THERMODYNAMIC AL SYSTEM OF GIBBS 133 



where pi is its partial vapor pressure above the solution, and 

 Ml its molecular weight in the vapor, provided that the vapor 

 behaves as a perfect gas. If pi" be the partial vapor pressure in 

 the standard state in which its activity is taken as unity, which 

 we will consider to be the pure liquid at the same temperature, 

 we have 



so that 



(166) 



and by (162), taking the molecular weight as that in the 

 vapor, 



ai = Pi/pi'. (167) 



When the amount of the solute is very small, it has been 

 shown that Raoult's law, 



PiM = Nr, (168) 



follows from the expression (126) for the variation of the poten- 

 tial. It has been found by experiment that in some solutions 

 this relation holds over the whole range of concentrations. The 

 solutions which exhibit this behavior are usually composed of 

 closely related substances, which might be expected to be less 

 influenced by effects due to the interaction of the components 

 than solutions of substances of different types or with widely 

 differing properties. Consequently such solutions have been 

 regarded as ideal solutions. 



Therefore, when the activity is defined as in (163), ai = A^i 

 in ideal solutions. The fraction ai/Ni which has been termed 

 by G. N. Lewis the activity coefficient, may be regarded as a 

 measure of the deviation of a solution from the ideal behavior. 

 In the case of dilute solutions for which we take a^ = ^2, when 

 ri2 = 0, the activity coefficient is taken as ailni. 



Table I gives the activities and activity coefficients at 35.17° 



