1898 - 99 .] Sulphuric Acid and Sulphates in Solution. 509 
The unknown factors in the general expression for the equilibrium 
are now determined, and for solutions containing sulphuric acid 
and potassium sulphate it may be written 
[C. H^O^l-cq)} 0 - 85 _ 0*259 
gkhso 4 (i - a 3 ) aK 2 so 4 (i - a 2 )' 
The accuracy of this formula was then tested by making use of 
it to calculate the percentage of free acid in the various solutions 
of sulphuric acid and potassium sulphate, the values so obtained 
being then compared with those actually observed. In this way 
we eliminate the exaggeration of experimental error which the 
formula causes, and can arrive at a better conclusion as to the 
value of the latter. If the expression is a good one, the differences 
between the observed and calculated values should not be much 
more than that due to experimental error. 
Let B represent the original concentration of the acid, and C 
that of the sulphate. At equilibrium let x be the concentration 
of the acid sulphate. According to the above equation the 
equilibrium is expressed by 
{(B-a?)(l-a 1 )} 0>86 _ A 
x{\ — a 3 ) (C — a?)(l — a 2 ) 
When B and C are known, the value of x is best calculated by 
an approximation method. Two values of x were chosen, one of 
which gave a larger value of A than that observed (0*259), the 
other a smaller value. The value of x , corresponding to the 
observed constant was then obtained by interpolation. After a 
little experience, it was easy to choose one value of x so that the 
constant corresponding to it differed very little from that ob- 
served, under which conditions it was possible to interpolate quite 
accurately. 
The above expression may be written thus : — 
(B - a:) 0,85 . (C - z) _ A (!-«,) 
* •(l-a 1 )»«.(l-a 2 )' 
As the last factor of the right hand member varies but little 
with small variations in x , its value was determined for each 
experiment, and treated as a constant. If we make it equal to a, 
the expression becomes 
(B- af-85(C -s)__ A 
xx a 
