`K_(a_1), K_(a_2)` and `K_(a_3)`, are the respective ionisation constants for the following reactions.
`H_2S hArr H^(+) + HS^(-)`
`HS^(-) hArr H^(+) + S^(2-)`
`H_2S hArr 2H^(+) + S^(2-)`
The correct relationship between `K_(a_1),K_(a_2),K_(a_3)` is

Options

A. `K_(a_3) = K_(a_1) xx K_(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_2S hArr H^(+)+ HS^(-)`
`K_(a_1)=([H^+][HS^-])/([H_2S])`
For this reaction, `HS^(-) hArr H^(+) + S^(2-)`
`K_(a_2) = ([H^+][HS^(2-)])/([HS^-])`
As, the above two reactions are added, their equilibrium constants are multiplied, As
`K_(a_3)=([H^+]^2[S^(2-)])/([H_2S]) K_(a_1)xxK_(a_2)`
So `K_(a_3)= K_(a_3) xx K_(a_2)`