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 gas phase reaction \( 2A(g) + B(g) \rightleftharpoons C(g) + D(g) \), we need to understand the factors that influence the equilibrium constant.

### Step-by-Step Solution:

1. **Understanding \( K_c \)**: The equilibrium constant \( K_c \) is defined for a reaction at a specific temperature and is given by the expression:
\[ K_c = \frac{[C][D]}{[A]^2[B]} \]
where \([C]\), \([D]\), \([A]\), and \([B]\) are the molar concentrations of the respective species at equilibrium.

2. **Factors Affecting \( K_c \)**: The value of \( K_c \) is influenced by:
- Temperature
- Changes in concentration of reactants or products (which affect the position of equilibrium but not \( K_c \))
- Addition of inert gases (which do not affect \( K_c \))
- Addition of catalysts (which speed up the reaction but do not change \( K_c \))

3. **Analyzing Changes**:
- **Addition of Inert Gas**: Adding an inert gas at constant volume does not change the partial pressures of the reactants and products, hence \( K_c \) remains unchanged.
- **Addition of Catalyst**: A catalyst speeds up the rate of reaching equilibrium but does not change the equilibrium constant \( K_c \).
- **Addition of Reactants**: Adding more reactants shifts the equilibrium position to the right (towards products) but does not change the value of \( K_c \).
- **Change in Temperature**: The only factor that changes the value of \( K_c \) is a change in temperature. According to Le Chatelier's principle and the van't Hoff equation, the equilibrium constant will change with temperature depending on whether the reaction is endothermic or exothermic.

4. **Conclusion**: The only change that affects the value of \( K_c \) is a change in temperature.

### Final Answer:
The change that will affect the value of \( K_c \) is **temperature**.

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