Chemical Affinity in terms of Electromotive Force. 359 



95. Under certain conditions, the value of W in the formulae 

 arrived at in § 91, representing the counter E.M.F. set up 

 during electrolysis, may become negative, but numerically 

 greater than 1\! -\-{\—n^)S. 1 — n'Ji 1 . In such a case negative 

 work must be spent (or work will be gained) during the de- 

 composition ; the cell is then termed an electromotor, and 

 constitutes an ordinary galvanic element. When this is the 

 case, E 3 >E 1 , — as, for instance, when the + electrode is zinc 

 and dilute sulphuric acid is electrolysed, or when copper sul- 

 phate is electrolysed as a partitioned cell, the one half con- 

 taining zinc sulphate with a plate of zinc therein constituting 

 the + electrode (DanielPs cell). The previous experiments 

 show that the value of the expressions 



7i' + (l—n 1 )H. 1 —nJi l and 7i / + (l—?i 1 )H 1 



(according as a gas or a solid is evolved at the negative elec- 

 trode) are positive even with very small currents, and increase as 

 the current increases. It hence results that the numerical value 

 of the negative counter E.M.F. set up in a simple voltaic cir- 

 cuit of zinc, another metal, and dilute sulphuric acid, or in a 

 Darnell's cell (i. e. the actual E.M.F. of the cell*), must de- 

 crease as the current produced by it increases. 



In the case of a simple voltaic circuit, this effect is wholly 

 distinct from one often observed in a newly set-up cell charged 

 with dilute acid containing dissolved air. When first set to 

 work the action of the cell is greatly intensified by the oxida- 

 tion of the evolved hydrogen by the dissolved oxygen (much 

 as is the case in a Leclanche element, the oxygen coming from 



* The E.M.F. of an electromotor is defined for the present purpose as 

 the difference of potential set up beticeen tivo poles of the same material 

 (e. g. the two brass quadrants of an electrometer, or two copper conduct- 

 ing-wires, the one connected with one plate of the electromotor, the other 

 with the other) corrected for the effect of the current passing (if appreciable) 

 due to the external resistance. "Whatever may be the influence of contact 

 actions upon this corrected potential-difference in any given case, this in- 

 fluence must be constant for a given apparatus, and independent of the 

 current generated, so that any change in the potential-difference set up is 

 not due in anyway to contact-action between the metallic plates and con- 

 ducting-wires &c. The correction is of this form : — LetEj be the actual 

 difference of potential and E 2 the E.M.F. of the electromotor, let R x be 

 the external resistance and R 2 the resistance of the electromotor, and let 

 C be the current passing (which =0 if R 1 is indefinitely great) j then 



E a = Rl J~ R a ? E^EiH-CRo: For the total work done by the current in 



a time t is (^(I^+Iia)*, which =E 2 C£, whilst the work done outside the 

 electromotor is G 2 ~R l t='E l Ct j whence 



E^x 2]+5- 2 =Ei+R a X g* -E^OB,,. 



