For reaction : `H_(2)(h)+I_(2)(g) hArr 2HI(g)` at certain temperature, the value of equilibrium constant is `50`. If the volume of the vessel is reduced to half of its original volume, the value of new equilibrium constant will be

Options

A. `25`
B. `50`
C. `100`
D. Unpredictable

Explanation

To solve the problem, we need to understand how the equilibrium constant (Kc) is affected by changes in volume and the stoichiometry of the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction and Kc Value**:
The reaction given is:
\[ H_2(g) + I_2(g) \rightleftharpoons 2HI(g) \]
The equilibrium constant (Kc) for this reaction at a certain temperature is given as 50.

2. **Determine the Change in Moles**:
To analyze how the equilibrium constant is affected by a change in volume, we need to calculate the change in the number of moles (Δn) of gas during the reaction.
- On the reactant side, we have 1 mole of \(H_2\) and 1 mole of \(I_2\), totaling 2 moles.
- On the product side, we have 2 moles of \(HI\).
- Therefore, the change in moles (Δn) is calculated as:
\[ Δn = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 2 = 0 \]

3. **Understanding the Effect of Volume Change**:
The equilibrium constant Kc is related to the concentrations of the reactants and products. The relationship can be expressed as:
\[ K_c = \frac{[HI]^2}{[H_2][I_2]} \]
When the volume of the system is reduced, the concentrations of the gases will change. However, if Δn = 0, it indicates that the number of moles of gas does not change during the reaction.

4. **Effect of Volume on Kc**:
The equilibrium constant Kc is not affected by changes in volume when Δn = 0. This is because the concentrations of reactants and products will change proportionally, keeping the ratio constant.

5. **Conclusion**:
Since the value of Δn is 0, the equilibrium constant Kc remains unchanged regardless of the volume change. Therefore, the new equilibrium constant after reducing the volume to half will still be:
\[ K_c = 50 \]

### Final Answer:
The new equilibrium constant after reducing the volume to half is **50**.

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