To estimate the half-life from a concentration–time graph, choose a concentration and find when it falls to half that value. For first-order kinetics, repeat the check from a lower concentration. The two time intervals should be about the same.
The 2027 H2 Chemistry 9476 syllabus covers the concentration-independent half-life of a first-order reaction. This example shows how to read two halving intervals and use them to estimate the rate constant.
- Mark a starting concentration.
- Read the time for that concentration and its half.
- Subtract the two times.
- Repeat the check from a different concentration.
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Measure elapsed time between two levels
Suppose the graph gives a concentration of 0.800 mol dm⁻³ at 0 min, 0.400 at 10 min, 0.200 at 20 min and 0.100 at 30 min. Read each time from the horizontal axis after locating the concentration on the vertical axis. The time for a later halving starts at the later reading.
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Worked example | Compare two halving intervals
From 0.800 to 0.400 mol dm⁻³ the time is 10 − 0 = 10 min. From 0.400 to 0.200 mol dm⁻³ it is 20 − 10 = 10 min. The equal halving intervals are consistent with first-order decay of the measured reactant under the test conditions.
For a first-order reaction, k = ln 2 ÷ t½. The rate constant is about 0.0693 min⁻¹. If the question asks for s⁻¹, use 600 s for the half-life to obtain about 1.16 × 10⁻³ s⁻¹.
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Compare with a constant absolute decrease
The concentration in the example falls by 0.400, then 0.200, then 0.100 mol dm⁻³ in successive ten-minute intervals. The decreases get smaller while the fraction lost stays the same. A straight concentration–time line with a constant negative gradient would instead show equal absolute decreases over equal times.
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Frequently asked questions
Do I have to start reading at zero minutes?
No. For first-order kinetics you can start from any clearly readable point with enough remaining data to locate its half.
Can I claim the order from just one halving interval?
One interval gives a half-life at that starting concentration. Compare several intervals, or use other kinetic evidence, to test the order.