Q2 Mr. W. Sutherland on Weak Electrolytes and 



distributed through unit volume. On the average these may 

 be assumed to be at the angles of a division of the unit 

 volume into 2x equal cubes. A typical sample set of these 

 neighbour pairs of ions for acetic acid may be represented by 

 the large square ABCD, and by the small square abed if 

 they have re-combined to form a double 

 molecule. This re-combination might j*t L 



be a quadruple event resulting from the A p 



fourindependent incidents of the journey D 



of A to a and so on, in which case its a b 



probability would be proportional to a. A . d c 



But it may be that there needs only a Q *+ 



favourable conjunction of the pair AB i &¥ 



with the pair DC to cause recombination, . V 4+ 



so that, as there are 2x of such pairs, 



the probability of recombination will be proportional to x 2 . 

 From the empirical success of the formula known as 

 Ostwald's dilution law, we conclude that the probability is 

 proportional to x 2 and not to A' 4 , unless indeed the rate of 

 dissociation were proportional to (a — x)'\ in which case the 

 probability measured by x 4 w r ould lead to that formula. 

 I shall assume that in dilute solutions the rate of dissociation 

 is proportional to a — x, and that of recombination to oc 2 . 



Turning to solutions which are not dilute as regards 

 double molecules we can interpret (59) as a more general 

 form of the relation 



x 2 = k'(a-x)/k or (\rj/\ v ) 2 = 'K{l-'\v/\iVoWi/PiP- • ( 60 ) 

 Apparently then k'/k, instead of being a constant in (59) 

 takes the form a Q (p 2 pypip/M. 1 \ 2 -i] 2 which causes p x p to 

 disappear from the equation. This implies that (a— x) 2 in 

 the general case takes the place of a — x in the special case 

 of dilute solutions. The form (p 2 pY(a — x) Cl means that dis- 

 sociation is brought about by a certain conjunction of six 

 molecules of water with two double molecules of acid. No 

 doubt other similar conjunctions promote dissociation, and 

 the probability of dissociation is expressed by a series wdiose 

 sum is equivalent to the probability of a conjunction of six 

 molecules of w T ater with two of acid in a position making 

 the double molecules unstable. In the transition from one 

 equation to the other {p%pfp\p becomes constant. Dis- 

 regarding p which does not vary much with p u let us find 

 the value of p ± which makes (1— pi) 6 pi a maximum. It is 

 p x = 1/7 = 0*143. We have already seen that the transition 

 occurs at a value of p x near this. The form (p2p) 6 pip applies 

 from /?! = 0*8 or 0*9 to p i = , 113 which makes it a maximum. 



