In which one of the following equilibria, `K_(p) = K_(c)` ?

Options

A. `2NO(g) rarr N_(2)(g) + O_(2)(g)`
B. `2C(s) + O_(2)(g) rarr 2CO(g)`
C. `2HI(g) rarr H_(2)(g) + I_(2)(g)`
D. `NO_(2)(g) + SO_(2)(g) rarr NO(g) + SO_(2)(g)`

Explanation

To determine in which equilibrium \( K_p = K_c \), we need to analyze the given reactions based on the relationship between \( K_p \) and \( K_c \). The relationship is given by the equation:

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

where:
- \( R \) is the ideal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas, calculated as \( \Delta n = n_p - n_r \) (moles of products minus moles of reactants).

### Step-by-Step Solution:

1. **Identify the Reactions**: We need to analyze the provided reactions to find \( \Delta n \) for each.

2. **Calculate \( \Delta n \)**:
- For each reaction, count the number of moles of gaseous products and reactants.
- Use the formula \( \Delta n = n_p - n_r \).

3. **Determine \( K_p \) and \( K_c \)**:
- If \( \Delta n = 0 \), then \( K_p = K_c \) because \( (RT)^{\Delta n} = (RT)^0 = 1 \).
- If \( \Delta n \neq 0 \), then \( K_p \) will not equal \( K_c \).

4. **Analyze Each Option**:
- For each reaction option provided, calculate \( \Delta n \) and check if it equals zero.

5. **Conclusion**:
- The reaction for which \( \Delta n = 0 \) is the one where \( K_p = K_c \).

### Example Calculation:

Assuming we have the following reactions:

1. \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \)
- \( n_p = 2 \) (from \( 2NO \))
- \( n_r = 2 \) (from \( N_2 + O_2 \))
- \( \Delta n = 2 - 2 = 0 \) → \( K_p = K_c \)

2. \( 2C(s) + O_2(g) \rightleftharpoons 2CO(g) \)
- \( n_p = 2 \) (from \( 2CO \))
- \( n_r = 1 \) (from \( O_2 \))
- \( \Delta n = 2 - 1 = 1 \) → \( K_p \neq K_c \)

3. \( H_2(g) + I_2(g) \rightleftharpoons 2HI(g) \)
- \( n_p = 2 \) (from \( 2HI \))
- \( n_r = 2 \) (from \( H_2 + I_2 \))
- \( \Delta n = 2 - 2 = 0 \) → \( K_p = K_c \)

### Final Answer:
The equilibria for which \( K_p = K_c \) are those where \( \Delta n = 0 \).