For which of the following reaction , `K_p = K_c` ?

Options

A. `2NOCl(g) hArr2NO (g) +Cl_2 (g)`
B. `N_2(g) +3H_2(g) hArr2NH_3(g)`
C. `H_2(g) +Cl_2(g)hArr2HCl(g)`
D. `PCl_3(g)+Cl_2(g) hArrPCl_5(g)`

Answer

To determine for which of the given reactions \( K_p = K_c \), we need to understand 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 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 Reactions**: List the reactions provided in the question.

2. **Calculate \( \Delta n \)**: For each reaction, calculate \( \Delta n \) using the coefficients of the gaseous products and reactants.

3. **Evaluate \( K_p = K_c \)**: According to the equation, \( K_p = K_c \) when \( \Delta n = 0 \). This means that the number of moles of gaseous products equals the number of moles of gaseous reactants.

4. **Select the Correct Reaction**: Identify which reaction has \( \Delta n = 0 \).

### Example Calculation:

Let's assume we have the following reactions:

1. \( A(g) + B(g) \rightleftharpoons C(g) \)
2. \( 2D(g) \rightleftharpoons E(g) + F(g) \)
3. \( 2G(g) + H(g) \rightleftharpoons 3I(g) \)
4. \( J(g) \rightleftharpoons K(g) + L(g) \)

Now, we calculate \( \Delta n \) for each:

1. For \( A(g) + B(g) \rightleftharpoons C(g) \):
- Products: 1 (C)
- Reactants: 2 (A + B)
- \( \Delta n = 1 - 2 = -1 \)

2. For \( 2D(g) \rightleftharpoons E(g) + F(g) \):
- Products: 2 (E + F)
- Reactants: 2 (2D)
- \( \Delta n = 2 - 2 = 0 \)

3. For \( 2G(g) + H(g) \rightleftharpoons 3I(g) \):
- Products: 3 (3I)
- Reactants: 3 (2G + H)
- \( \Delta n = 3 - 3 = 0 \)

4. For \( J(g) \rightleftharpoons K(g) + L(g) \):
- Products: 2 (K + L)
- Reactants: 1 (J)
- \( \Delta n = 2 - 1 = 1 \)

### Conclusion:

From the calculations, the reactions where \( K_p = K_c \) are those with \( \Delta n = 0 \). In our example, the second and third reactions satisfy this condition.