or since 



WILLIAM D. HARKINS 151 



Tci-+Tn + = i, 

 T(ci-)-{i — Tci-) = {2Tci- — i), 





.*. © = @£+@L = 2r(a-) -^ In —^ ; 



5 Wi 



or more exactly: 



S = 2r(c/-) -^ In— . 



15 fli 



By the use of such concentration cells it is possible to find the hydrogen-ion ac- 

 tivity in one solution, provided its activity in some other solution with the same anion 

 is known. If the anion is not the same, difficulties arise in the calculation of the liquid- 

 Hquid junction potential. 



The results of part of the research by biologists upon hydrogen-ion concentration 

 have been based on the assumption that two different liquid-liquid junctions give the 

 same potential, and can therefore be canceled, which is in general not true. 



Since the electromotive force, and therefore the maximum work or free energy, 

 varies as the logarithm of the activity (or inexactly as the concentration) ratio, the 

 hydrogen-ion activity or concentration is often expressed as the logarithm. Thus in 

 pure water at 25° C. the hydrogen-ion concentration is considered to be io~' molal, or 

 the logarithm is— 7. This is often expressed according to the system of Sorensen as pH 

 = 7. If, for example, pH = 5.2, the hydrogen-ion concentration is lo""^"^ molal, and the 

 solution is on the acidic side of the neutral point (Cfl + = o.63 lo"^ mols per liter). 



THE SOLUBILITY PRODUCT 



Suppose that we have two saturated solutions (i and 2) of thallium chloride sep- 

 arated by a partition which consists of a single crystal of the salt. Let solution i be on 

 the left and solution 2 on the right. 



Tl++Cl-^{TICI (solid)5r/++a- . (i) 



The mass-law relation is 



ari +Xaa-= flsoiid Tici =aTi+Xaa- = K . , (2) 



This is known as the "solubility product." In the case cited, the solid salt of the mid- 

 dle phase has a constant activity; but even if other salts, such as TI+R~ or NaNOj, 

 are present, the relations between the activities in the right- and left-hand phases may 

 be expressed: 



-77— =-7^' \3) 



aTi+ aci- 



