368 EEPORT — 1886. 



[which may he written more symmetrically, though less usefully for present pur- 

 poses — 



dn _ n_n — l n+p~\ 



dx .V a; — 1 x + p J 



Differentiating again, we get * — ' 



rf^w ^ 2(p + l){n-x) 

 dx'^ .r(p + .r)(l — x)-' 



which is always positive, since x cannot be greater than n. This we can render 

 into words thus : — • 



(26) If one adds a feeble base to a feeble acid, or vice versa, there is necessari/ 



for the formation of a given quantity of salt (dx) a quantity of base 

 (dn) so much the greater as the formation of salt has proceeded further. 



Moreover, equation (4) shows that if n is greater than 1, the denominator is 



not very great, hecause \ — x differs sensibly from zero ; so -^ will have a sensible 



positive value even for n>l, which means — 



(27) If one adds a feeble base to a feeble acid, or vice versa, the formation of 



salt continues sensibly, even after the number of equivalents of the body 

 added has surpassed that of the other body. 



The figures calculated for boracic acid and ammonia exhibit this property clearly. 

 Between the two examples cited are a crowd of transitions which are realised by 

 mixing a strong acid with a feeble base, or vice versa. Everything depends on the 

 magnitude of the factor adj^y, and on p, the amount of water present. The laws 

 deduced above have been long known by chemists. They are fundamental, and 

 occur in most reactions — that is to say, in all reactions of electrolytes. 



If in equation (5) the factor aS//3y is a small number, as is probably the case 



for alcoholates,- the quantity of salt formed is almost zero. So if one mixes 



alcohol with any base, it only forms a very little alcoholate. But, according to law 



(23), final equilibrium only depends on relative quantities of the ions present, so if 



one adds water to an alcoholate it is destroyed, and turns into alcohol and hydrates. 



Here the roles are changed ; water is an acid stronger than alcohol, so it is necessary 



that water shall displace most of the alcohol, as nitric acid displaces water from a 



hydrate, and this is in full agreement with fact. What is common to every case is 



the necessity of regarding water as an acid (or, if one likes it better, as a base), 



which concurs with other acids (or bases) in the equilibria. 



/J ■)' 

 As, according to equation (4), ■ is always negative, one perceives that the 



presence of salt (q) has always an opposing influence on its formation, just as 

 water has. However, the quantity of salt present in the reactions is generally 

 small enough for this influence not to be noticeable. 



§ 7. Important case of double decomposition. 



From the simplified formula indicated above by an 'A,' one can at once deduce 

 some important propositions. From (2A), -vaz. — 



abO--x)in-x) =.T«/3y 



one finds, by a discussion like that preceding prop. 24, that if one mixes two bodies 

 AB and CD, the bodies AD and CB will also form ; and that the more as aSj^y is 

 greater. 



' [Dr. Arrhenius's mathematical expressions are sometimes unnecessarily long, so 

 I rearrange them whenever convenient without compunction.] 



* According to all authors, alcohol is a conductor very inferior to water. On 

 the other hand, the conductivity of an alcoholate is comparable to that of a hydrate. 

 (See my work on the conductivity of alcoholic solutions.) [Author's note.] 



