`K_(a1)`,`K_(a2)`and `K_(a3)` are the respective ionisation constants for the following reactions.
`H_(2)ShArrH^(+)+HS^(-)`,`HS^(-)hArrH^(+)S^(-2)`
`H_(2)ShArr2H^(+)+S^(2-)`
The correct relationship between `K_(a1)`,`K_(a2)`and `K_(a3)` is

Options

A. `K_(a_(3))=K_(a_(1))xxK_(a_(2))`
B. `K_(a_(3))=K_(a_(1))+K_(a_(2))`
C. `K_(a_(3))=K_(a_(1))-K_(a_(2))`
D. `K_(a_(3))=K_(a_(1))//K_(a_(2))`

Answer

A

Explanation

For the reaction : `H_(2)ShArrH^(+)+HS^(-),K_(a_(1))`
`K_(a_(1))=([H^(+)][HS^(-)])/([H_(2)S])` . . . (i)
For the reaction :
`HS^(-)hArrH^(+)+S^(2-),K_(a_(2))`
`K_(a_(2))=([H^(+)][S^(2-)])/([HS^(-)])` . . .(ii)
For the reaction :
`H_(2)ShArr2H^(+)+S^(2-),K_(a_(3))`
`K_(a_(3))=([H^(+)]^(2)[S^(2-)])/([H_(2)S])` . . . (iii)
By multiplying eqn. (i) and eqn. (ii), we get
`K_(a_(1))xxK_(a_(2))=([H^(+)][Hs^(-)])/([H_(2)S])xx([H^(+)][S^(2-)])/([HS^(-)])`
`=([H^(+)]^(2)[S^(2-)])/([H_(2)S])=K_(a_(3))`