222 J. W. Gibbs — Equilibrmm of Heterogeneous Substances. 



sarily the cmly common component of the gas and liquid. If there 

 are others, we may find the increase of the part of the pressure in the 

 gas-mixture belonging to any one of them by equations differing from 

 the last only in the subscript numerals. 



Let us next consider the effect of a gas which is absorbed to some 

 extent, and which must therefore in strictness be regarded as a com- 

 ponent of the liquid. We may commence by considering in general 

 the equilibrium of a gas-mixture of two components /8, and IS^ with a 

 liquid formed of the same components. Using a notation like the 

 previous, we shall have by (98) for constant temperature, 



and 



dp = y^^^ di.i^-\-yf^ dji^ ; 

 whence 



Now if the gas is an ideal gas-mixture, 



a.t -, dp. -, , a^t ^ dp„ 



du.=i —^ dpx-=. -^-', and au^ =i — ^ rt», = -=-^, 



^' Pv Vx Pz 72 



therefore 



l^-\]^dp,= [\-^^l dp^. (288) 



We may now suppose that S^ is the principal component of the 

 liquid, and aS's 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 S2 in the liquid and in the gas is for a given tem- 

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

 we shall have 



^r.L- ^^^dp^={\-A)dp^. (289) 



It would be easy to integrate this equation regarding ;/ j as variable, 

 but as the variation in the value of », is necessarily very small we 



(L) 



shall obtain sufficient accuracy if we regard }^i as well as ;(/i as con- 

 stant. We shall thus obtain 



(^'^-l)(/>,-^p,')=(l-^)i5„ (290) 



where ^1' denotes the pressure of the saturated vapor of the pure 

 liquid consisting of S^. It will be observed that when ^=1, the 

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

 gas S^. When ^<^1, the pressure and density of the gas S^ are 

 greater than if S.^ were absent, and when A^\, the revei-se is true. 



