



/v (L) \ / *v (L) \ 



therefore ( -- - 1 ) dp 1 = ( 1 - 2-L ) dp (288) 



yi V2 



We may now suppose that $j is the principal component of the 

 liquid, and S 2 is a gas which is absorbed in the liquid to a slight 

 extent. In such cases it is well known that the ratio of the densities 

 of the substance S 2 in the liquid and in the gas is for a given tempera- 

 ture approximately constant. If we denote this constant by A, we 

 shall have 



,-.(L) 



(289) 



It would be easy to integrate this equation regarding y x as variable, 

 but as the variation in the value of p : is necessarily very small we 

 shall obtain sufficient accuracy if we regard y l as well as y\* as con- 

 stant. We shall thus obtain 



where p^ denotes the pressure of the saturated vapor of the pure 

 liquid consisting of S r It will be observed that when A = l, the 

 presence of the gas S 2 will not affect the pressure or density of the 

 gas $ r When A < 1, the pressure and density of the gas 8 l are 

 greater than if $ 2 were absent, and when A > 1, the reverse is true. 



The properties of an ideal gas-mixture (according to the definition 

 which we have assumed) when in equilibrium with liquids or solids 

 have been developed at length, because it is only in respect to these 

 properties that there is any variation from the properties usually 

 attributed to perfect gases. As the pressure of a gas saturated with 

 vapor is usually given as a little less than the sum of the pressure 

 of the gas calculated from its density and that of saturated vapor 

 in a space otherwise empty, while our formulae would make it a 

 little more, when the gas is insoluble, it would appear that in this 

 respect our formulae are less accurate than the rule which would 

 make the pressure of the gas saturated with vapor equal to the sum 

 of the two pressures mentioned. Yet the reader will observe that 

 the magnitude of the quantities concerned is not such that any 

 stress can be laid upon this circumstance. 



It will also be observed that the statement of Dalton's law which 

 we have adopted, while it serves to complete the theory of gas- 

 mixtures (with respect to a certain class of properties), asserts nothing 

 G. T. L 



