LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 2G5 



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

 nition 



e = c'. 



Hence at infinite dilution 



£ — c' = P c. 



£ 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, 



£ = 9 c. II* 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, 



U = cET. 



Hence ^ ~ Ur' "^ ' 



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 Hoff can be 

 proved by familiar methods to be entirely exact. 



d In n U, 



(IV) 



dT RT 1 



IV 



where In signifies natural logarithm, and tjv) 7 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 tka,t from each one of the following exact equations two important 

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



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

 under special conditions, will be marked with the asterisk. 



7 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. 



