For a first order reaction, the half-life period is independent of:(A) Initial concentration(B) Cube root of initial concentration(C) First power of final concentration(D) Square root of final concentration

For a first-order reaction, the half-life period is independent of the (A) initial concentration.

The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease by half. In a first-order reaction, the rate of the reaction is proportional to the concentration of the reactant, so the rate equation can be written as:

Rate = k[A]

Where [A] is the concentration of the reactant at any given time, and k is the rate constant.

The integrated rate equation for a first-order reaction is:

ln([A]₀/[A]) = kt

Where [A]₀ is the initial concentration of the reactant, [A] is the concentration of the reactant at time t, and k is the rate constant.

The half-life (t₁/₂) is the time it takes for [A] to decrease to half its initial concentration [A]₀. We can substitute these values into the integrated rate equation:

ln([A]₀/([A]₀/2)) = k(t₁/₂)

Simplifying:

ln(2) = k(t₁/₂)

From this equation, we can see that the half-life (t₁/₂) is only dependent on the rate constant (k) for a first-order reaction. It is independent of the initial concentration [A]₀ or any other power or root of the concentration. Therefore, the correct answer is (A) initial concentration.