For a reaction $2A\to Products$ following Second-Order Kinetics, the integrated rate law is: $\frac{1}{[A{]}_t}=\frac{1}{[A{]}_0}+kt$ At half-life ($t=t_{1/2}$), $[A{]}_t=\frac{[A{]}_0}{2}$. Substituting this into the equation: $\frac{1}{[A{]}_0/2}=\frac{1}{[A{]}_0}+k{t}_{1/2}$ $\frac{2}{[A{]}_0}-\frac{1}{[A{]}_0}=k{t}_{1/2}$ $t_{1/2}=\frac{1}{k[A{]}_0}$

• Thus, the half-life is inversely proportional to the initial concentration. This distinguishes it from first-order reactions where $t_{1/2}$ is independent of concentration.