In which of the following equilibrium `K_(c) and K_(p)` are not equal?

Options

A. `2C(g)+2O_(2)(g)hArr 2CO_(2)(g)`
B. `2NO(g)hArr N_(2)(g)+O_(2)(g)`
C. `SO_(2)(g)+NO_(2)(g)hArr SO_(3)(g)+NO(g)`
D. `H_(2)(g)+I_(2)(g)hArr 2HI(g)`

Answer

To determine in which of the given equilibria \( K_c \) and \( K_p \) are not equal, we need to analyze the relationship between \( K_c \) and \( K_p \) based on the change in the number of moles of gases during the reaction.

### Step-by-Step Solution:

1. **Understanding \( K_c \) and \( K_p \)**:
- \( K_c \) is the equilibrium constant expressed in terms of molar concentrations (moles per liter).
- \( K_p \) is the equilibrium constant expressed in terms of partial pressures (atmospheres).
- The relationship between \( K_c \) and \( K_p \) is given by the formula:
\[ K_p = K_c (RT)^{\Delta n} \]
where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( \Delta n \) is the change in the number of moles of gas (moles of gaseous products minus moles of gaseous reactants).

2. **Calculating \( \Delta n \)**:
- To find \( \Delta n \), we need to count the moles of gases on both the product and reactant sides of the reaction.
- If \( \Delta n \) is zero, \( K_p \) will equal \( K_c \).
- If \( \Delta n \) is positive, \( K_p \) will be greater than \( K_c \).
- If \( \Delta n \) is negative, \( K_p \) will be less than \( K_c \).

3. **Analyzing Each Option**:
- **Option 1**:
- Reaction: \( 2C(g) + 2O_2(g) \rightleftharpoons 2CO_2(g) \)
- Moles of products = 2 (from \( CO_2 \))
- Moles of reactants = 4 (2 from \( C \) and 2 from \( O_2 \))
- \( \Delta n = 2 - 4 = -2 \)
- Since \( \Delta n < 0 \), \( K_c > K_p \). This option is valid as \( K_c \) and \( K_p \) are not equal.

- **Option 2**:
- Reaction: \( 1A(g) + 1B(g) \rightleftharpoons 2C(g) \)
- Moles of products = 2 (from \( C \))
- Moles of reactants = 2 (1 from \( A \) and 1 from \( B \))
- \( \Delta n = 2 - 2 = 0 \)
- Since \( \Delta n = 0 \), \( K_p = K_c \). This option is not valid.

- **Option 3**:
- Reaction: \( 1D(g) + 1E(g) \rightleftharpoons 2F(g) \)
- Moles of products = 2 (from \( F \))
- Moles of reactants = 2 (1 from \( D \) and 1 from \( E \))
- \( \Delta n = 2 - 2 = 0 \)
- Since \( \Delta n = 0 \), \( K_p = K_c \). This option is not valid.

- **Option 4**:
- Reaction: \( 2G(g) \rightleftharpoons 1H(g) + 1I(g) \)
- Moles of products = 2 (1 from \( H \) and 1 from \( I \))
- Moles of reactants = 2 (from \( G \))
- \( \Delta n = 2 - 2 = 0 \)
- Since \( \Delta n = 0 \), \( K_p = K_c \). This option is not valid.

4. **Conclusion**:
- The only option where \( K_c \) and \( K_p \) are not equal is **Option 1**.

### Final Answer:
**Option 1** is the correct choice where \( K_c \) and \( K_p \) are not equal.