Question

Statement-I: When temperature is increased from 298 K to 308 K, having \( E_a = 12.72 \, \text{Kcal mol}^{-1} \), Rate constant (K) is doubled.
Statement-II: For a first (1st) order reaction \( A \rightarrow B \), the following graph is valid.

• A. Both Statement I and Statement II are correct.
• B. Statement I is correct but Statement II is incorrect.
• C. Statement I is incorrect but Statement II is correct.
• D. Both Statement I and Statement II are incorrect.

Answer 1

The Correct Option is B

Step 1: Understanding Statement-I.
Statement-I describes the effect of temperature on the rate constant (K) according to the Arrhenius equation. According to the equation, the rate constant \( K \) increases with an increase in temperature. The relationship is given by: \[ \ln \left( \frac{K_2}{K_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \] Given that the rate constant doubles, we can use this equation to confirm the correctness of Statement-I.
Step 2: Understanding Statement-II.
Statement-II refers to a first-order reaction. For a first-order reaction, the concentration of the reactant \( [A] \) decreases exponentially with time, which means the correct graph for \( [A] \) vs. \( t \) should be a straight line when plotted on a semi-logarithmic scale. The graph shown in the question represents a plot of \( [A] \) vs. \( t^{1/2} \), which is incorrect for a first-order reaction.
Step 3: Conclusion.
Thus, Statement-I is correct, but Statement-II is incorrect because the graph is not valid for a first-order reaction. The correct answer is (B). Final Answer: Statement I is correct but Statement II is incorrect.