[macgkegor] conductivity OF ELECTROLYTES 73 



V of llie solution in its |)i'('p;ir;ition. Let tlicsc Ix' //, uiid v.^. Then il. is 

 obvious that we Ikivc. 



(d) from the luw of tlic (•onservation of mass, apjdicd t(j tlic pi-cK-css of 

 double deeompositiou. 



— V 4- V '" ' ^ independent equations, 



/,, = iV, + ^ 



;] 



since each of tJiese four equations is deducible from the other three. 



We have thus in all 12 equations for the determination of 12 un- 

 known quantities, viz.. -4 as, 4 JV's, and 4 Vs. 



To solve these equations by a graphical method, ^ve may first reduce 

 the second, third and last three to two, by eliminating all but one of the 

 iV's. We thus obtain : 



AT — > ^' — "^^1^1 — "^2>'2 



'~ v,+ v,-(v,-{- v,y 



(V. V \ 

 -p^' — 1 1 4- X, (m + '*2) = "i"2- 



Now draw curves for all four electrolytes, from ex]5erimental data ob- 

 tained from observations on their simjjle solutions, with values of the 

 concentration of ions as abscissae and the corresponding values of the 

 dilution as ordinates. Select what seems a probable value of the common 

 concentration of ions in the complex solution, and read off from the 

 curves the corresponding values of Fj, Vo, Fg, F^. Determine iVg from 

 the first of the last two equations by substituting these values in it, and 

 see whether this value of iVg is, first, a possible value, and, secondly, one 

 that will satisfy the last equation. If not we must make another shot 

 at the common value of the concentration of ions ; and so on until a value 

 of iN-^j is obtained which does satisfy the last equation. Such a value 

 having been found, the common value of (^/V, and the values of Fi, 

 ^^2^ 1^31 y^v become known, and a^, a.2, «'.•., a^ may be determined b}- mul- 

 tiplication. Also «1, 112 and iVg being known, j\\, X and iV^ "^ay be 

 determined from equations (d) above. And thus all the data are avail- 

 able for calculating the conductivity. The a])plication of this method 

 would require th;«.t the curves based on the oltservations on simple solu- 

 tions should be very accurately drawn. For the denominator of the 

 above expression for iVg is the difference between the sums of two dilu- 

 tions, and this difference uiay be small. Hence even a small error in 

 their determination may lead to a great error in the value of JY^ which is 

 found. 



If we w ish not to calculate the conductivity ot a given solution, but 

 merely to test the dissociation theory by comparing the observed and 



Sec. II r., 1896. G. 



