Reaction Kinetics and Rate Equations

Rate of reaction

The rate is the change in concentration of a reactant or product per unit time (mol dm⁻³ s⁻¹). Collision theory: reactions occur when particles collide with at least the activation energy and correct orientation. Rate is increased by higher concentration/pressure, temperature, surface area and catalysts.

The rate equation

The rate equation is found experimentally (not from the balanced equation):

rate = k [A]^m [B]^n

• k = the rate constant.
• m, n = the orders of reaction with respect to A and B.
• The overall order = m + n.

Orders of reaction

• Zero order ([A]⁰): rate is unaffected by [A]. Doubling [A] → no change.
• First order ([A]¹): rate is proportional to [A]. Doubling [A] → rate doubles.
• Second order ([A]²): doubling [A] → rate ×4.

Orders are found from experiments — e.g. the initial rates method: change one concentration at a time and see how the initial rate responds.

Finding the rate constant

Once orders are known, substitute one set of data into the rate equation and solve for k. The units of k depend on the overall order (e.g. first order: s⁻¹; second order: mol⁻¹ dm³ s⁻¹).

Concentration–time graphs

• Zero order: straight line with constant (negative) gradient — rate = the gradient.
• First order: curve with a constant half-life (the time for concentration to halve is the same throughout).

The rate-determining step

The slowest step in a multi-step reaction mechanism is the rate-determining step. Only species that appear in or before this step (up to and including it) appear in the rate equation. So the rate equation gives evidence about the mechanism.

The Arrhenius equation & temperature

Increasing temperature increases the rate constant k (more molecules exceed the activation energy). The Arrhenius equation (k = Ae^(−Ea/RT)) links k, activation energy and temperature; a plot of ln k against 1/T gives a straight line whose gradient = −Ea/R.

Worked example

When [A] doubles, rate ×4; when [B] doubles, rate is unchanged. Write the rate equation and overall order.

• A is second order (×4), B is zero order (no change). Rate = k[A]²; overall order = 2. ✓

Common mistakes

• Reading orders from the balanced equation — they must be found experimentally.
• Forgetting zero-order species are left out of the rate equation.
• Getting the units of k wrong (they change with overall order).

Exam tips

• Use the initial rates method: compare experiments where only one concentration changes.
• Deduce orders, write the rate equation, then calculate k with units.
• Link the rate equation to the rate-determining step when discussing mechanisms.

Key facts to remember

• rate = k[A]^m[B]^n; orders found experimentally; overall order = m + n.
• Zero order (no effect), first order (∝, constant half-life), second order (×4 when doubled).
• The rate-determining (slowest) step controls the rate; only species up to it appear in the rate equation.