WILLIAM D. HARKINS 147 



so the activity of the dissolved substance is equal to the activity of the solid: 



a(solid) = ^(dissolved A) = Const. ; (4) 



but since 



a(dissolved) = ;»a , (5) 



moao = m,ai = m2a2 , (6) 



where Wo designates the solubility in water and nij and W2 refer to the solubility of the 

 substance A in aqueous solutions to which different salts have been added. From (6), 



m (7) 



Wo 



If the activity coefficient of the pure substance in its aqueous solution is arbitrarily 



fixed as unity, then 



Wo (8) 



a = — . ^ 



m 



If the solute (dissolved substance) is a salt, its mean molality (w ± ) should be used. 



a = Const.-i-. ^9) 



The mean molality is a geometric mean as defined by the equation 



/„Z+„Z-\i/Z 



tn^=myZ Z_ j , 



and Z = Z+-\-Z-. 



The extremely simple relation which emerges is that iJie activity coefficient for a 

 saturating salt in solutions of other salts is inversely proportional to the (geometric) mean 

 molality of its own ions.^ 



IONIZATION OF SUBSTANCES NOT COMPLETELY IONIZED 



Many acids and bases, and some salts, are not completely ionized. In general, the 

 activities of such substances in aqueous solution have not been determined; but the 

 percentage ionization (aj) has been calculated from the ratio of the electrical con- 

 ductance (A) of the solution at the given concentration to its conductance at zero 

 concentration or from this conductance ratio corrected by the ratio of viscosities (77), 



An 

 Ac?/, • 



Table II gives the percentage ionizations of a few acids and bases. At the same 



' This system gives entirely correct values of the activity coefficient, but the values become 

 greater than unity in extremely dilute solutions. It is more common to extrapolate some function 

 oimjni to zero concentration. Thus in dilute solutions if log {m/in^) is plotted against ^2, a straight 

 line is commonly obtained. From (8) — log a = log {m/ni^. If for m = o, log {m/m^) is put equal to 

 zero, then a becomes unity, and all of the other activity coefficients are on this basis: thus a is unity 

 at zero concentration of the salt. This is the svstem used in Table I. 



