1898-99.] Sulphuric Acid and Sulphates in Solution. 485 
between the numbers which, according to the law, should be equal. 
The differences were especially large at the highest dilutions. 
The following investigation was undertaken with a view to 
determine the hitherto unascertained nature of the equilibrium 
which exists in solutions of the acid sulphates, and in solutions 
containing sulphuric acid and a neutral sulphate in other than 
equivalent proportions. It is evident from the results obtained by 
the above mentioned investigators, that the equilibrium is one of 
peculiar interest, as being disturbed by mere dilution of the acid 
salt solution. 
The free acid, neutral sulphate and acid sulphate, in the solution 
of an acid sulphate, are partially dissociated, so that, besides these 
substances, the ions derived from them are concerned in the final 
equilibrium. Chief among the equilibria existing between the 
various substances in solution, is that, however, which obtains 
between the undissociated portions of the free acid, neutral and 
acid sulphates, and it was the particular aim of the present 
investigation to determine the nature of this equilibrium. The 
problem was treated quite empirically, and from the experimental 
results obtained, it was sought to ascertain the law of the equi- 
librium, and to formulate an expression by means of which it 
would be possible to calculate the percentage of free acid in a 
solution containing sulphuric acid and a neutral sulphate in any 
proportions. 
The Equilibrium. 
The chemical equation representing the formation of an acid 
sulphate as a balanced reaction is written thus : — 
H 2 S0 4 + M 2 S0 4 2MHS0 4 . 
According to the law of mass action, the equilibrium between the 
undissociated portion of these three substances in solution is given 
by the expression 
C.H 2 S0 4 (1 - cq) x C.M 2 S0 4 (1 - a 2 ) = K { a.MHS0 4 (l - a 3 )} 2 
where (7.H 2 S0 4 , (7.M 2 S0 4 and C.MHS0 4 are the concentrations at 
equilibrium of the acid, neutral sulphate and acid sulphate 
respectively, (1-oq), (l-a 2 ) and (l-a 3 ) the undissociated pro- 
portions of each of these substances, and K is a constant. 
