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 |
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
- Determine the reaction order
