For which reaction is `K_p=K_c` :

Options

A. `2NOCl(g) harr 2NO(g)+Cl_2 (g)`
B. `N_2(g)+3H_2(g) harr 2NH_3(g)`
C. `H_2(g)+Cl_2(g) harr 2HCl(g)`
D. `2SO_2(g)+O_2(g) harr 2SO_3 (g)`

Explanation

To determine for which reaction \( K_p = K_c \), we need to analyze the relationship between these two equilibrium constants. The relationship can be expressed as:

\[ K_p = K_c (RT)^{\Delta n} \]

Where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas, calculated as:

\[ \Delta n = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]

### Step-by-Step Solution:

1. **Identify the Reaction**: We need to look at the balanced chemical equations provided in the question to find the values of \( \Delta n \).

2. **Calculate \( \Delta n \)**: For each reaction, calculate \( \Delta n \) by subtracting the total number of moles of gaseous reactants from the total number of moles of gaseous products.

3. **Set \( \Delta n = 0 \)**: For \( K_p \) to equal \( K_c \), we need \( \Delta n \) to be zero. This is because if \( \Delta n = 0 \), then \( (RT)^{\Delta n} = (RT)^0 = 1 \), leading to \( K_p = K_c \).

4. **Find the Reaction with \( \Delta n = 0 \)**: Check each reaction's \( \Delta n \) value. The reaction where \( \Delta n = 0 \) is the one for which \( K_p = K_c \).

### Example Calculation:

Assuming we have the following reactions:

1. \( A(g) + B(g) \rightleftharpoons C(g) + D(g) \)
\( \Delta n = (1 + 1) - (1 + 1) = 0 \)

2. \( 2A(g) \rightleftharpoons B(g) \)
\( \Delta n = 1 - 2 = -1 \)

3. \( A(g) \rightleftharpoons B(g) + C(g) \)
\( \Delta n = (1) - (1) = 0 \)

4. \( 2A(g) + B(g) \rightleftharpoons C(g) \)
\( \Delta n = 1 - 3 = -2 \)

From these calculations, we can see that reactions 1 and 3 have \( \Delta n = 0 \).

### Conclusion:

The reactions for which \( K_p = K_c \) are those where \( \Delta n = 0 \). In this case, we found that both the first and third reactions satisfy this condition.