H2 reaction kinetics: initial rates, rate constants and half-life
A rate equation is inferred from evidence. The powers in rate = k[A]ᵐ[B]ⁿ are reaction orders, and usually cannot be copied from the overall chemical equation. Compare experiments in which one concentration changes while the others stay fixed.
Choose the method
If doubling [A] doubles the rate, the data support first order in A. A fourfold rate increase supports second order; no change supports zero order over the measured range.
Substitute one complete experiment into the established rate law to find k. Derive its units by dividing the rate units by the concentration units raised to the overall order.
For a first-order reaction, successive half-lives are equal under constant conditions. A catalyst changes the reaction pathway and rate; it does not change the equilibrium constant at a fixed temperature.
Worked examples
Example 1
With [B] fixed, doubling [A] from 0.10 to 0.20 mol/dm³ raises the rate from 0.0020 to 0.0080 mol/dm³/s. With [A] fixed, doubling [B] doubles the rate. Find the rate law.
For A, 2ᵐ = 4, so m = 2.
For B, 2ⁿ = 2, so n = 1.
Rate = k[A]²[B]. Overall order is 3.
Example 2
For rate = k[A]²[B], the rate is 0.0020 mol/dm³/s at [A] = 0.10 mol/dm³ and [B] = 0.20 mol/dm³. Find k.
k = 0.0020/(0.10² × 0.20) = 1.0.
Units = (mol dm⁻³ s⁻¹)/(mol³ dm⁻⁹) = dm⁶ mol⁻² s⁻¹.
Check by substitution: 1.0 × 0.10² × 0.20 gives the stated rate.
Try it yourself
A first-order reactant has a half-life of 40 s. Its concentration starts at 0.80 mol/dm³. Find the concentration after 120 s.
Show the worked answer
120/40 = 3 half-lives.
Concentration = 0.80 × (1/2)³ = 0.10 mol/dm³.
Common mistakes
Changing two concentrations at once requires accounting for both effects.
Keep the temperature fixed when comparing rates to infer orders; otherwise k may change.
Original Rae practice, prepared with AI assistance. Selected numerical results and their displayed working are automatically checked at publication; this does not verify every explanation. Curriculum references checked on 5 September 2026. No teacher review or SEAB endorsement is claimed.
What the syllabus expects
Explain and apply this vocabulary: catalysis; the activation energy; the rate-determining step; a reaction's half-life; the rate constant; the order of a reaction; the rate equation; and the overall rate of reaction.
Build and work with rate equations shaped like rate = k[A]^m[B]^n, including: Scope: limited to single-step reactions or multi-step ones with a rate-determining step, m and n each being 0, 1 or 2; integrated rate-equation forms are not needed
fixing a reaction's order by the initial rates method
justifying the order for zero- and first-order cases from concentration-time graphs
checking that a proposed mechanism squares with the kinetics actually observed
working out which order a particular mechanism would produce
computing an initial rate from concentration data
Recognise that a first-order reaction's half-life does not hinge on concentration.
Bring a first-order reaction's half-life into your calculations.
Find a rate constant by the initial rates method.
From the information given, design an experiment fit for following a reaction's rate.
Explain qualitatively, through how often molecules collide, why a change in concentration alters the rate.
Explain what activation energy means, calling on the Boltzmann distribution.
Using both the Boltzmann distribution and collision frequency, explain qualitatively how a temperature change moves the rate constant, and hence the rate.
Explain that a catalyst opens an alternative route of lower activation energy, so the rate constant becomes larger.
Read this catalytic lift to the rate constant through the Boltzmann distribution.
Outline how homogeneous and heterogeneous catalysis each operate, taking in:
the Haber process
the catalytic clearing of nitrogen oxides from car exhaust gases Scope: see also Section 11.4
the part played by atmospheric nitrogen oxides in oxidising atmospheric sulfur dioxide
the catalytic action of Fe2+ within the I-/S2O82- reaction
Portray enzymes as proteins that catalyse biological reactions with great selectivity, choosing their substrates as the lock-and-key model suggests, while being sensitive to temperature and to pH. Scope: the structural levels of proteins and the detail of denaturation are not examined
How it's examined
Questions on this topic most often ask you to explain, describe, determine, show. About 7% of the past-paper style questions in Rae's bank for this subject sit in this topic.
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