Chemical Kinetics Practice Test 2026 - Free Chemical Kinetics Practice Questions and Study Guide

For a second-order reaction where rate = k[A]^2, the rate equation is d[A]/dt = -k[A]^2. Integrating gives 1/[A] = kt + 1/[A]0. To find the half-life, set [A] = [A]0/2 and substitute:

1/([A]0/2) = kt1/2 + 1/[A]0

2/[A]0 = kt1/2 + 1/[A]0

kt1/2 = 1/[A]0

t1/2 = 1/(k[A]0)

So the half-life is 1/(k[A]0). This shows why the half-life for this second-order process depends on the initial concentration, unlike first-order reactions where t1/2 is constant.