V O L U M E 2 3 , N O . 8, A U G U S T 1 9 5 1
1179
that a t high concentrations essentially all the H' ions arise from this dissociation of the comples acid, the relationship
(4) van be shown t o apply. On the coordinates selected in Figure 3 this also becomes the equation for a straight line, with the following characteristics:
LITERATURE CITED
.4t the intercept, log [HA] = 0 PH =
'/* ( P K I
+ P&)
(6)
For line A these quantities may be evaluated as follows:
- n3
= -1.6
n = 3.2 l,'~
at a lower temperature, 18" C. Thygesen interprets his data on the assumption of a doubly dissociated tetramer rather than a singly dissociated complex. He further elects to assign dissociation constants to his complex acid in the same ratio as the two dissociation constante of glutaric acid. Inasmuch as both of these judgments appear to be arbitrary to the present writer, it is deemed preferable t o describe concentrated solutions of boric acid as behaving as if they contained a far stronger complex acid than orthoboric acid of an average molecular weight 3 2 times that of the monomer.
+ pKt) 3.43 + pKz = 6.86
(pKi pKi
Bearing in mind the assumptions which have been made it may be concluded that the complex is made up, on the average, of 3.2 monomeric molecules and that the product of polymerization and dissociation constants of this complex, Kl.Kz = 10-6.8". The undue acidity of concentrated boric acid solutions ha< previously been investigated by Thygesen ( 1 4 ) n ho, on the basiq of electrical conductivity measurements, collpcted data indirating the occurrence in concentrated solution of a complex borate made up of approximatelv 3 monomeric molecules. Calculations f i om his data give rise t o points included in Figure 3. These points
