572 SCIENCE PROGRESS 



the number of gramme-molecules N of the solvent in a given 

 volume. 



This equation is valid only for very dilute solutions and 

 utterly fails to represent the experimental figures, e.g. in the 

 case of the normal solution the observed and calculated figures 

 are in the ratio 3 : 2 approximately. 



The thermodynamic equation which expresses the properties 

 of an ideal solution over the whole range of concentration takes 

 the form 



P=^{-I0 ge (l-X)} 



= v7* {1 + %x + }x* . . .} 



This gives the figures shown in the sixth column. These 

 agree quite closely with those calculated by Morse from a 

 modified form of Van't Hoff's equation in which the con- 

 centrations are reckoned in gramme-molecules of sugar per 1000 

 grammes of water instead of per 1000 c.c. of solution. Morse's 

 equation may be written in the form 



r Vo \i - x) 



The close agreement of the values in columns 5 and 6 is 

 accounted for by the fact that the two equations differ only 

 by %x 2 + %x z . . . , quantities that are not important except at 

 very high concentrations. 



But neither Morse's equation nor the thermodynamic 

 equation is completely satisfactory, as both are inaccurate to 

 the extent of some 10 per cent, throughout. The thermo- 

 dynamic equation is based on the assumptions that solvent and 

 solute mix without liberation of heat or change of volume 

 to form an incompressible solution in which the components 

 are present in their normal molecular form, without association, 

 dissociation or combination. Such a description cannot be 

 applied to a solution of cane sugar in water and ample ex- 

 planations are here forthcoming to account for the breakdown 

 of the thermodynamic formula. Foremost amongst these is the 

 explanation suggested by Morse and Fraser, that the sugar at 

 low temperature probably forms hydrates which break down 

 when the temperature is raised. The figures given in the seventh 



