In an experiment the equilibrium constant for the reaction `A+BhArr C+D` is `K_(C)` when the initial concentration of A and B each is 0.1 mole. Under similar conditions in an another experiment if the initial concentration of A and B are taken to be 2 and 3 moles respectively then the value of equilibrium constant will be

Options

A. `(K_(C))/(2)`
B. `K_(C)`
C. `K_(C)^(2)`
D. `(1)/(K_(C))`

Answer

To solve the problem, we need to understand the concept of equilibrium constant (Kc) and how it is affected by changes in concentration.

### Step-by-Step Solution:

1. **Identify the Reaction and Initial Conditions**:
The reaction given is:
\[ A + B \rightleftharpoons C + D \]
In the first experiment, the initial concentrations of A and B are both 0.1 moles.

2. **Write the Expression for the Equilibrium Constant (Kc)**:
The equilibrium constant expression for the reaction is:
\[ K_c = \frac{[C][D]}{[A][B]} \]
In the first experiment, we denote the equilibrium concentrations as:
- \([A] = 0.1 - x\)
- \([B] = 0.1 - x\)
- \([C] = x\)
- \([D] = x\)

Therefore, the expression for \(K_c\) becomes:
\[ K_c = \frac{x^2}{(0.1 - x)(0.1 - x)} \]

3. **Consider the Second Experiment**:
In the second experiment, the initial concentrations of A and B are 2 moles and 3 moles, respectively. The equilibrium concentrations will be:
- \([A] = 2 - x\)
- \([B] = 3 - x\)
- \([C] = x\)
- \([D] = x\)

The expression for \(K_c\) in this case is:
\[ K_c = \frac{x^2}{(2 - x)(3 - x)} \]

4. **Understanding the Dependence of Kc**:
The key point is that the equilibrium constant \(K_c\) is dependent only on the temperature and not on the initial concentrations of the reactants. Therefore, even though the initial concentrations are different in the two experiments, the value of \(K_c\) remains the same.

5. **Conclusion**:
Since the equilibrium constant does not change with the initial concentrations, the value of \(K_c\) in the second experiment will be the same as that in the first experiment.

### Final Answer:
The value of the equilibrium constant \(K_c\) in the second experiment will be the same as in the first experiment.