Given a gas phase reaction `2A(g)+B(g)hArr C(g)+D(g)`. Which one of the following changes will affect the value of `K_(c)`?

Options

A. Addition of inert gas
B. Addition of catalyst
C. Addition of reactants
D. Increasing in temperature

Answer

To determine which change will affect the value of \( K_c \) for the given gas phase reaction \( 2A(g) + B(g) \rightleftharpoons C(g) + D(g) \), we need to analyze the factors that influence the equilibrium constant.

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant \( K_c \)**:
The equilibrium constant \( K_c \) is defined as:
\[ K_c = \frac{[C][D]}{[A]^2[B]} \]
where \([C]\), \([D]\), \([A]\), and \([B]\) are the molar concentrations of the respective species at equilibrium.

2. **Effect of Adding Inert Gas**:
Adding an inert gas at constant volume does not change the concentrations of the reactants and products. Therefore, it does not affect the value of \( K_c \).

3. **Effect of Adding a Catalyst**:
A catalyst speeds up the rate at which equilibrium is reached but does not change the position of equilibrium or the concentrations of reactants and products at equilibrium. Thus, \( K_c \) remains unchanged.

4. **Effect of Adding Reactants**:
Adding more reactants will shift the equilibrium position to the right (toward products) according to Le Chatelier's principle. However, this does not change the value of \( K_c \) itself; it only changes the concentrations of the species at equilibrium.

5. **Effect of Temperature Change**:
The value of \( K_c \) is dependent on temperature. For an endothermic reaction, increasing the temperature increases \( K_c \), while for an exothermic reaction, increasing the temperature decreases \( K_c \). Therefore, temperature is the only factor that can change the numerical value of \( K_c \).

### Conclusion:
The only change that will affect the value of \( K_c \) is a change in temperature. Thus, the correct answer is that \( K_c \) is affected by temperature changes.