148 
MR. W. R. BOUSFIELD: IONIC SIZE IN RELATION TO 
If, as in the comparison with ionic volumes, we take two slightly different constants 
for KC1 and NaCl, we obtain differences between observed and calculated values which 
are substantially identical with those given in Tables XXY. and XX\ I. 
Since, in the case of non-electrolytes such as sugar, we have in dilute solutions the 
solution volume practically constant and the ionisation nil, we arrive again at an 
expression which is valid both for electrolytes such as KC1 and NaCl, and non¬ 
electrolytes such as sugar, viz. : 
A/N (1 + a) = 1‘86 + C SV s . 
This result is, of course, quite independent of the hypothesis which it is the purpose 
of this paper to test, and gives us a ready means of extrapolation for arriving at the 
true molecular freezing-point depression at infinite dilution based on simultaneous 
density observations. 
Whether expressed in terms of ionic volumes (according to our hypothesis) or in 
terms of solution volumes, the meaning of the relation seems to be clear. Both 
81,, and SY s are proportional to the decrease in the amount of water in combination 
with a given weight (say a gramme equivalent) of the solvent as concentration 
increases. Hence we get the result that in dilute solutions the increment of the 
effective molecular depression of the freezing-point above 1*86 as concentration 
increases is proportional to the decrement of the amount of water in combination 
with a gram-molecule of the solute. To discuss the physical meaning of this relation 
would carry us too far from the main lines of the present paper. 
(d) Correction of Freezing-point Depression by Reference to Ionic Volumes .—In 
Part Y. (/) our experimental results were shown to lead to the view that the 
viscosity of an aqueous solution was proportional to the average molecular size of all 
the molecules. We were able also to calculate approximately from the viscosity data 
the actual volume occupied by a gramme equivalent of the solute at a given concen¬ 
tration. If I„ be the ionic volume at a given concentration, and the volume in litres 
of a gramme equivalent of ions be taken as yl t „ it was found in the case of KOI, from 
the viscosity data, that y = 0*032. Hence the volume of a gramme equivalent of 
KC1 in solution is 32l„, reckoned in cubic centimetres. 
To find the volume of the KC1 itself, we have the density of solid fused KC1 which 
is given by Quincke as 1*87, which gives for the volume of I gramme of liquid KC1 
0*551 cub. centims., allowing 3 per cent, for expansion from the solid to the liquid 
state. This gives the volume of a gramme equivalent of liquid KC1 as 41T cub. 
centims., and therefore the volume of water combined with 1 gramme equivalent of 
* s 32l„—41T cub. centims. 
Hence, if we have a solution of KC1 containing N gram-molecules dissolved in 
1000 grammes water, we have approximately for the amount of free water 
w = 1000 —N (32l„—41*1). 
