Statement I: If in a zero-order reaction, the concentration of the reactant is doubled, the half-life period is also doubled

Statement II: For a zero-order reaction, the rate of reaction is independent of the initial concentration

Statement I and statement II are correct but statement II is not the correct explanation of statement I

The correct answer is option 2. Statement I and statement II are correct but statement II is not the correct explanation of statement I.

Let us delve into the concepts of zero-order reactions and the correctness of the statements provided.

Statement I: If in a zero-order reaction, the concentration of the reactant is doubled, the half-life period is also doubled.

In a zero-order reaction:

The rate law is given by \( \text{Rate} = k \), where \( k \) is the rate constant. The integrated rate law for a zero-order reaction is \( [A]_t = [A]_0 - kt \), where \( [A]_t \) is the concentration of the reactant at time \( t \) and \( [A]_0 \) is the initial concentration. The half-life (\( t_{1/2} \)) for a zero-order reaction is defined as the time it takes for half of the initial concentration to react. It can be derived from the integrated rate law:

\(t_{1/2} = \frac{[A]_0}{2k} \)

This equation shows that \( t_{1/2} \) is inversely proportional to the rate constant \( k \) and directly proportional to the initial concentration \( [A]_0 \). Therefore, if \( [A]_0 \) is doubled, \( t_{1/2} \) will also double, assuming \( k \) remains constant. This makes Statement I true.

Statement II: For a zero-order reaction, the rate of reaction is independent of the initial concentration.

In a zero-order reaction:

The rate of reaction (\( \text{Rate} \)) is constant and is equal to \( k \), the rate constant. It does not depend on the initial concentration of the reactant \( [A]_0 \). This characteristic arises because in zero-order kinetics, the rate-determining step is independent of the concentration of the reactant. Therefore, whether \( [A]_0 \) is high or low, as long as the reaction proceeds under zero-order conditions, the rate remains constant. This makes Statement II true as well.

Relationship between the Statements:

Both statements are correct independently: Statement I correctly describes the relationship between the initial concentration and the half-life in a zero-order reaction. Statement II correctly describes the independence of the rate of reaction from the initial concentration in a zero-order reaction.

However, Statement II does not provide an explanation for why doubling the concentration doubles the half-life. The doubling of the half-life in Statement I is a consequence of the mathematical relationship derived from the integrated rate law for zero-order reactions.

Conclusion:

Therefore, the correct choice based on the explanation is Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I. This choice accurately reflects the individual correctness of both statements about zero-order reactions, with Statement II not providing a direct explanation for the relationship described in Statement I.