The correct difference between first and second order reactions is that
Explanation
First-order $t_{1/2}$ is concentration-independent; second-order $t_{1/2} \propto 1/[A]_0$.
Detailed Solution
For a first order reaction, $t_{1/2} = \frac{0.693}{k}$, which is independent of the initial concentration of reactant.
For a second order reaction, $t_{1/2} = \frac{1}{k[A]_0}$, which depends on the initial concentration of reactant.
