99 



Mr. W. Sutherland on Weak Electrolytes and 



It is assumed that we have properly chosen the measure 

 of the property so that its amount is obtained correctly by 

 the additive process. This mixture formula (1) being 

 of the second degree in n x and n 2 is markedly different from 

 the usual empirical mixture formula linear in ??j and n 2 . 

 Let p denote density, and p mass of pure liquid per unit 

 mass of mixture, then 



n Q1 m 1 =p 1 , n 02 m 2 =p 2 , ™i™i=PiPj and n 2 m 2 =p 2 p } 



so pu = u 1 p 1 2 p 2 /p 1 +pip 2 p\u 12 /p 2 + ihi/Pi) + U2p 2 2 p 2 /p 2 . (2) 



To see how this formula of the second degree in p can 

 reduce to the usual empirical formula of the first degree, 

 let us suppose that 



Ul2/p2 + U 2l/pl= zU l/P2 + U 2/Pl .... (3) 



with u 12 = u x and u 21 = u 2 as the simplest case of all, then 



pu=p 2 (p 1 u 1 +p 2 u 2 )(p 1 /p 1 +p 2 /p 2 ) ... (4) 



If p\lpi-\-pilp2 =1 '^IP9 that i s to say, if there is no contrac- 

 tion on mixing, the last formula takes the usual empirical 

 form of the first degree in p, namely 



u=p 1 u 1 +p 2 u 2 (5) 



Our kinetic principle gives us, as it ought, the ordinary 

 result when each molecule is supposed to carry all its 

 properties unaltered into the mixture. Thus (1) and (2) are 

 the equations that we need for investigating the changes 

 occurring in the properties of molecules when they mingle 

 with others of a diffei^ent kind. A convenient way of using 

 them is to write in general 



m 12 ==Wi + #i, u 21 =u 2 + x 2} p 1 /p 1 + p 2 /p 2 —l/p^A, 



thus fixing attention on the unknowns x Y and x 2 which are 

 the changes of u x and u 2 on mixing, and on A which is the 

 contraction per unit mass on mixing, we write (2) as 



u^pjU! +p 2 u 2 +.pA(p 1 u 1 +p 2 u 2 ) +pip 2 p(x 2 jp 2 + <%/Pi> (6) 



This equation separates the change of u from the value 

 Piu l +p 2 u 2 given by the linear mixture formula into two 

 parts, that depending on the contraction, and that depending 



