Assertion : `K_(p)` can be less than, greater than or equal to `K_(c)`
Reason : Relation between `K_(p)andK_(c)` depends on the change in number of moles of gaseous reactants and products `(Deltan)`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the question regarding the relationship between \( K_p \) and \( K_c \), we will analyze the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that \( K_p \) can be less than, greater than, or equal to \( K_c \).

### Step 2: Understanding the Reason
The reason provided states that the relationship between \( K_p \) and \( K_c \) depends on the change in the number of moles of gaseous reactants and products, denoted as \( \Delta n_g \).

### Step 3: The Relationship Between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the equation:
\[ K_p = K_c (RT)^{\Delta n_g} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n_g \) is the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.

### Step 4: Analyzing \( \Delta n_g \)
- If \( \Delta n_g > 0 \): This means there are more moles of gaseous products than reactants. In this case, \( (RT)^{\Delta n_g} \) is greater than 1, so \( K_p > K_c \).
- If \( \Delta n_g < 0 \): This means there are fewer moles of gaseous products than reactants. Here, \( (RT)^{\Delta n_g} \) is less than 1, which implies \( K_p < K_c \).
- If \( \Delta n_g = 0 \): This indicates that the number of moles of gaseous products and reactants are equal. Therefore, \( K_p = K_c \).

### Step 5: Conclusion
Since the assertion states that \( K_p \) can be less than, greater than, or equal to \( K_c \), and the reason explains that this relationship depends on \( \Delta n_g \), both the assertion and the reason are true.

### Final Answer
Both the assertion and the reason are true, and the reason correctly explains the assertion.

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