724 EARNED 



ART. M 



With this fundamental consideration in view, it immediately 

 becomes clear that the reversible electrical work of the cell 

 without liquid junction just described measures the change in 

 thermodynamic potential when one mol of hydrochloric acid 

 at a concentration m2 is removed from one solution and then 

 added to the solution at a concentration mi. Therefore, for the 

 transfer of one mol of acid, we obtain by (38) 



/i/ - Ml" = Af = ±F(E, - E,). (39) 



These considerations show that the measurements of electro- 

 motive forces of reversible cells containing various electrolytes 

 of the same or different valence types afford direct measurements 

 of the changes in chemical potentials of ionized components with 

 their concentrations. Further, by measurements of the tem- 

 perature coefficients of electromotive forces of cells of this type, 

 and by employing the fundamental equations (34) and (36), 

 the corresponding changes Ax of heat content, as well as of 

 entropy may be determined. Further, by equation [97] (Gibbs, 

 I, 88) the chemical potential of one component, the solvent for 

 example, may be computed from that of the solute, or vice versa. 

 Therefore, since we may measure the chemical potential of the 

 solute from cell measurements, we may compute that of the 

 solvent. In this way we may relate the electromotive force of 

 a cell with the lowering of the vapor pressure, the lowering of 

 the freezing point, and the osmotic pressure of the solution. 



Since the development of both the experimental side and the 

 theory of the physical chemistry of solutions has depended to a 

 considerable extent upon the evaluation of the chemical poten- 

 tials, the value of this powerful and direct method of measure- 

 ment of these quantities cannot be overestimated.* 



IV. Developments of Importance to the Theory of the Physical 

 Chemistry of Solutions since Gibbs 



The general thermodynamics of Gibbs is complete and 

 affords a basis for the exact treatment of the problems 



* A more detailed and systematic presentation of recent work on this 

 subject is given by Harned in Taylor's Treatise on Physical Chemistry, 

 Chap. XII. 



