138 
MR. W. R. BOUSFIELD : IONIC SIZE IN RELATION TO 
meet with difficulties which are small for very dilute solutions, but increase with the 
concentration. 
In considering what we are to take as the radion ot the group of un-ionised 
molecules, our difficulties begin. But we saw that in our rough viscosity formula 
for KC1 and NaCl no serious error up to 6 per cent, was introduced by taking the 
radion of the un-ionised molecule as the sum of the radii ot the united ions. This 
would probably give too large a value, which would vitiate our equations at higher 
concentrations, but, within the range of concentration with which we are dealing, 
does not introduce a serious error. 
The calculation of the volumes of the un-ionised molecules presents a further 
difficulty. The un-ionised molecules must be combined with less water than the pairs 
of ionised molecules, hut a consideration of the density law showed us that we might 
without serious error up to 6 per cent, reckon the volumes of the molecules as 
though they were composed of pairs of spheres, the radii ot which followed the same 
law as the ionic radii. We shall therefore continue to reckon the volume in this way, 
though it may give too much volume to the un-ionised molecule, in a proportion which 
will increase with increasing concentration. 
The total fraction of volume of the solution occupied by any set of ions will be 
approximately proportional to the number and volume of the individual ions, but not 
exactly. If r x , r 2 be the radions of the separate ions of an electrolyte (reckoned in 
ionic units), we reckoned the separate ionic volumes as -- r{ i x 10 6 , v 2 = r 2 x 10 , 
leaving out the multiplier -$tt and introducing the multiplier 1U 6 for the sake of con¬ 
venience. We also took the volume of either a pair of ions or a molecule as 
I„ = V 1 + V 2 = ( n 3 +r 2 3 )xl0 6 . 
In order to calculate the absolute volumes from the ionic volumes, we must 
introduce a suitable factor y. The total volume occupied by the hydrated ions and 
molecules in a litre of solution being approximately proportional to ml e , let us 
represent the fraction of a unit of volume of the solution which is occupied by the 
ions and molecules of the solute by ym\ 0 . y will be nearly the same for different 
molecules, but not quite, since molecules of different volumes do not exactly displace 
proportionate numbers of molecules of the solvent. 
If a be the coefficient of ionisation, the volumes occupied by the ions and molecules 
respectively will then be 
aymVi, aymV 2 , (l — a) ym (Vi + V 2 ). 
Therefore in unit volume of solution the total volume of the hydrated ions and 
molecules is ym (Vi + V 2 ) or yml v , and the volume of uncombined water is (1— yml v ). 
Hence, if r is the radion of water, the general equation rj = CSfir becomes 
h- z= (1 — y ml v ) r + uyiuYi r, + aymV 2 r 2 + (l — a) ym (\ 1 J t- V 2 ) (rj + r 2 ), 
