Chemical kinetics
The idea
Kinetics measures how fast reactions run and what molecular pathway they follow. The central object is the rate law, rate = k[A]ᵐ[B]ⁿ, where the orders m and n must come from experiment — typically the method of initial rates, where you change one concentration at a time and watch how the rate responds. The rate constant k bundles in temperature dependence through the Arrhenius equation, k = A·e^(−Ea/RT): a higher activation energy Ea means a steeper sensitivity to temperature.
Integrated rate laws convert the same information into concentration-versus-time predictions; first-order processes have the special property of a constant half-life, t½ = 0.693/k. Mechanisms connect rate laws to molecular events: a multistep pathway moves only as fast as its slowest (rate-determining) step, and a proposed mechanism is acceptable only if it reproduces the observed rate law and sums to the overall equation.
The cardinal error is reading orders from the balanced equation's coefficients. Coefficients describe overall bookkeeping; orders describe the rate-determining molecular encounter, and they match only for a true elementary step. A catalyst, likewise, speeds the trip by lowering Ea on a new pathway — it never shifts where equilibrium lies.
Worked example
For A + B → C, initial-rate experiments give: run 1, [A] = 0.10 M, [B] = 0.10 M, rate = 2.0 × 10⁻⁴ M/s; run 2, [A] = 0.20 M, [B] = 0.10 M, rate = 8.0 × 10⁻⁴ M/s; run 3, [A] = 0.10 M, [B] = 0.20 M, rate = 4.0 × 10⁻⁴ M/s. Determine the rate law and the value of k with units.
- Compare runs 1 and 2, where only [A] changes: doubling [A] multiplies the rate by 8.0/2.0 = 4 = 2², so the reaction is second order in A.
- Compare runs 1 and 3, where only [B] changes: doubling [B] doubles the rate (4.0/2.0 = 2 = 2¹), so it is first order in B.
- Assemble the rate law: rate = k[A]²[B], overall order 2 + 1 = 3 — note this could never be read off the 1:1 coefficients of the equation.
- Solve for k using run 1: k = rate/([A]²[B]) = 2.0 × 10⁻⁴/((0.10)² × 0.10) = 2.0 × 10⁻⁴/1.0 × 10⁻³ = 0.20 M⁻²·s⁻¹, with units chosen so the rate comes out in M/s.
- Verify against an unused data point: run 2 predicts 0.20 × (0.20)² × 0.10 = 8.0 × 10⁻⁴ M/s, exactly as observed — the rate law is consistent.
Answer. Rate = k[A]²[B] with k = 0.20 M⁻²·s⁻¹; the reaction is third order overall.
Check your understanding
- Why must reaction orders be measured rather than copied from stoichiometric coefficients, and when do the two coincide?
- What does a zero-order dependence on a reactant suggest about the mechanism, and where might you see one in a catalyzed reaction?
- How does the Arrhenius equation explain the rule of thumb that rates roughly double for a 10 °C rise, and when does that rule fail?
- If two proposed mechanisms both reproduce the observed rate law, what further experiments could distinguish them?
Build the foundations first
Chemical kinetics builds on these concepts. If any feel shaky, start there.