Properties of Aqueous Solutions to their State of Ionization. 53 



ponderating influence ; and their superiority is greater in 

 increasing the refractive power than in increasing the density. 



Mixtures of Solutions. 



For a solution containing several salts, 1, 2, &c, the value 

 of a property, according to the conception under considera- 

 tion, will be : — 



P = P w + k x (1 — a x ) n i + h^h + k 2 (1 — a 2 )w s + ^ a 2 w 2 + &c., . (2) 



the ns being numbers of gramme-equivalents per unit volume 

 of the solution. If the solution have been formed by the 

 mixture of the volumes i? x and v 2 of two simple solutions of 

 salts, having one ion in common, for which, before the 

 mixing, the property had the values : — 



Pl=P W +^(l — aiH + WhjJ (3>y 



P 2 = P IP + & 2 (1 — a 2 )n 2 + Z 2 a 2 n 2 ,J 



then, since, on mixing, the state of ionization will, in general, 

 change, we shall have as the value of the property for the 

 mixture, assuming no change of volume on mixing, 



Y = F w + (ki(l-* 1 ')ni + Wni) -^- +(h(l-x 2 ')n 2 + l 2 */n 2 )-^, (4) 



V 1 -f v 2 Vi + v 2 



the ?i's being numbers of gramme-equivalents per unit volume 

 of the original simple solutions, and a/ and a 2 being the 

 ionization-coefficients in the mixture. As the values of the 

 Fs and Z's have been determined above for sodium and 

 potassium chloride for a number of properties, and as I have 

 shown in my paper on the " Conductivity of Mixtures," cited 

 above, how the ionization-coefficients after mixing may be 

 determined, it should be possible to predict the values of these 

 properties for mixtures of solutions of these salts. 



The following tables show that this can be done. The 

 ionization-coefficients were determined in the way described 

 in the paper referred to. The constants k and I employed in 

 the calculations were those determined above. The observa- 

 tions were made by the authors whose determinations for 

 simple solutions were used above ; in fact in most cases it 

 was the solutions of the tables given above which were mixed. 

 The limits of experimental error are thus of about the magni- 

 tudes mentioned above in each case. All remarks made above 

 with regard to the reduction of observations to 18° C, the 

 values of the property for water, &c, apply also to the mix- 

 tures. In all cases, except that of surface-tension, the solutions 

 mixed were mixed in equal volumes. Unfortunately, Bender 

 made no observations on the refracting power of mixtures. 



