38 DIFFUSION AND OSMOTIC PRESSURE 



holds for osmotic pressures of dilute solutions. This opera- 

 tion is expressed in the following: 



P T T f =P f T , 



in which P T is the osmotic pressure, in millimeters of mer- 

 cury, at required temperature T (absolute), and T f is the 

 absolute freezing-point of the solution. From the equation 



we get: 



T 

 P * = P >T, 



In the case of weak aqueous solutions, the freezing-point of 

 the solution may be considered, for this calculation, as prac- 

 tically the same as that of the solvent. Thus T f =273 

 (the freezing-point of pure water), and T becomes 273 + /, 

 where t is the desired temperature in the Centigrade scale. 

 Now the equation given above becomes: 



P = 



= p f (l + ^L t ^ = Pf (i + 0.00367 1) . 



This is sufficiently accurate for dilute aqueous solutions. 



The freezing-point method is the simplest and most satis- 

 factory method for general use. 



2. The boiling-point method: The boiling-point of a solu- 

 tion is always higher than that of the pure solvent, and its 

 elevation is proportional to the osmotic pressure at that tem- 

 perature. The relation between the two quantities for 

 aqueous solutions is expressed as follows: 



wherein P b is the osmotic pressure in millimeters of mercury 

 at the boiling-point of the solution, and A 6 is the elevation 

 of the boiling-point. The determination of the boiling- 

 point of the solution and of distilled water is best made 



i NEBNST-PALMEB, Theoretical Chemistry (London, 1895), p. 129. The pressure is 

 again reduced to millimeters of mercury. 



