Half-Life (Cambridge International A-Level Chemistry)

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 concentration-time graph for a first-order reaction is a downward curve with a constant half-life.

• 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

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

1. Draw a graph of concentration against time for these results.
2. Determine the first and second half-lives and hence determine the order of the reaction.

Answer

1. Draw a graph of concentration against time for these results.

2. 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] (x10-4mol 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