Kinetics
Kinetics: rates, mechanisms, and energy
The rate law expresses rate as k[A]^m[B]^n; exponents are determined experimentally, not from coefficients. Use the method of initial rates: compare trials where one concentration changes while others stay fixed. Units of k follow from the overall order-zero order mol/(L·s), first order 1/s, second order L/(mol·s).
Integrated laws: zero order [A] = [A]0 − kt (linear in [A] vs t); first order ln[A] = ln[A]0 − kt (linear in ln[A] vs t, half-life 0.693/k, independent of concentration); second order 1/[A] = 1/[A]0 + kt (linear in 1/[A] vs t). Half-life for second order depends on initial concentration.
Collision theory: molecules must collide with sufficient energy and proper orientation. The Arrhenius equation k = A e^(−Ea/RT) shows that raising T or lowering Ea increases k. A catalyst lowers Ea and speeds both forward and reverse reactions equally, so it does not change ΔH or K. On an energy profile, the highest peak is the transition state, and the rate-determining step has the largest activation barrier.
Mechanisms: elementary steps have rate laws from their molecularity. Only the slow step appears in the overall rate law; if a fast equilibrium precedes it, substitute the intermediate using the equilibrium expression. Intermediates are produced then consumed; catalysts are consumed then regenerated.
Traps: a catalyst does not increase yield, and a concentration change does not change k-only temperature, and activation energy via a catalyst, does.
Worked example: doubling [A] doubles the rate; doubling [B] quadruples it. Then rate = k[A][B]^2 and the overall order is 3.
Rule of thumb: compare experiments, find each exponent, then solve for k.