154 ATOMS, IONS, SALTS, AND SURFACES 



ent on the two sides of the junction. The same equations have been applied without 

 change when a membrane has been supposed to be present. Thus, with the cell given 

 below 



Na+ Cl- 



aNa+ aci- 



Na+ CI- R- 



III 



aNa oci aR~ 



let I Faraday of positive electricity be passed from left to right. The decrease of free 

 energy is 



-AF=TNa+ RT In ^^+Tcr RT In ^ = {2TNa+-i) RT In ^ . (8) 



aNa+ act- aNa+ 



Since the number of equivalents of sodium and chlorine ions which cross the boundary 

 are given by their transference numbers {T!fa+ and Tci-) the decrease of free energy 

 is also equal to the electrical work done, or 



-AF=(S9^5 (9) 



or, since in the special case given above the number of equivalents of electricity (^l) 

 transferred is one, 



^==(2TNa+-i)^ln^, (10) 



^ aNa + 



which is the equation commonly given for the membrane potential. In general, 



(^ = iTc-TA)^ln^. 

 F a+ 



Up to the present time no trustworthy experimental verification of these equa- 

 tions has been obtained from any membrane equilibrium, since in the tests of these 

 relations thus far the assumption has been made that other liquid-liquid junction 

 potentials involved are negligible, without proving that this is true. 



SURFACES AND SURFACE ENERGY 



The importance of the energy stored up in the surfaces of bodies and in the inter- 

 faces between the particles of the bodies is due in part to the influence which the sur- 

 face tension exerts upon the form of the bodies and the particles. However, the effect 

 of the surfaces upon the chemical composition and action, and upon the electrical 

 phenomena, are of even greater moment. 



Interfaces are of particular significance in living organisms, since the motion of an 

 organism as a whole is evidently brought about by transformation of one kind or 

 another of the interfacial energy resident in it. The term "surface" unfortunately im- 

 plies the entire absence of a third dimension in space, that of thickness, but physical 

 surfaces and interfaces, sometimes designated as "phase boundaries," although they 

 are exceedingly thin, commonly have a thickness as great as the sum of the diameters 

 of several atoms, or a distance of the order of a millionth of a millimeter (10 A), which 

 is by no means negligible. At many interfaces films or membranes collect, and these 



