LEWIS. — THERMAL PRESSURE. 157 



freezing point. It may be stated iu words thus : The "relative" diminu- 

 tion in the escaping tendency of the solvent upon the addition of an infin- 

 itesimal amount of a solute is equal to the ratio of the number of gram 

 molecules of solute and solvent. It is probable that equation (12 b), 

 besides being more general than the equation of Raoult, is also more 

 accurate; for it will appear likely from the theory here developed that 

 Raoult's law is exact only when the vapor of the solvent follows the gas 

 law, but that equation (12 b) represents a universal law. 



Our problem is now to show that equations (11) and (12) are directly 

 deducible from the idea of thermal pressure contained in equation (10). 

 Since the reasoning would be the same whether our goal is the general 

 equation (12) or the special form of Raoult, for the sake of concreteness 

 it will be convenient to develop first the latter equation, and in the 

 simple case of a solution in a solvent to whose vapor the gas law may be 

 applied. Let us determine theoretically in this case the influence of the 

 solute on the vapor pressure of the solvent. This effect may be divided 

 into two which are entirely independent; the first is the effect of the 

 thermal pressure of the solute on the condition of the solvent (this may 

 be pictured kinetically as the influence of the mere motion of the solute 

 molecules) ; the second is the effect of the attraction or repulsion of the 

 solute for the particles of the solvent. It will therefore simplify the 

 discussion if we study these two influences separately, beginning with 

 the latter. 



In a hypothetical case in which we may imagine the particles of the 

 solute to be evenly distributed through a solution, and to have no effect 

 except by an attraction for the solvent particles, the only practical effect 

 of the presence of the solute will be to increase the attractive pressure of 

 the solvent inward. Then, in order to maintain equilibrium, according 

 to equation (4), 



P=(3-a, 



since the external pressure is unchanged, the total volume will decrease 

 on account of the new attraction until the thermal pressure of the solvent 

 is increased by the same amount as the attractive pressure, and we may 

 write, therefore, 



rf|3 = rfa; or, dp — da = 0. 



Comparing this with equation (5) or equation (7), it is evident that the 

 attraction of solute for solvent is not the cause of the lowering of vapor 

 pressure in a solution, and that a mere attraction or repulsion between 

 the solvent and solute does not change the vapor pressure of the solvent, 



