In chemical equilibrium, the value of `Delta n` (number of molecules), is negative, then the relationship between `K_(p) "and" K_(c)` will be

Options

A. `K_(P)-K_(c) = 0`
B. `K_(c) = K_(P) xx (RT)^(+Deltan)`
C. `K_(P) = K_(c) xx (RT)^(-Deltan)`
D. `K_(c) = 1/K_(p)`

Explanation

To solve the question regarding the relationship between \( K_p \) and \( K_c \) when the value of \( \Delta n \) (the change in the number of moles of gas) is negative, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- \( K_p \) is the equilibrium constant in terms of partial pressures.
- \( K_c \) is the equilibrium constant in terms of molar concentrations.
- \( \Delta n \) is defined as the difference between the number of moles of gaseous products and the number of moles of gaseous reactants.

2. **Write the Relationship**:
- The relationship between \( K_p \) and \( K_c \) is given by the formula:
\[ K_p = K_c \cdot R T^{\Delta n} \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

3. **Substituting \( \Delta n \)**:
- Since it is given that \( \Delta n \) is negative, we can denote it as \( \Delta n < 0 \).
- This means that when we substitute \( \Delta n \) into the equation, we have:
\[ K_p = K_c \cdot R T^{\Delta n} \]

4. **Rearranging the Equation**:
- To express \( K_c \) in terms of \( K_p \), we can rearrange the equation:
\[ K_c = \frac{K_p}{R T^{\Delta n}} \]
- Since \( \Delta n \) is negative, \( T^{\Delta n} \) can be rewritten as \( \frac{1}{T^{|\Delta n|}} \), where \( |\Delta n| \) is the positive value of \( \Delta n \).

5. **Final Relationship**:
- Therefore, we can express the relationship as:
\[ K_c = K_p \cdot \frac{1}{R T^{|\Delta n|}} \]
- This indicates that \( K_c \) is inversely related to \( K_p \) when \( \Delta n \) is negative.

### Conclusion:
When \( \Delta n \) is negative, the relationship between \( K_p \) and \( K_c \) can be summarized as:
\[ K_c = \frac{K_p}{R T^{|\Delta n|}} \]