the Relative Affinities of certain Acids. 559 



them all to bibasic sulphuric acid, and therefore the number 

 just found must be divided by 2. Therefore 13*68 may be 

 taken as the index of the affinity of hydrochloric acid, in 

 comparison with those of other acids determined in like 

 manner. 



Similarly with pyrophosphoric acid. The mean value 

 found for the quantity necessary to extinguish the free sul- 

 phuric acid in one gram-molecule of sulphuric acid was found 

 to be 0*963 gram-molecule of sodium pyrophosphate. At 

 this point the liquid contains 



Na 2 S0 4 + i(HJP 2 7 ) + -463(Na,P 2 7 ) 



in equilibrium. The number *463 therefore represents the 

 comparative affinity of pyrophosphoric acid, except that as the 

 acid is quadribasic the number found must be multiplied by 

 2 in order to bring it into comparison with bibasic acids. 

 Therefore the index of pyrophosphoric acid is *926. This acid 

 being quadribasic, half a molecule contains the quantity of 

 sodium requisite to saturate a molecule of sulphuric acid, and 

 therefore only half a molecule of pyrophosphoric acid is set 

 free. 



In other words : It is found by experiment that the quantity 

 of sodium pyrophosphate necessary to extinguish the reaction 

 for free sulphuric acid with one thousand molecules of that 

 acid, is 963 molecules ; out of this, five hundred molecules of 

 pyrophosphoric acid are set free as just mentioned, and there 

 remain 463 molecules of undecomposed pyrophosphate. This 

 number 463 multiplied by 2 because of the basicity of the 

 acid, and divided by 1000 to make it correspond to one 

 molecule of sulphuric acid ; gives '926 as the index of pyro- 

 phosphoric acid. 



The state of equilibrium is always conditioned by the degree 

 of concentration. If to any solution of sulphuric acid a salt 

 is added in just sufficient quantity to extinguish the sulphuric- 

 acid reaction, it is then only necessary to add a little water 

 and the equilibrium is at once changed ; a certain portion of 

 the salt that had been added is re-formed and the sulphuric 

 reaction reappears. In order, therefore, to obtain true com- 

 parative results, it is necessary to use the sulphuric acid always 

 at exactly the same dilution and to add the dry salt to it. 



The affinity of sulphuric acid for water is a most important 

 factor in all determinations of this nature. Mendel^ef indeed 

 expresses the opinion* that most of the affinities hitherto 



* l Principles of Chemistry,' English edition, vol. i. p. 377, footnote. 



2Q2 



