`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))`

Explanation

To find the correct relationship between the ionization constants \( K_{a1} \), \( K_{a2} \), and \( K_{a3} \) for the given reactions, we will analyze each reaction step by step.

### Step 1: Write the reactions and their ionization constants

1. The first reaction is:
\[ H_2S \rightleftharpoons H^+ + HS^- \]
The ionization constant \( K_{a1} \) for this reaction is given by:
\[ K_{a1} = \frac{[H^+][HS^-]}{[H_2S]} \]

2. The second reaction is:
\[ HS^- \rightleftharpoons H^+ + S^{2-} \]
The ionization constant \( K_{a2} \) for this reaction is given by:
\[ K_{a2} = \frac{[H^+][S^{2-}]}{[HS^-]} \]

3. The third reaction is:
\[ H_2S \rightleftharpoons 2H^+ + S^{2-} \]
The ionization constant \( K_{a3} \) for this reaction is given by:
\[ K_{a3} = \frac{[H^+]^2[S^{2-}]}{[H_2S]} \]

### Step 2: Combine the first two reactions

To derive the relationship between \( K_{a1} \), \( K_{a2} \), and \( K_{a3} \), we can add the first and second reactions:

From the first reaction:
\[ H_2S \rightleftharpoons H^+ + HS^- \]

From the second reaction:
\[ HS^- \rightleftharpoons H^+ + S^{2-} \]

When we add these two reactions, the \( HS^- \) on the product side of the first reaction cancels with the \( HS^- \) on the reactant side of the second reaction, resulting in:
\[ H_2S \rightleftharpoons 2H^+ + S^{2-} \]

### Step 3: Relate the ionization constants

According to the principle of equilibrium constants, when two reactions are added, their equilibrium constants multiply. Therefore, we can write:
\[ K_{a3} = K_{a1} \times K_{a2} \]

### Conclusion

The correct relationship between the ionization constants is:
\[ K_{a3} = K_{a1} \times K_{a2} \]