370 



EEPOET — 1886. 



§ 8. Systems more complex. 



Concerning these salts we have already said enough. [Then follows a physiological 

 application of law 29, and a reply to some feeble ohjections to the Williamson- 

 Clausius hypothesis.] 



Tn general the case in which four electrolytes alone establish a chemical equui- 

 brium is rather rare. The most frequent case is that of six or nine electrolytes 

 acting on one another. However, it is not difficult to establish general equations 

 for a system of nv electrolytes, composed of v cations and n anions. Let them be 

 the following : — 



ii Ji , ii Jj . . . ■ ii Jn ; ij Ji > ^2 Ja • • • • • • i« Jn ; • • • 



! -'n*'! • • • ■ ^n"n'i 



with the respective coefficients of activity — 



Oji rti2 . . . «in ; «2i • • • • '^•2n ; • • • • ' ""l • •"'•«• 



Moreover, let the original number of equivalents in the solution be similarly — 



m. 



7)1-1 



and the extra number formed at the end of the process — 



.r, 



i-in, 



Further, let us call the quantity — 



the active mass of the electrolyte Ij J; . 



Then, in the same manner as in § 6 above, we find a set of equations analogous to 

 (1) and (2), and they take this form : 



t = V j = n 



Vij . 2 2 >v 

 .= 1 ; = 1 



= 2 r., 



2 r^. 



} - 1 



These equations may be written — 



(»*) ^ ^(i~)(X) ^ constant as regards » ; 



So-jC*-) 2(fl2(,-)(r) 



that is, 



2ro 



r 



which we may split up into — 



'JJ = 5lli = const. ; 



And 80 finally we write down — 



Tai rj2 >'23 

 ^ = !i? = !^ = 



»*31 *'32 '33 



>'(»-!)! _ >'(v-l)2 _ 



2r. 



^-^ = const.; 



'fv-n/ , 



■■ const. 



'•2n 

 fin 



'iv-11n 



(A) 



r. 



which are (w-1) (" — 1) independent equations. 



But there are n v unknown quantities {xu) to be determined. So it is neces- 

 sary to have n + v — \ fresh equations. These are not difficult to get. We notice 



