LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 265 



At infinite dilution the vapor of X becomes a perfect gas, and by defi- 

 nition 



^' = c'. 

 Hence at infinite dilution 



I = c' = pG. 



i is the activity of X in the ideal solvent, and c is its concentration, 

 and by definition $ is proportional to c for all concentrations which we 

 shall consider. Hence, not merely at infinite dilution but in general 

 one of the fundamental equations of the ideal solution is, 



$ = pc. H*6 



From this another useful equation may be obtained. In the case of 

 the ideal solution we have for the osmotic pressure, IT, the equation, 



n = cRT. 



Hence ^^m^' ^^^* 



The quantity p varies with the temperature. In order to find the 

 law of this variation we may once more consider the equilibrium at 

 infinite dilution between the vapor of X and the solution of X in the 

 ideal solvent. 



Since we are dealing here with the ideal solution and with a perfect 

 gas, the following special form of the equation of van't Hofif can be 

 proved by familiar methods to be entirely exact. 



U, 



(IV) 



ur 



IV 



where In signifies natural logarithm, and U(iy^ is the increase of 

 internal energy when one mol of X passes from the ideal solvent into 

 the infinitely attenuated vapor. 



With the aid of these equations we are now prepared to undertake 

 a systematic study of the laws of physico-chemical change. It is to be 

 noted that /row each one of the following exact equations two important 

 approximate equations may be obtained directly, — one for solubility, 



6 Numbered equations, sucli as those of the ideal solution, which are only true 

 under special conditions, will be marked with the asterisk. 



' Since it will be necessary to use the symbol U for various kinds of internal 

 energy change, a particular value of U will be designated by the number of the 

 equation in which it first appears. 



