The Osmotic Pressure of Solutions. 137 



Connection between Osmotic Pressure and the Concentration 

 of the Solution. 



The equations obtained so far are quite general, and 

 apply to solutions of any substance in any solvent, and show 

 how the freezing point, vapour pressure, heat of dilution 

 and osmotic pressure of a solution are connected among , 

 themselves and how they are affected by changes of tem- 

 perature. The effect of a change of concentration (that is 

 of the volume of solution which contains a gram molecule 

 of the dissolved substance) has not yet been considered.. 

 Consider the simple case of a dissolved body consisting of 

 only one kind oi molecules, the nature of which is not 

 affected by dilution. That is no dissociation of more 

 complex molecules into more simple ones, and no chemical 

 action is to take place on diluting the solution. In these 

 circumstances suppose the solution consists* of n gr. mols. of 

 the solvent to 1 gr. mol. of the dissolved body. From 

 equation 7 we have 



Fnv. = RTn£+.JM fl p^- 



aw 



This equation is very similar to Van der Waals' well-known 

 equation connecting pressure, temperature, and volume of a 

 gas or liquid. 



To make this clear, consider a quantity of a solution (or 

 of a gas or vapour) in a cylinder which is closed by a 

 piston, the pressure on which just balances the osmotic 

 pressure of the solution (or the pressure of the gas). In 

 case of a solution the piston must be permeable for the 

 solvent, but not for the dissolved substance. The whole 

 arrangement is kept at temperature T. 



Allow the piston to rise so that dw gram, of solvent is 



added to the solution, increasing its volume by K-— — dV. 

 In the case of the gas let the volume simply increase by a V* 



