332 HEAT. 



where n : N = number of gramme molecules of salt : number of gramme 

 molecules of solvent. 



It is not necessary to show how the lowering of the freezing-point 

 follows from the value of the osmotic pressure. 



Molecular Theory of Osmotic Pressure. Since a solvent and a 



solution are in equilibrium on the two sides of a semi-permeable mem- 

 brane when the solution is under pressure equal to what we have termed 

 the gas pressure of the solute, we are naturally led to look upon the 

 pressure of the solution as consisting of two parts, that of the pure 

 solvent and that of the solute, the latter being equal to its gas pressure. 

 Hence the solvent alone has the same pressure on the two sides of the 

 membrane. If the solute were actually gas, with the gas velocity 

 assumed in the kinetic theory, and if its molecules moved among those of 

 the solvent, quite independent of them, it would produce the observed 

 osmotic pressure by its impacts against the membrane. 



But it is difficult to imagine how this independent motion exists, and 

 it is remarkable that if, instead of supposing that the molecules of solute 

 move freely among those of the solvent, we go to the other extreme and 

 suppose that they enter into some sort of combination with them, we can 

 obtain the same value of the osmotic pressure.* 



Let us suppose that there are n molecules of solute to N of solvent, 

 and let the vapour pressure of the pure solvent be o>. Now, if each of 

 the n molecules of solute attached itself to a molecule of solvent, and 

 loaded it so that it had no tendency to evaporate, there would be N n 

 evaporating molecules in the solution to N in the solvent. Then the 

 rate of escape from the liquid surface would be as N n : N. If the rate 

 of return were equally hindered, so that with equal density of vapour 

 over solution and solvent the return of vapour molecules were also in the 

 ratio N n : N, then we should have equilibrium with the same vapour 

 pressure in each case just as we have equilibrium with the same vapour 

 pressure over an open surface and over a surface partially covered with 

 a perforated plate. But if, as is more natural in this case, we suppose 

 the rate of return the same for the same vapour pressure, that is, if 

 we suppose a vapour molecule to run the same chance of getting en- 

 tangled whether it descends into solution or pure solvent, then over the 

 solution the return will balance the reduced escape when the pressure of 

 the vapour is less in the ratio N - n : N. Hence 



o> : at = N" : N - n 



or ft> : W - a/ = N : n 



, 



,, a> a) n 

 ana = == 



a> N 



the approximate form of Raoult's law. 



* Phil. Mag., xlii., 1896, r- 289. 



