For a homogeneous chemical reaction, `K_(p)=K_(c)` when

Options

A. `Deltan=0`
B. `Deltan=1`
C. `Deltan=2`
D. `Deltan=oo`

Explanation

To determine the condition under which \( K_p = K_c \) for a homogeneous chemical reaction, we need to understand the relationship between these two equilibrium constants.

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constants**:
- \( K_p \) is the equilibrium constant expressed in terms of partial pressures of the gases involved in the reaction.
- \( K_c \) is the equilibrium constant expressed in terms of the concentrations of the reactants and products.

2. **Relationship Between \( K_p \) and \( K_c \)**:
- The relationship between \( K_p \) and \( K_c \) is given by the equation:
\[ K_p = K_c (RT)^{\Delta n} \]
- Here, \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( \Delta n \) is the change in the number of moles of gas, calculated as:
\[ \Delta n = \text{moles of gaseous products} - \text{moles of gaseous reactants} \]

3. **Condition for \( K_p = K_c \)**:
- For \( K_p \) to equal \( K_c \), the term \( (RT)^{\Delta n} \) must equal 1.
- This occurs when \( \Delta n = 0 \) because any number raised to the power of 0 is 1.

4. **Conclusion**:
- Therefore, \( K_p = K_c \) when \( \Delta n = 0 \), which means that the number of moles of gaseous products is equal to the number of moles of gaseous reactants.

### Final Answer:
For a homogeneous chemical reaction, \( K_p = K_c \) when \( \Delta n = 0 \).

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