154 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



It is a rule which admits of a very general and in many cases very 

 exact experimental verification, that if several liquid or solid sub- 

 stances which yield different gases or vapors are simultaneously in 

 equilibrium with a mixture of these gases (cases of chemical action 

 between the gases being excluded), the pressure in the gas-mixture 

 is equal to the sum of the pressures of the gases yielded at the same 

 temperature by the various liquid or solid substances taken separately. 

 Now the potential in any of the liquids or solids for the substance 

 which it yields in the form of gas has very nearly the same value 

 when the liquid or solid is in equilibrium with the gas-mixture as 

 when it is in equilibrium with its own gas alone. The difference of 

 the pressure in the two cases will cause a certain difference in the 

 values of the potential, but that this difference will be small, we may 

 infer from the equation 



(272) 



/ t>m \drn t,p,m 



which may be derived from equation (92). In most cases, there will 

 be a certain absorption by each liquid of the gases yielded by the 



by its composition, except that the letters A, B y C, and D must in this case be under- 

 stood to denote quantities which vary with the composition of the liquid. But to 

 consider the case more in detail, we have for the liquid by (A) 



-=ifA=kt-1etlogt- H't + Vp + E', 

 tn\i 



where k, H', V, E' denote quantities which depend only upon the composition of the 

 liquid. Hence, we may write 



where k, H, V, and E denote functions of m^ m 2 , etc. (the quantities of the several 

 components of the liquid). Hence, by (92), 



dk . dk , dB. dV dE 



T. j j :5 ^ 



dm 1 dm^ drn^ dm 



If the component to which this potential relates is that which also forms the gas, we 

 shall have by (269) 



. p H-c-a c + a, 

 log- = - H -- 

 6 



a a a at 



Eliminating ^ , we obtain the equation 



in which A, B t G, and D denote quantities which depend only upon the composition 

 of the liquid, viz. : 



dS dk\ 



-- c-a + j ), 

 dm l j 



\ 



c-a ), 

 /' 



j-**.\ D=~ 

 'a\^ dmj' adrn^ 



With respect to some of the equations which have here been deduced, the reader 

 may compare Professor Kirchhoff " Ueber die Spannung des Dampfes von Mischungen 

 aus Wasser und Schwefelsaure," Pogg. Ann., vol. civ. (1858), p. 612; and Dr. Rankine 

 " On Saturated Vapors," Phil. Mag., vol. xxxi. (1866), p. 199. 



