ELECTROCHEMICAL THERMODYNAMICS 729 



or 



27?/ -v'm. 



(45) 



Thus, ifwe know y at one concentration, we may compute it at 

 another. The activity coefficient, however, is always computed 

 in reference to unity at infinite dilution. If we let Eq equal 

 the electromotive force of the cell when y[ini equals unity, and 

 refer all values of E and y"m2 to this standard value, we obtain 



r. ^ 2i2i , „ 2Rt , , 



E -Eo= - ]^log7" - -^ \0gm2 (46) 



or 



2Rt 2Rt 



E -\- — \ogm2 = E,-— log y". (47) 



Since y" is taken to be unity as m2 equals zero, the left-hand mem- 

 ber of the equation (at zero concentration) equals the normal 

 electrode potential, Eo. By plotting the left-hand member 

 against a convenient function of the concentration, Ea may be 

 evaluated, and subsequently 7 may be calculated by equation 

 (47) at any concentration, nii, at which E is known. Such a 

 method permits the determination of 7 at a constant tempera- 

 ture from electromotive force data only. 



In recent years the activity coefficients of many electrolytes 

 have been determined by measurements of cells of this type. 

 If we replace the hydrochloric acid by a halide of an alkali 

 metal and the hydrogen electrode by a dilute alkali metal 

 amalgam, the cell, 



Ag I AgZ 1 MX{m2) I ilfxHg 1 MX{m,) \ AgX | Ag, 



is formed. The electromotive force of this cell measures the 

 change of thermodynamic potential corresponding to the reaction 



MX{m2) -^ MX{mi), 



whence n" and n' may be determined.* 



*MacInnes and Parker, J. Am. Chem. Soc, 37, 1445 (1915). Mac- 

 Innes and Beattie, J. Am. Chem. Soc, 42, 1117 (1920). Harned and 

 Douglas, J. Am. Chem. Soc, 48, 3095 (1926). Harned, /. Am. Chem. 

 Soc, 51, 416 (1929). 



