Chapter IV — 35 — Osmosis 



what closer ; Morse's equation is even nearer. This is to be expected be- 

 cause van't Hoff's law was proposed to apply only to very dilute solutions ; 

 equation (3) is calculated from the mol fraction of solvent but does not 

 take into account the departure from ideal behavior of the solvent water; 

 Morse's equation is based on weight normal solutions but does not include 

 a correction for hydration. Lewis shows that Morse's equation fails at 

 high concentrations of solute because upon expansion it gives, in contrast 

 to equation (4), the relation 



P„ V = RT (X2 + X22 + X23 + . . . .) (8) 



Whereas the higher powers of X2 may be neglected at low concentrations, 

 at higher ones the differences between equations (4) and (8) become great 

 and Morse's equation gives excessive values. For examples, see Lewis, 

 Tables V and VL 



Further refinements of the osmotic pressure laws involved corrections 

 for hydration, association of the solvent, the volume occupied by the 

 solute molecules, and for the mutual attraction between solute and solvent 

 molecules as in the van der Waals equation for gases. An equation in- 

 volving a correction of the latter type is that of Porter (1917) 



P„ (V-b) = RT (9) 



where b represents the space occupied by solute molecules with a consequent 

 reduction in free space. Values for the osmotic pressure of cane sugar 

 solutions calculated according to van't Hoff (equation 1), Morse (equa- 

 tion 7), FiNDLAY (1919) (equation 3), and Porter (equation 9) are pre- 

 sented in Table 9. 



Table 9. — Osmotic pressure of cane sugar solutions at 20° C; observed and calculated 



values: — 



The values presented by Porter show almost perfect agreement but this 

 does not represent a fundamental improvement in the osmotic pressure 

 formula for Porter selected by trial and error a value for b to bring about 

 such agreement. The value proved to be 0.310 liters per mol. The actual 

 volume of cane sugar is 0.214 liters per mol at 20° C. The difference 

 between these, 0.096 liters per mol, Porter assumed to represent water of 

 hydration corresponding to -^ or 5.3 molecules of water per molecule of 

 sucrose. 



Assuming that sugar solutions are hydrated throughout the range of 

 temperatures from 0° C. to 60° C. and the range of concentration from 

 0.1 to 1.0 weight normal. Porter calculated a series of hydration numbers 



