244 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 



That no satisfactory conclusion can he drawn from experi- 

 ments of this kind, unless conducted at extreme dilution, may 

 be shown roughly in the case of density by the aid of the 

 results obtained above. For we may assume that the ionization- 

 constants for density obtained above will not be very different 

 from those which would be derived from observations made at 

 greater dilution*. We know from Kohlrausch and Hallwachs's 

 observations that if ap and bp represent NaCl and JNa 2 C0 3 

 respectively, (P a P ft ) /n will have the value 0'0139 for solu- 

 tions containing '005 grm.-equivalents per litre, and that for 

 NaCl and HC1 it will have the value of 0'0235. We may 

 assume that for NaCl and KC1 it will be about '02. From the 

 values of k for these salts we find the first two terms of (12) to 

 be '0 3 64. If we assume I to have half the mean value of I for 

 NaCl and KC1, the third term will amount to '0 4 9S. The 

 first three terms thus amount to about '0 3 54, or say 3 per cent, 

 of the value of (P P. In. Thus, observations of the kind 



^ ap op' 



referred to, for density, could give no satisfactory result, even if 

 conducted at this very great dilution, At a dilution of '001 

 grni. -molecules per litre, the first three terms of (12), calculated 

 in the same way, amount to '0 3 1, or about 0*5 per cent of 

 (P fl P 6 ) In. A proved independence of p at this dilution 

 would be more satisfactory. 



Observations at such extreme dilutions, in the case of most 

 properties of solutions, are probably impracticable. But they 

 are fortunately unnecessary for the settling of the question 

 under consideration. For if the values of the ionizatton- 

 constants for any property have been obtained as above from 

 observations over a range extending to great, though not neces- 

 sarily extreme, dilution, the values so obtained may fairly be 

 assumed to apply very approximately to much greater dilutions ; 

 and from the values of l a + l p , ^, + ^y ^a + V ^> + ^' etc< > tnus 

 obtained, it may readily be determined whether or not l a l b 

 is independent of the ions p, q, etc. Unfortunately, Kohlrausch 

 and Hallwachs's observations on specific gravity are not suffi- 

 ciently numerous for this purpose. 



* Mr. E. H. Archibald, one of my students, tells me that for magnesium sulphate 

 Kohlrausch and Hallwachs's data give k = '05663 and I = 'OG6887. 



