Rate of reaction

The essentials

The rate of a reaction is the change in concentration of a reactant or product per unit time. For R → P, rate = −Δ[R]/Δt = +Δ[P]/Δt. The minus sign makes the rate positive because the reactant concentration falls. The average rate is measured over a time interval; the instantaneous rate is the rate at a particular moment, found from the slope of the tangent to the concentration–time curve (−d[R]/dt).

Key points

• For a reaction with unequal coefficients, divide each rate by its coefficient. For 2HI → H₂ + I₂: rate = −½ d[HI]/dt = d[H₂]/dt = d[I₂]/dt.
• For 2N₂O₅ → 4NO₂ + O₂: rate = −½ d[N₂O₅]/dt = ¼ d[NO₂]/dt = d[O₂]/dt.
• Units of rate: mol L⁻¹ s⁻¹; for gases, atm s⁻¹ can be used.
• Factors affecting rate: concentration (or pressure) of reactants, temperature, presence of a catalyst, surface area of solid reactants, and the nature of the reactants.
• The rate usually decreases with time because reactant concentration falls.

Exam tips

• Example: if N₂O₅ is used up at 0.02 mol L⁻¹ s⁻¹ in 2N₂O₅ → 4NO₂ + O₂, NO₂ forms at 0.04 mol L⁻¹ s⁻¹ and O₂ at 0.01 mol L⁻¹ s⁻¹.
• The instantaneous rate at t = 0 is the initial rate.

Common mistakes

• Forgetting the negative sign for reactants or the stoichiometric divisor.
• Confusing the rate of reaction with the rate constant k; the rate changes with concentration, k does not.