Which statement for equilibrium constant is true for the reaction `A+BhArrC`?

Options

A. Does not change with temperature
B. Changes when catalyst is added
C. Both (1) and (2)
D. Changes with temperature

Answer

To determine which statement regarding the equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is true, we need to analyze the options provided in the context of chemical equilibrium principles.

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant**:
The equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is defined as:
\[ K = \frac{[C]}{[A][B]} \]
where \([C]\), \([A]\), and \([B]\) are the molar concentrations of the products and reactants at equilibrium.

2. **Effect of Temperature on \( K \)**:
The value of the equilibrium constant \( K \) is dependent on temperature. If the temperature changes, the value of \( K \) will also change.
- For an **endothermic reaction**, increasing the temperature shifts the equilibrium to the right (towards products), increasing \( K \).
- For an **exothermic reaction**, increasing the temperature shifts the equilibrium to the left (towards reactants), decreasing \( K \).

3. **Effect of Catalysts**:
Catalysts do not change the value of the equilibrium constant. They only speed up the rate at which equilibrium is reached but do not affect the position of equilibrium or the concentrations of reactants and products at equilibrium.

4. **Analyzing the Options**:
- **Option 1**: "It does not change with temperature." - **False** (as established, \( K \) changes with temperature).
- **Option 2**: "It changes when a catalyst is added." - **False** (catalysts do not affect \( K \)).
- **Option 3**: "Both 1 and 2 are correct." - **False** (since both statements are incorrect).
- **Option 4**: "It changes with temperature." - **True** (this is correct).

5. **Conclusion**:
The correct statement regarding the equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is that it changes with temperature.

### Final Answer:
The true statement for the equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is **Option 4: It changes with temperature.**