﻿Constitution of Aqueous Solutions. 3 



positive ion and N for the negative. Hence by means of (3) 

 and a list of values for P and N we can obtain the density of 

 a solution of any compound containing the ions in the list. 

 Bender's values of P and N at 18° C. are given in Table I. 

 below. 



We must now consider how these densities are connected 

 with the changes occurring in water during solution. Let 

 1 gramme of water contain p 1 dihydrol and p 3 trihydrol. 

 Let n gramme equivalents e of solute in dissolving dissociate 

 nr gramme-molecules of (H 2 0) 3 into 3/it/2 of (H 2 0) 2 in a litre 

 of solution, which contains ne grammes of solute and 10 s p n — ne 

 of water. Hence 



Pi = ne/Wp n , p 3 =l — ne/10*p n . 



Before solution p z consists of pj/>3(H 2 0) 2 and ;? 2 /> a (H 2 0) 3 . 

 After solution the water of a litre consists of p l (10 3 p, l — ne) 

 + 54nT grammes of (H 2 0) 2 and p 2 (10*p, l — ne) —ohirg ram mes 

 of (H 2 0) 3 . If pi and p 2 denote the fractions of the water in 

 a solution which are (H 2 0) 2 and (H 2 3 ), we have 



pi =p x + 54?iT/(10 3 p n — ne) =p x + 54?it/10 3 approx . =p l + 54-rjjJe "I (5) 



P3=P9—54TpJ e J 



Let vi, v 2 , and u 4 be the volumes of a gramme of (H 2 0) 2 , 

 (H 2 0) 3 , and solute at 18°; then, on the assumption that no 

 other changes of volume occur during solution than that due 

 to dissociation of (H 2 0) 3 , we have for the volume v n of a 

 gramme of solution 



n,= V/^=M/Vi'i+iV'r 2 ) +i? 4 «4= {l—Pi){pi(vi-v 3 )+v s } +jW ( 6 ) 



Hence for the change of volume on solution 



Po(Pl^l +P2V2) +P4V4 c -Vn 



we have 



54p 4 (l— pjfa— v^t/* (7) 



In p±{l— p±) this reminds us of mass action at work. It 

 was shown from experiments by A. Geritsch to be the law of. 

 contraction (Nature, xxxix. p. 334; Journ. Kuss. Chem. 

 Phys. Soc. xx.). Recently Happart has shown contraction 

 to be proportional to p 4 (l—p 4 ) for a large number of solutions 

 (Landolt and Bornstein, Tabellen, 3rd edition). 



Substituting, making the approximations 



Wi + }hv 2 = l=piv l +p 2 f v 2 and p n =l, 



after expanding as far as the first power of p± we get 



Vn=l+pd*4-l + teT(vi-v 2 )fe}. ... (8) 



B 2 



