Statement I: For a first-order reaction t_1/2 is independent of the initial concentration of reactants

Statement II: For a first-order reaction t_1/2 is twicethe t _3/4

Statement I is true but statement II is false

The correct answer is 3. Statement I is true, but statement II is false.

Statement I: For a first-order reaction, t_1/2 (half-life) is independent of the initial concentration of reactants. This statement is true. In a first-order reaction, the half-life is a constant value that remains the same regardless of the initial concentration. The reaction rate depends solely on the rate constant of the reaction, which is independent of the initial concentration.

Statement II:  For a first-order reaction, t_1/2 is twice the t_3/4. This statement is false. In a first-order reaction, the half-life is defined as the time required for the concentration of the reactant to decrease by half. It is not directly related to the time required for the concentration to decrease by three-fourths (t_3/4). The relationship between t_1/2 and t_3/4 in a first-order reaction is not a fixed ratio of 2:1.

Therefore, the correct answer is that Statement I is true, but Statement II is false.