5.6.3 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]

CH₃CN (g) → CH₃NC (g)

Rearrangement of the CH₃ group in CH₃CN

• Experimental data of 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

In 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

Answer

• Step 1: Plot the concentration-time graph using appropriate scales and labels for the axis

• Step 2: Find the first and second half-lives by determining when the concentrations halve using the graph

Step 2 table

• Step 3: Determine the reaction order
  It is a first-order reaction as the successive half-lives remain reasonably constant (around 450 seconds) throughout the reaction