ON ELECTROLYSIS IN ITS PHYSICAL AND CHEMICAL BEARINGS. 365 



As now, from the preceding, the conductivity of the active parts of all salts is 

 the same — that is to say, according to M. Kohlrausch, the velocity with which the 

 ions move relatively to each other is independent of the nature of the salt, and only 

 depends on the strength of the current — it is natural enough to suppose that the 

 said velocity is the same for all salts, even when the strength of current is zero, 

 [This is rather an overstraining of Kohlrausch's results, but it may pass as a first 

 approximation any way.] 



Suppose, moreover, the mean distance at which A need find itself from B in 

 order that it may abandon B and attach itself to B' is the same for all B ions 

 whatever their nature (as is probably the case in gases). In this case M. 

 Clausius has shown that the mean path of the cation A between the moments of 

 encountering B and B' is — 



I = const/??, 



where n is the total number of anions in unit volume. 



True, M. Clausius has given this proof for the case where the paths are 

 rectilinear, but according to the premisses of the demonstration it is equally valid 

 if the path is a broken line or any other form. Suppose, for simplicity, that the B 

 ions are motionless ; then, from what precedes, the mean time of existence of the 

 molecules A B is — 



f _ I _ const 

 V nv 



V being the mean velocity of an A io:;. So, in unit time, of m molecules A B, a 

 number equal to — 



— = Iv VI n 



t 



are destroyed {v, being the same for all electrolytes, is included in the constant K). 

 In reality the B ions are also moving, but since v is the same for all, the onlv 

 effect will be to change the constant K in such a way as to leave it nevertheles's 

 the same for all salts. 



In the same way we can show that if p is the number of A ions, and q the 



number of B ions in unit vol., the number of molecules A ^ foi-med in unit time is 



Kpq. . 



Hence the number of A B molecules at the end of unit time in excess of those at 

 the beginning — that is to say, the velocity of the reaction by which A B is being 

 formed— is — 



'K(^pq — mn). 



If the hypotheses supposed in the foregoing are only approximately true, the 

 above deductions are no more so. The effect would be to multiply the numbers 

 p q m and n by different factors, so that the general aspect of the above-deduced 

 expressions will be only slightly modified. The same thing can be said for the 

 equations we deduce in the sequel. However, as in the actual state of science it is 

 impossible to judge of the validity of these hypotheses, and as they have a certain 

 degree of probability, and of all hypotheses are the simplest we can imagine, it is 

 my intention to prove that the deductions which it is possible to draw from what 

 has just been said are compatible with experimental facts — facts of which we thus 

 give a certain explanation. With the progress of science it is possible that one 

 may see the necessity of modifying these hypotheses ; the general reasonino-s will 

 persist nevertheless, as well as the conclusions drawn from them. 



Now, suppose we have four electrolytes, A B, A D, C B, and C D, intermino-led- 

 let the number of equivalents of each, existing at a given moment, be m, q, p n 

 respectively ; and the corresponding coefiicients of activity a, j3, y, and 6 : the 

 velocity of reaction will be, according to the foregoing, — 



K{{ma + q^) (ma +py) -ma (ma + q^+py + n8)}, 

 an expression which transforms itself into the following : — 



K(q ^ . py — ma . nd) n\ 



