THE STRUCTURAL FEATURES OF CELLULOSE 75 



importance in the field of high polymers particularly since it possesses a 

 sound thermodynamic basis. With substances of low molecular weight 

 it is often preferable, if only on account of the simplicity of the experi- 

 mental technique, to determine, not osmotic pressure itself, but the 

 other, related, coUigative properties such as the depression of the 

 freezing point or the elevation of the boiling point. These cannot be 

 used here, however, for a very simple reason (29(c)). Suppose we have a 

 substance of molecular weight, say 68,000 (which is much lower than 

 that of most normal celluloses) and prepare a solution of 10% concen- 

 tration. Assuming that the depression of the freezing point for water 

 containing 1 gm. mol. of solute in 1000 gm. of water is 1-86° C, then 

 the depression for this solution would be (10/68,000)l-86=0-00027°C. 

 Not only is this too small to be measured with any accuracy, but a small 

 contamination with a low molecular weight substance would cause a 

 depression of a similar magnitude and therefore vitiate any result 

 obtained. On the other hand, again assuming ideal behaviour, the 

 osmotic pressure itself would be about 34 mm. of water. Not only can 

 this be measured accurately but the effect of low molecular weight con- 

 taminants can be eliminated. 

 Ideal osmotic behaviour can be expressed by the van't Hoff equation 



P^(clM)RT, 



where P is the osmotic pressure, c the concentration in gm. per litre, 

 M the molecular weight, T the absolute temperature and R the gas con- 

 stant. Obviously if this equation is valid, a plot of P against c should 

 be a straight line passing through the origin. With polymers this is 

 generally not so; and it must be remembered that the van't Hoflf equation 

 is in fact valid only for low concentrations, i.e. in solutions such that 

 there is no interaction between the dissolved particles themselves. With 

 substances of high molecular weight, i.e. with bulky molecules, the 

 concentration required to fulfil these conditions is likely to be very 

 small indeed, much smaller than that necessary for the more normal 

 low molecular weight substances. Correspondingly, it is found that at 

 low concentration a plot of P against c becomes approximately linear. 

 At higher concentrations the relation is of the form 



P^iclM)RT+kc\ 

 k being a constant, or 



Plc=RTIM-\-kc. 



A plot of Pjc against c is therefore approximately a straight line, and 

 the intercept on the ordinate {Pjc axis) at the point c=0 is equal to 



