Half-Life (Cambridge (CIE) A Level Chemistry): Revision Note
First Order Reaction Half-life
The half-life of a first-order reaction is independent of the concentration of reactants
This means that despite the concentrations of the reactants decreasing during the reaction
The amount of time taken for the concentrations of the reactants to halve will remain the same throughout the reaction
The graph is a straight line going downwards
The rearrangement of the methyl group (CH3) in ethanenitrile (CH3CN) is an example of a first-order reaction with rate equation rate = k [CH3CN]
Rearrangement of the CH3 group in CH3CN
CH3CN (g) → CH3NC (g)
Experimental data on the changes in concentration over time suggests that the half-life is constant
Even if the half-lives are slightly different from each other, they can still be considered to remain constant
This means that no matter what the original concentration of the CH3CN is, the half-life will always be around 10.0 minutes
Half-life table
Change in [CH3CN] (mol dm-3) | Half-life (minutes) |
|---|---|
8.00 - 4.00 | 10.0 |
4.00 - 2.00 | 9.50 |
2.00 - 1.00 | 9.25 |
Graph of [CH3CN] over time
Since this is a first-order reaction, the time taken for the concentration to halve remains constant
Worked Example
Using the half-life of first-order reactions in calculations
The change in concentration of a reactant over time is recorded in the following table:
Time (s) | 0 | 200 | 400 | 600 | 800 | 1000 | 1200 | 1400 | 1600 |
|---|---|---|---|---|---|---|---|---|---|
[reactant] x10-4 (mol dm-3) | 5.8 | 4.4 | 3.2 | 2.5 | 1.7 | 1.2 | 0.8 | 0.5 | 0.3 |
Draw a graph of concentration against time for these results.
Determine the first and second half-lives and hence determine the order of the reaction.
Answer
Draw a graph of concentration against time for these results.
Determine the first and second half-lives and hence determine the order of the reaction.
Find the first and second half-lives by determining when the concentrations halve using the graph:
| Change in [reactant] (x10-4 mol dm-3) | Half-life (s) |
|---|---|---|
First half-life | 5.80 - 2.90 | 470 - 0 = 470 |
Second half-life | 2.90 - 1.45 | 920 - 470 = 450 |
Determine the reaction order
It is a first-order reaction
The successive half-lives remain reasonably constant (around 450 seconds) throughout the reaction
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