OSMOTIC PRESSURE 167 



Macallum (1911, p. 617) appears to suggest that the van't Hoff-Arrhenius theory of 

 osmotic pressure does not hold in physiological phenomena. The osmotic pressure of the cell- 

 contents is said not to be given by the total concentration of electrolytes in the cell, because 

 these may be concentrated by surface tension at the cell-membrane. This does not seem to 

 me to be quite the correct way of putting the matter. Osmotic pressure is only shown by 

 free electrolytes. In estimating, therefore, the osmotic pressure due to the potassium salts in 

 a cell, that part of the salts adsorbed on surfaces must be left out of account. Although the 

 actual concentration of potassium may be greater at the cell boundary, it does not follow that 

 its osmotic pressure is any greater here, because it is concentrated on account of its property 

 of lowering surface energy, and, to do this, it must be held in constraint by the surface, 

 adsorbed in fact, and thus unable to possess the kinetic energy necessary for the manifestation 

 of osmotic activity. 



SUMMARY 



When any substance is dissolved in a solvent, the solution, as compared with 

 the pure solvent, behaves as if the solute were exercising pressure. 



This pressure is known as " osmotic pressure," because, when the solution is 

 separated from pure solvent by a membrane which is impermeable to the solute, 

 but permeable to the solvent, it is found that the solvent passes to the solution, - 

 increasing its volume, by the process known for many years as "osmosis." 



The existence of the pressure can be shown by connecting the vessel, containing 

 the solution as above, to a manometer, so that increase of volume is prevented, and 

 the manometer indicates the rise of pressure. Indirectly, the effect of the solute 

 on the vapour pressure of the solvent, and the various phenomena dependent upon 

 this, show the pressure exerted by the solute. 



The amount of this pressure was shown by van't Hoff, on the basis of the 

 experiments of Pfeffer and De Vries, to be identical with that which would be 

 exercised by the solute if converted into gas and compressed to the same volume 

 which it occupied in the solution. 



Since the simple gas law only applies, even to gases, under limited conditions, 

 it is not to be expected that it would apply to solutions, especially to concentrated 

 ones, without correcting factors. 



Such factors are present in van der Waals' " equation of state " as applied to 

 gases and to pure liquids. They result from the considerations of the actual space 

 occupied by the molecules themselves, so that the space left free for movement is 

 diminished, and of the mutual attraction exercised by the molecules upon each 

 other, by which the pressure due to their kinetic energy is reduced. 



If similar additional correcting factors are introduced into the van der Waals 

 equation to take account of the interaction between the molecules of the solvent 

 and of the solute, an equation can be formed which expresses the osmotic pressure 

 of solutions in general. 



The kinetic theory of the origin of osmotic pressure satisfies physiological 

 requirements better than other theories do. 



Hydration of solute, or imbibition of solvent by it, has a negligible effect, 

 except in the case of very concentrated solutions, owing to the enormous 

 preponderance in number of the free molecules of the solvent in comparison with 

 those fixed by the solute. 



In practice, osmotic pressure is measured either directly or by methods 

 depending on changes in vapour pressure, of which the depression of the freezing 

 point of the solvent is that most frequently used. In the case of water, this value 

 is called A- 



In whatever way the osmotic pressure of a solution is raised by removal of 

 solvent, the same amount of work must be done to produce the same amount of 

 change. The mathematical expression is identical with that for the isothermal 

 compression of a gas. 



It follows that, by appropriate means, a solution can be made to do work by 

 dilution ; the capacity factor of this work is the volume of the solution undergoing 

 dilution. Solutions, then, like gases, possess volume energy. 



