ON ELECTROLYSIS IN ITS PHYSICAL AND CHEMICAL BEARINGS. 373 



its ?I is not an ion. So that the part of HjSO^ contained in NaHS04 has no 

 effect, i.e., is totally inactive. Thus equilibrating systems are set up which do not 

 agree with calculations based upon the coefficient of activity of H,S04 above given. 

 And an equivalent of an acid- salt-forming acid (such as sulphuric, oxalic, &c.) 

 ■cannot completely displace an equivalent of a more feeble acid from its salt, as 

 prop. 33 asserts. [References to Berthelot.] 



The calculation of the relative quantities of electrolytes contained in a system 

 where acid salts occur goes on in the manner indicated above. Only it is necessary 

 to observe that if the acid is r-basic, and if an acid salt is found in which a hydro- 

 gen atoms of the acid are replaced by a metal radical, it loses, for each equivalent of 

 acid salt formed, r/o- equivalents of acid. So equation (2) becomes — 



(1 _ ar) (w - 1:^') ab\ ={,q + x){p + x) /3y, 



O"/ 



where n is the number of equivalents of acid added since the commencement, 

 and \, p, q are the corresponding quantities for base, water, and salt. 



If several salts (acid and neutral) form simidtaneously, the calculation will be 

 more complicated, as is seen most clearly by an example. Suppose one has at 

 the beginning n . H.^SO^ and 1 . KCl ; let there be formed x . K^SO^, y . KHSO^, 

 and some HCl ; the equation (2a) will take the form — 



{l-x-y) (w-.r~2y)aS = {x^ + y^') {x + i/)y, 



where a, (3, /3', y, 8 are the coefficients of activity of KOI, ^K^SO^, KHSO^, HOI, 

 and IH0SO4 respectively. 



Between .r and y there is a i-elation which is also a function of the quantities 

 present in the equilibrium of free acids, neutral salt, and solvent, a relation of 

 which the form still remains to be determined by experimental methods. 



§ 11. Equilibrium of heterogeneous systems. 



[By ' heterogeneous,' Arrhenius means systems out of which one constituent 

 is separated from solution in either the solid or gaseous form, and so removed 

 from action to whatever extent it is insoluble. He quotes from Berthelot and 

 Williamson about the formation of precipitates by double decomposition, and 

 the continual postponement of equilibrium by the dropping out of one consti- 

 tuent. 



He then considers a system of four bodies, IjJj, l^J^, l.Ji, IjJo, of which one 

 (say the last) is but slightly soluble. A constant quantity, e, of this remains in 

 jsolution, however much of it is formed or destroyed (time being allowed for pre- 

 cipitate to re-dissolve ad lib.). 



Then, a, /3, y, 8 being the respective coefficients of activity, and .r the amount of 

 I] Jj, and of loJi, formed from an original one equivalent of IjJi and any amount 

 •of IjJj, the equation (2a) is — 



a(l-x)cdl= x'^y- 



So X has a magnitude depending on e, and if c happen to be zero, x vanishes.] 

 We have thus given an analytic proof of the law of Berthelot, 



(37) If of four bodies, (1,1), (1,2), (2,1), (2,2), one of them (2,2) has 

 such physical propeHies that it separates wholly or nearly so from 

 the system, this body (2,2) and its conjugate (i,l) are formed, 

 to the exclusion more or less entire of the opposite bodies, (1,2) and 

 (2,1). 



If more than one substance is insoluble the equation may be, either 



.r-/3-y = cc'ab, 



c'x^y = c(l -x)ab. 



