The correct difference between first and second order reactions is that

The rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction does depend on reactant concentrations

The half-life of a first-order reaction does not depend on [A]₀; the half-life of a second-order reaction does depend on [A]₀

The rate of a first-order reaction does depend on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

A first-order reaction can catalyzed; a second-order reaction cannot be catalyzed

Solution

The half-life of a first-order reaction does not depend on [A]₀; the half-life of a second-order reaction does depend on [A]₀

The first-order reaction is given by, $t_{1 / 2} = \frac{0.693}{k}$ which is independent of the initial concentration of reactant.

Second order reaction, $t_{1 / 2} = \frac{1}{k [A_{0}]}$ , which depends on the initial concentration of reactant.

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