OSMOTIC PRESSURE 



is the difference between the concentration of the solvent outside the membrane 

 and in the solution itself. 



We note that a of the van der "Waals equation is diminished by a factor 

 expressing the attraction between the molecules of the solute and those of the 

 solvent, which acts in the opposite direction as regards osmotic pressure to 

 that between the molecules of the solute itself. The attraction between the 

 molecules of the solvent and solute pulls the molecules of the solute away from 

 each other, in opposition to their mutual attraction. The necessity for the 

 introduction of * - x is that the concentration of the solvent inside the 

 membrane is less than that outside by the space taken by the molecules of 

 the solute. For similar reasons, the repulsive forces expressed by b are less 

 than in the simpler case of a pure liquid. 



The whole process of derivation of the formula is beyond the limits of this book, but there 

 are one or two points to be noted in connection with it. 



Owing to the fact of its containing two additional constants, it is not to be wondered 

 at that it can be made to satisfy experimental results. These new constants, unfortunately, 

 cannot as yet be tested experimentally by an independent method, but, at the same time, it is 

 a matter of some satisfaction to possess an equation, similar in form to that of van der Waals, 

 containing only factors to which a physical meaning can be assigned. 



If the solvent is an associated liquid, like water, the equation still applies, although, 

 of course, the numerical values of the constants will not be the same. 



Consider further that the two van der Waals constants have opposed to them 

 other constants by which their value is reduced, and it will be obvious that in 

 solution a substance should obey the ideal gas law more closely than in the gaseous 

 state. Suppose that we are dealing with two easily miscible substances whose 

 critical points are not very far removed from one another, so that their molecular 

 state may be considered to be similar, then a^^ and b V2 are of the same order as 

 ! and b v Moreover, the difference between the concentrations of the pure solvent 

 itself and that .which it has in the solution is nearly identical with the concentra- 

 tion of the solute, or x o~ x . j s very nearly equal to -, which is the concentration 



of the solute ; x - x is, therefore, practically unity. This being so, the factors 

 representing a will nearly cancel out, as will also those representing b, and a gas 

 in solution will obey the ideal gas law more closely than it does in the gaseous 

 state. 



This remarkable result was tested by Otto Stern in the case of solutions of 

 carbon dioxide in methyl and ethyl alcohols, acetone, and methyl and ethyl 

 acetates, at low temperatures in order to avoid high pressures. The values actually 

 measured were the absorption coefficients, and from these the osmotic pressures 

 were calculated by a formula due to Nernst, taking account of the increase of the 

 coefficient as the pressure increased. 



The following numbers were obtained in the case of methyl alcohol at -78 C., 

 and will serve as an illustration. The column headed "Theoretical osmotic 

 pressure " gives the values calculated from the simple gas equation, and it will be 

 noticed how closely the observed values correspond to these, deviating only at the 

 higher pressures. The last column gives the corresponding pressures in the gaseous 

 state, as calculated by the van der Waals formula. 



