OSMOTIC AND MEMBRANE EQUILIBRIA 203 



are physically determinate, the most important is the "mean 

 activity coefficient" of an electrolyte. Thus for an electrolyte 

 consisting of q+ positive ions of valency z+ and g_ negative ions 

 of valency z-, the condition of electrical neutrality is 



q+z+ + q-z- = 0. (82) 



It follows that the quantity /±, defined by 



q+ log/+ + 9_ log/_ = (g+ + qJ) log/±, (83) 



where /+, /_ are the ionic activity coefficients, or by 



(/J ..+ ._ = (/+)^.(/_)s (84) 



is completely determinate although the ionic activity coefficients 

 /+ and /_ are to some extent arbitrary. The function /^ is 

 called the mean activity coefficient of the electrolyte. 



Another example of a combination of ionic activity coeffi- 

 cients that is definite is the ratio of the activity coefficients of 

 two cations, or of two anions, in the same solution and of the 

 same valency. 



W. Membrane Equilibrium, of Ideal Ionic Solutions. We are 

 now in a position to write down directly the conditions of 

 membrane equilibrium for ionic solutions. We have merely to 

 substitute the values of the potentials [m] in the general con- 

 dition of membrane equilibrium 



[Mi]' = U.r'. (85) 



For ideal solutions we obtain according to (75) 



p' Vi*(l - ^Kip' ) + At log Ni' + Zi FV 



= p"vi*(l - iKip") + At log Ni" + ZiFV". (86) 



Introducing [v^, the partial molar volume at infinite dilution 

 at the given temperature and at a pressure equal to the mean 

 of those {p' and p ") at either side of the membrane, this becomes 



At log -^= ip' - p") k] + ZiF{V' - V"). (87) 



