MIXTURES OF ELECTROLYTES—MACGREGOR. 109 
N./n, times the dilution (V’,) of the latter solution. Then, since 
On i By! 1 
Vy SS Sn a ee eee 
Ny Vy Mey No Vo Nye 
we have 
= No 
V2 Sv 
Vey 
Hence F EK and H G are equal. In order to determine the con- 
centration of ions after mixing, we must find two points J, K, 
on the curves A Band C D respectively, having according to 
equation 1, a common abscissa O L, and having according to 
equation 2, ordinates L K and L J which together ware equal to 
p times the sum of F Eand H G. If p is equal to unity (7. e., if 
the change of volume on mixing is negligible), the line J K 
joining the points J and K, when properly selected, will obviously 
be bisected by the ine EG. The points J and K may thus be 
easily found by inspection. If p is not equal to unity, we must 
cut off from F EK and HG or from these lines produced, portions 
F N and H P, equal to p. F E and p. H G respectively. Then, 
as before, the proper points Q, R will be so situated that the line 
@ R will be bisected by the line N P. Thus in this ease also the 
points Q, R may readily be found by inspection. The points J, 
K (or Q, R) being thus found, O L (or OS) will represent the 
common concentration of ions in the mixture, and L K and 
LJ (orS R and 8 Q) will represent the dilution of electrolyte 1, 
and 7,/7, times the dilution of electrolyte 2, respectively, in the 
mixture. 
If the solutions to be mixed have unequal volumes (v,’ and v,’) 
we must draw the curve c d having as abscissee the concentrations 
, 
9 
Vo 
: n 
of ions, and as ordinates > —,; 
1 1 
times the corresponding dilu- 
tions of a series of solutions of electrolyte 2. Let Oh and hg 
represent the concentration of ions, and the dilution (V,’) 
respectively, of the solution of electrolyte 1, which is to be 
mixed with a solution of electrolyte 2, and let Of and fe represent 
the concentration of ions, and —2 2, times the dilution (V,’) of 
1 1 
the latter solution, respectively. 
