1912-13.] Precipitation of Salts by the Corresponding Acids. 65 
where b = the solubility of the salt corresponding with acidity = a, and k 0 
and h are constants for the particular case. It was further stated that the 
same expression holds for Engel’s data. 
The factor to which attention is to be directed is Jc 0 , which, as is evident, 
expresses the initial slope of the curve, i.e. the slope at low values of a, 
when 
da 
~db 
( 2 ) 
The limits within which these curves retain their initial slopes — that is to 
say, are straight lines — were found to be wide. Within these limits, then, 
equation (2) gives 
a 
B ^b 
= k, 
(3) 
where B = the initial solubility in pure water. 
Now turn to the cases in which the precipitation method is used to 
study the same salt. Let a small volume, v, of acid whose concentration = A 
be added to unit volume of the saturated aqueous salt solution. The con- 
D 1 • 
centrations will then be A and B respectively. But the solu- 
1+v 1+v * J 
bility of the salt in this particular strength of acid, as follows from 
equation (3), is B — — . A 
rCn 
1 + V 
If this be less than 
B 
1+v 
precipitation 
will occur ; if it be greater, the solution will become unsaturated ; and 
the critical condition is, therefore, that 
B 
1+v 
= B 
. A 
1+v’ 
or 
A = & 0 B 
(i) 
Equation (4), then, gives the desired relationship between the two 
methods; the “ critical ” concentration of acid which just fails to pre- 
cipitate salt when it is added to the pure saturated salt solution (as found 
by the precipitation method) is equal to the product of the aqueous solubility 
of the salt and the initial slope of the solubility-acidity curve (as found by 
the solubility method). 
There might, however, be some initial fluctuation in the solubility- 
acidity curve, which would render interpolation doubtful. Hence some 
experiments were carried out to test the relationship directly, precipitation 
trials being made with salts whose solubility-acidity curves had previously 
been determined. 
The method was as follows : — A saturated solution of the salt at 30° was 
VOL. xxxm. 5 
