﻿2 Mr. W. Sutherland on the Molecular 



solutions: 1. Density; 2. Theory of Density; 3. Special case 

 of Acids and Alkalies ; 4. Specific Heat ; 5. Surface Tension : 

 6. Summary. 



1. Density. 



As a typical instance of the variation of density with con- 

 centration the data of Bousfield and Lowry for NaOH (Phil. 

 Trans. A. 204. 1904) will be studied first. Suppose 1 gramme 

 of solution to be made oi p z grm. of water and p± of solute. 

 Bousfield and Lowry show that for values of p 4 from 0'05 to 

 0'18 the density p at 18° C. is given by 



iO = l-05454 + l-105(p 4 -0-05) (1) 



This reproduces the experimental densities within 2 parts 

 in 10 5 . For values of p 4 between and 0*05 their formula is 



^ = 0-99866 + l-141p 4 -0-52p 4 2 . ... (2) 



Similarly the data of Kohlrausch for NH 4 C1 at 18° C. 

 from p 4 = 0*05 to 0*25 can be expressed by 



p = l + 0'2856p 4 , . . . , . . (3) 



with a maximum error of 4 in 10 4 . For values of p 4 less than 

 0*05 a term in p± would have to be introduced also, as in (2), 

 with modification of the coefficient of p 4 . Bat we shall 

 confine our attention to those solutions in which a linear 

 relation between p and /? 4 suffices. Now to facilitate the 

 study of solutions in general, we can use the principle of 

 modular properties discovered by Yalson (Comptes Ilendus, 

 lxiii. 1871) and extended by Bender (Wied. Ann. xx.). 

 Yalson studied solutions made by dissolving gramme equi- 

 valents in 1 litre of water, and found that if such a solution 

 of a salt MR has its density compared with that for another 

 QR, the difference of the two is independent of R ; so that if 

 NH 4 is made a fixed standard of reference M, pqci—pMci when 

 added to /dmk, the density of NH 4 R solution, gives that of QR 

 solution, whatever R may be. This difference is Yalson's 

 modulus for the positive ion Q. Similarly a modulus exists 

 for the negative ion, and was specified by Yalson with refer- 

 ence to CI as the fixed standard. He gave moduluses for 13 

 positive and 6 negative ions. Bender, in extending the prin- 

 ciple to other strengths of solutions, found it better to compare 

 solutions having equal numbers of gramme equivalents in a 

 Jitre of solution, and gave the following formula for the density 

 of a solution containing n equivalents per- litre, 



P„=R„ + »(P+N), (4) 



where R« is the density of a solution of NH 4 C1 containing n 

 gramme equivalents per litre, P being the modulus for the 



