5.1 Rate Factors

Reaction Rate Factors

Pick from 5 reactions and watch particles merge on collision. Tune concentration, temperature, surface area, and catalyst to see rate = k[A]ᵐ[B]ⁿ update live in M/s.

5 ReactionsRate = k[A]ᵐ[B]ⁿArrhenius4 Rate Factors
Topic 5.1

Reaction Rates

Explain the relationship between the rate of a chemical reaction and experimental parameters.

Kinetics is defined as the rate at which an amount of reactants is converted to products per unit time. Concretely, rate is a change in concentration per unit time, with units of M·s⁻¹.

The rates of change of reactant and product concentrations are determined by the stoichiometry of the balanced equation. For a A + b B → c C + d D:

rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = +(1/c)Δ[C]/Δt = +(1/d)Δ[D]/Δt

The negative signs on reactants make the rate a positive number, and dividing by the coefficient makes all four expressions agree. For 2 N₂O₅ → 4 NO₂ + O₂, NO₂ appears four times as fast as O₂ appears, and N₂O₅ disappears twice as fast as O₂ appears.

Rate falls as the reaction proceeds because reactant concentration falls. That is why the instantaneous rate — the slope of the tangent to a concentration-versus-time curve — differs from the average rate over an interval. The initial rate, at t = 0, is the one used for rate-law determination, because no product has yet accumulated to complicate matters.

EK 5.1.A.3 lists the factors that influence rate: reactant concentrations, temperature, surface area, catalysts, and other environmental factors. Each will be explained mechanistically in 5.5 and 5.11 — they all come down to changing the number of effective collisions per unit time.

Key points

  • Rate is always reported as a positive number; the negative sign handles reactant depletion.
  • Divide by the stoichiometric coefficient so all species give the same reaction rate.
  • Initial rate (t = 0) is what rate-law experiments measure.
  • Concentration, temperature, surface area, and catalysts all change rate; none of them changes ΔH or K.

Equations

  • not on the sheetNot on the equation sheet; follows from conservation of atoms.
    • stoichiometric coefficients

Common mistakes

  • Forgetting the coefficient division. Δ[NO₂]/Δt is not the reaction rate for 2 N₂O₅ → 4 NO₂ + O₂; ¼Δ[NO₂]/Δt is.
  • Reporting a negative rate. The convention makes rate positive.
  • Confusing average with instantaneous rate. A secant is not a tangent.
  • Assuming a faster reaction is more product-favored. Rate and equilibrium are independent (see 9.4).

Worked example

For 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), oxygen is forming at 0.024 M/s. Find the rate of the reaction and the rates of change of N₂O₅ and NO₂.

Reaction rate. O₂ has coefficient 1, so
rate = Δ[O₂]/Δt = 0.024 M/s

N₂O₅ (coefficient 2, being consumed):
−½ Δ[N₂O₅]/Δt = 0.024 → Δ[N₂O₅]/Δt = −0.048 M/s

NO₂ (coefficient 4, being formed):
¼ Δ[NO₂]/Δt = 0.024 → Δ[NO₂]/Δt = +0.096 M/s

Sanity check: NO₂ appears four times as fast as O₂, exactly as the coefficients demand.

Full notes for topic 5.1 →