THE NEW THEORY OF SOLUTIONS. 177 



The experimental work on the freezing-point has shown 

 that M'AT/V = -02T7W, consequently 



P = -0819 pgTliooM' (4). 

 Since g grams of dissolved substance are present in 100 gr. 

 of solvent, the volume, V, of solvent containing M' grams 

 of dissolved substance will be 1 00 M'/pg litres. In a dilute 

 solution, since the weight of the dissolved substance is small 

 and the density of the solution differs little from that of the 

 solvent, this may be taken as the volume of the solution. 

 Hence equation (4) reduces to 



PV = -oSioT. 

 Equation (3) makes it possible to calculate the osmotic 

 pressure from observations on the freezing-point ; it in- 

 dicates that osmotic pressure is independent of the chemical 

 nature of the solvent ; and just as in the case of vapour- 

 pressure and boiling-point, the entire discussion demon- 

 strates the validity of the gas-equation as applied to dilute 

 indifferent solutions. 



CONSEQUENCES OF THE VALIDITY OF THE GAS- 

 EQUATION FOR DILUTE SOLUTIONS. 



We have now considered the most straightforward evi- 

 dence which can be adduced to prove that the equation 

 PV = -08 1 9T is applicable to dilute solutions. As will 

 have been seen, the validity of the application rests solely 

 upon the results of experiment or upon deductions drawn 

 from such results by the aid of well-established thermo- 

 dynamical principles. It is independent even of any 

 assumption as to whether osmotic pressure is to be 

 ascribed solely to the dissolved substance. Since the 

 data indicate, however, that osmotic pressure is proportional 

 to the concentration of the solution and is not affected by 

 the chemical nature of the solvent, it seems but reasonable 

 to attribute this pressure to the dissolved substance alone, 

 and hence, for the reason already given, it is regarded as 

 the kinetic pressure of the dissolved molecules. 



temperature-variation of W be allowed for, the equation still gives good 

 results for the ismotic pressure at T, in the case of aqueous solutions 

 where the lowering of the freezing point is as high as io°. 



