﻿Constitution of Aqueous Solutions. 13 



containing a gramme-molecule per litre. c x — c 2 = 0*2, and 

 P 2 '-j O2 =-54t/10 3 ; but 



t=1-96-1-39 = 057, so {c 1 -c 2 )(p 2 '-p 2 ) = -0 0062. 



At 18° p 2 = 0-326; so from (16) I) +-dh/dp 2 = -110. Now 

 dp 2 jdt is of the order — O006 ; and we see that the term 

 (J) + dli\dp 2 )dp 2 \dt is about 100 times (c L — c 2 ) {p 2 — p-i). 

 Hence there is a strong a priori probability that the variation 

 caused in this term by the presence of the solute is large 

 compared with (q — c 2 ){p 2 — p 2 ). Moreover, experiment 

 shows that this {c 1 — c 2 )(p 2 '—p 2 ) is of opposite sign to 

 Ps G + P± c 4,— G ' • Hence, as pointed out above, the chief phe- 

 nomenon in the specific heat of solutions is connected with 

 (D + dhjdp 2 )dp 2 jdt. The corresponding term for pure water 

 having a value about 0*66, it follows that with (ci — c 2 ){p 2 — p 2 ) 

 neglected (D -|- dh/dp 2 )dp 2 /dt must have a value less than 

 0*66 by sufficient to leave a difference equal to the experi- 

 mental (p%c+p±c A ~c')lp z , which for our particular solution 

 of NaCl is about 0*02. It appears then that a rise of tem- 

 perature in a solution generally produces a smaller total 

 absorption of heat due to the change of (H 2 0) 3 into (H 2 0) 2 

 than occurs in the water of the solution when separate from 

 the solute. 



The simplest assumption we can make about the somewhat 

 complicated difference 



(D + dhldp 2 )dp 2 ldt - (D + dlijdp 2 )dp 2 ' jdt 



is that it is proportional to the amount of trihydrol dissociated 

 by p± of solute, namely rpje, in which we can merge 

 (C] — c 2 )(p 2 —p 2 ) i as it also is proportional to rpje. This 

 assumption transforms (17) into p^+p4C i — c / = ap 3 p i T/e J in 

 which a is an absolute constant. An appeal to the experi- 

 mental data shows that {pzC-^p^c^ — c')jp z p± is not constant, 

 but a linear function of p±. Thus we are led to adopt 



(PzC+P^—c'j/psp^aT/e — bpi, . . . (18) 



in which b is a parameter characteristic of each solute. From 

 the data for NaCl given by Thomsen (T/ierjuoch&mische Unter- 

 suchunf/en, Bd. i. p. 40), aT/# = 0'49 and 6=1*76, furnishing 

 the following comparison : — 



1000^... 



245 



139 



97 



61 



31 



16 



1000c' exp.... 

 „ calc... 



791 

 794 



863 

 861 



895 

 896 



931 

 930 



962 

 963 



978 

 980 



lOOOfoe+JV^-c')... 



16 



28 



29 



21 



14 



9 



m 0O 3 c+p 4 c 4 -r)//y> 4 exp. ... 

 „ „ „ calc... 



9 



7 



23 



25 



33 

 32 



37 

 39 



46 

 44 



58 



46 



