LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 51 



Second, that the vapor obeys the gas law, 



RT 



i\ — 



P 

 These two equations substituted in (4) give the familiar equation, 



d In p _ Q 



dT ~ RT Z 



(5) 



While neither of the two assumptions made above is in any case 

 strictly true, they differ in that the second represents a true limit as the 

 vapor approaches the perfect gas in its behavior, but the first is always 

 mathematically absurd, for the volume of a liquid cannot be made to 

 approach zero even as a limit. For an exact equation, therefore, we 

 must return to equation (4), notwithstanding its rather complicated form. 

 There is in fact a lack of simplicity in this equation which does not 

 appear in certain analogous expressions that will be developed in this 

 paper. That this lack of simplicity is, however, not inherent in every 

 exact equation for the influence of temperature on vapor pressure, but is 

 due rather to the complex conditions for which equation (4) is proved, 

 will be evident from the following considerations. 



It is well known that at constant temperature the vapor pressure of 

 any substance is changed by a change in the total pressure on its surface, 

 according to the equation first obtained by Poyntiug,* 



i£ = % ( 6) 



dP v x 



in which p represents vapor pressure ; P, total pressure ; v. 2 and v h mo- 

 lecular volumes of liquid and vapor respectively. When, therefore, the 

 temperature of a liquid is raised, the resulting increase in vapor pressure 

 brings an increase in the total pressure on the surface, and this in itself is 

 a cause of further change in vapor pressure. The observed change in 

 vapor pressure is the sum of the change due merely to temperature 

 change and the change due to the change in total pressure upon the 

 surface. Let us therefore determine the change in vapor pressure with 

 change of temperature when the total pressure on the surface is kept 

 constant by artificial means. Figure 1 represents such an arrangement. 

 The space E D contains liquid kept at constant pressure by a piston, F. 

 B D contains an inert insoluble gas. B C is a membrane impermeable 

 to this gas, but permeable to the vapor of the liquid used. A B contains 



* Phil. Mag., (5) XII. 32 (1881). 



