Assertion (A) : For the reaction
`H_(2)+I_(2) hArr 2HI, K_(p)=K_(c)`
Reason (R) : In this reaction, the sum of stoichiometric coefficient of reactants is equal to the sum of stoichiometric coefficients of products.

Options

A. If both (A) and (R) are correct, and (R) is the correct explanation for (A)
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A)
C. If (A) is correct, but (R) is incorrect
D. If (A) is incorrect, but (R) is correct.

Answer

To solve the question, we need to analyze the assertion and the reason provided.

### Step-by-step Solution:

1. **Understanding the Reaction**:
The reaction given is:
\[ H_2 + I_2 \rightleftharpoons 2HI \]
Here, we have 1 mole of \(H_2\) and 1 mole of \(I_2\) as reactants, and 2 moles of \(HI\) as products.

2. **Assertion Analysis**:
The assertion states that for this reaction, \(K_p = K_c\). To verify this, we need to understand the relationship between \(K_p\) and \(K_c\):
\[ K_p = K_c (RT)^{\Delta n} \]
where \(\Delta n\) is the change in the number of moles of gas, calculated as the moles of products minus the moles of reactants.

3. **Calculating \(\Delta n\)**:
- **Products**: 2 moles of \(HI\)
- **Reactants**: 1 mole of \(H_2\) + 1 mole of \(I_2\) = 2 moles
- Therefore, \(\Delta n = n_{products} - n_{reactants} = 2 - 2 = 0\).

4. **Substituting \(\Delta n\) into the \(K_p\) and \(K_c\) relationship**:
Since \(\Delta n = 0\), we can substitute this into the equation:
\[ K_p = K_c (RT)^0 = K_c \cdot 1 = K_c \]
Hence, the assertion \(K_p = K_c\) is true.

5. **Reason Analysis**:
The reason states that in this reaction, the sum of the stoichiometric coefficients of reactants is equal to the sum of the stoichiometric coefficients of products.
- The sum of stoichiometric coefficients for reactants: \(1 (H_2) + 1 (I_2) = 2\)
- The sum of stoichiometric coefficients for products: \(2 (HI) = 2\)
- Since both sums are equal, the reason is also true.

6. **Conclusion**:
Both the assertion and the reason are correct, and the reason correctly explains the assertion because the equality of the stoichiometric coefficients leads to \(\Delta n = 0\), which in turn leads to \(K_p = K_c\).

### Final Answer:
Both assertion (A) and reason (R) are correct, and R is the correct explanation of A.

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