The Lewis/Randall Rule:
 
A simple equation for the fugacity of a species in an ideal solution follows from the following equations. In general, for any solution:
 
(6.158)  
Applying to ideal solution,  (6.159)  
However we know (eqn. 6.77) that:  (6.160)  
Also, from eqn. 6.86:  
Thus,  (6.161)  
On comparing eqns. 6.158 & 6.160:  (6.162)  
The last relation is known as the Lewis/Randall rule, and applies to each species in an ideal solution at all conditions of temperature, pressure, and composition. It shows that the fugacity of each species in an ideal solution is proportional to its mole fraction; the proportionality constant is the fugacity of pure species i in the same physical state as the solution and at the same T and P.

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