Statement I: Half-life period is always independent of initial concentration

Statement II: Half-life period is inversely proportional to rate constant

Statement I is false but statement II is correct

The correct answer is option 4. Statement I is false but statement II is correct.

Statement I: Half-life period is always independent of initial concentration.

The half-life (\( t_{1/2} \)) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. The independence of half-life from initial concentration is true only for first-order reactions. For first-order reactions:

\(t_{1/2} = \frac{\ln 2}{k}\)

Here, \( t_{1/2} \) is indeed independent of the initial concentration \([A]_0\).However, for other orders of reactions, the half-life does depend on the initial concentration:

Zero-order reactions:

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

Here, \( t_{1/2} \) is directly proportional to the initial concentration \([A]_0\).

Second-order reactions:

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

Here, \( t_{1/2} \) is inversely proportional to the initial concentration \([A]_0\).

Because the half-life is not always independent of the initial concentration (it is only independent for first-order reactions), Statement I is false.

Statement II: Half-life period is inversely proportional to rate constant

This statement refers to the relationship between the half-life \( t_{1/2} \) and the rate constant \( k \). For first-order reactions, this relationship is:

\(t_{1/2} = \frac{\ln 2}{k}\)

This shows that the half-life is inversely proportional to the rate constant \( k \).

For zero-order reactions:

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

Here, the half-life is still inversely proportional to \( k \), but it also depends on the initial concentration \([A]_0\).

For second-order reactions:

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

Again, the half-life is inversely proportional to \( k \), but it is also inversely proportional to the initial concentration \([A]_0\).

Therefore, while the statement is strictly true for first-order reactions, it also correctly states the inverse proportionality for zero-order and second-order reactions, albeit with additional dependencies on the initial concentration. Hence, Statement II is correct.

Conclusion:

Statement I is not universally true (it's only true for first-order reactions), it is false. Statement II correctly describes the inverse relationship between the half-life and the rate constant, making it true.

The correct answer is: Statement I is false but statement II is correct.