The following equilibrium exists in an aqueous solution of hydrogen sulphide `H_(2)S hArr H^(+) + HS^(-)`
If dilute HCl is added to an aqueous solution of `H_(2)S` without any change in temperature

Options

A. The equilibrium constant will change
B. The concentration of `HS^(-)` will increase
C. The concentration of undissociated `H_(2)S` will decrease
D. The concentration of `HS^(-)` will decrease

Explanation

To solve the problem, we need to analyze the equilibrium reaction of hydrogen sulfide (H₂S) in the presence of a strong acid (HCl) and understand the effects on the concentrations of the species involved in the equilibrium.

### Step-by-Step Solution:

1. **Identify the Equilibrium Reaction**:
The equilibrium reaction for hydrogen sulfide in water is:
\[ H_2S \rightleftharpoons H^+ + HS^- \]
Here, \(H_2S\) dissociates into \(H^+\) ions and \(HS^-\) ions.

2. **Initial Conditions**:
Let’s assume the initial concentration of \(H_2S\) is \(C\) mol/L. At equilibrium, let \(X\) be the amount that dissociates:
- Concentration of \(H_2S\) at equilibrium = \(C - X\)
- Concentration of \(H^+\) at equilibrium = \(X\)
- Concentration of \(HS^-\) at equilibrium = \(X\)

3. **Adding Dilute HCl**:
When dilute HCl is added, it completely dissociates into \(H^+\) and \(Cl^-\):
\[ HCl \rightarrow H^+ + Cl^- \]
Assume the concentration of HCl added is \(Y\) mol/L, which means the concentration of \(H^+\) increases by \(Y\).

4. **Effect of Common Ion**:
The increase in \(H^+\) concentration due to HCl introduces a common ion effect. The new concentration of \(H^+\) becomes:
\[ H^+ = X + Y \]

5. **Le Chatelier’s Principle**:
According to Le Chatelier’s principle, if we increase the concentration of a product (in this case, \(H^+\)), the equilibrium will shift to the left to counteract this change. Therefore, the reaction will favor the formation of \(H_2S\) and reduce the concentration of \(HS^-\).

6. **Changes in Concentrations**:
- The concentration of \(H_2S\) will **increase** as the equilibrium shifts left.
- The concentration of \(HS^-\) will **decrease** as the equilibrium shifts left.
- The concentration of \(H^+\) will be higher due to the addition of HCl, but the equilibrium will adjust to minimize the effect.

7. **Equilibrium Constant**:
The equilibrium constant \(K\) for the reaction remains unchanged because it is only affected by temperature changes, not by the concentration of reactants or products.

### Conclusion:
- The concentration of undissociated \(H_2S\) will **increase**.
- The concentration of \(HS^-\) will **decrease**.
- The equilibrium constant will **not change**.