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Reaction Kinetics

Topic 2 of 5

Concentration-time graphs and half-life

Recognise constant loss versus a constant fraction lost.

A-Level 9476 (2026-2027)

Zero order loses equal amounts; first order loses equal fractions

Only first-order half-life stays constant as concentration falls.

Zero-order concentration-time graph

Concentration falls in a straight line from 0.20 mol per cubic decimetre to zero over 60 seconds. The constant negative gradient means a constant disappearance rate.

Illustrative zero-order behaviour while the same rate law remains valid. Going from 0.20 to 0.10 takes 30 s; going from 0.10 to 0.05 takes only 15 s. Do not extend the line below zero concentration.

First-order concentration-time graph

Concentration falls from 0.20 to 0.10, 0.050 and 0.025 mol per cubic decimetre at 0, 20, 40 and 60 seconds. The curve becomes less steep, but each halving takes 20 seconds.

Illustrative first-order decay. The magnitude of the gradient decreases with concentration; the half-life stays 20 s under the same conditions.

The half-life is the time for a reactant concentration to fall to half its value at the start of the interval. For first order, each equal time interval removes the same fraction, so half-life is independent of the starting concentration. Look for several successive halvings on a graph; a single halving interval alone cannot establish first-order behaviour.

Worked example

Use repeated half-lives without an integrated rate equation

A first-order reactant has a half-life of 12.0 min. Starting at 0.160 mol dm-3, find its concentration after 36.0 min and the percentage reacted.

  1. 36.0/12.0 = 3 half-lives.
  2. Halve three times: 0.160 → 0.0800 → 0.0400 → 0.0200 mol dm-3.
  3. Fraction remaining = 1/8; fraction reacted = 7/8.
Answer

0.0200 mol dm-3 remains; 87.5% has reacted. The first-order model approaches zero but does not reach it after a finite number of half-lives.

When another reactant is maintained effectively constant, an observed simple decay can describe the dependence on the changing reactant under those conditions. State that constraint before attributing the entire reaction an overall order. Integrated rate equations are not required for this syllabus.