230 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 



It will be noticed that in the case of the third mixture of 

 the density and thermal expansion series (the same mixture) 

 the differences are comparatively large ; but it is obvious from 

 the data of the fourth column in these series that the ionization- 

 coefficients have not been accurately determined for mixtures of 

 about the concentration of the one referred to. With these 

 exceptions the agreement between observed and calculated 

 values is satisfactory, the differences being either well within, 

 or at worst on, the limit of observational error, up to mean 

 concentrations of about 1.5. The determination of the ioniza- 

 tion-coefficients was especially difficult in the case of the 

 surface-tension observations, because Rother mixed equal 

 weights of his simple solutions, not equal volumes. Neverthe- 

 less, in all except the strongest of these mixtures, the differences 

 are probably not beyond the limits of experimental error. 

 Obviously, alternation of sign is not to be expected in these 

 calculations. 



RELATIVE VALUES OF A PROPERTY FOR A MIXTURE AND FOR 

 ITS CONSTITUENTS : " CORRESPONDING '' SOLUTIONS. 



As change of ionization in general occurs on mixing two 

 solutions, it follows from (3) and (4) that the value of a pro- 

 perty for a mixture of two solutions having one common ion 

 will differ from the volume-mean, (Vj?! +v 2 P< i )/(v 1 +v 2 ) ) of. its 

 values for the constituents by the amount 



(5) 



The name of " corresponding " solutions has been given to 

 solutions for which this quantity vanishes. In general it will 

 obviousty have a value, though that value may be small. 



In most cases this conclusion is borne out by experience. 

 But Rother has concluded from his observations that, in the 

 case of surface-tension, throughout a wide range of concentra- 

 tion, solutions of all concentrations are " corresponding." Were 

 this the case it would throw serious doubt on the possibility of 

 expressing surface-tension in terms of state of ionization. If, 



