Rate of reaction equations, year 12 A level

1. T U E S D A Y , 1 4 F E B R U A R Y 2 0 1 7
Rate of reaction equations

2. A rate equation
 An equation can be written which summarises the
results of practical analysis of the rate of a reaction.
 The equation shows how the change in the
concentration of reactants affects reaction rates.
 Consider the theoretical example:
 x A + y B  z C
 The rate equation appears as follows:
 Rate = k [A]n[B]m

3. Explaining the rate equation
 Rate = k [A]n[B]m
 In the above equation [A] and [B] represent the
concentrations of substances A and B in mol/dm3.
 The power n and m are the so called order of reaction
with respect to A and B. The overall order of reaction
is (n+m)
 The units for the rate of reaction are moldm-3s-1.
 k is the rate constant. Note that the value of k is only
constant for a specific temperature.

4. Units for the rate constant.
 The units for the rate constant will vary in order to
make the units for the rate equal to moldm-3s-1.
Overall order
Units for rate
constant
0 - Zero mol dm-3s-1
1 - First s-1
2 - Second mol -1dm3s-1

5. First order reactions
 The rate expression for a first order reaction looks
like this - Rate = k [A].
 This means that doubling the concentration of A
leads to a doubling in the rate of the reaction.
 The rate of reaction is proportional to the
concentration of substance A – so a plot of the graph
of concentration of A against the rate of reaction
leads to a straight line.

6. First order reactions
 The rate expression for a first order reaction looks
like this - Rate = k [A].
 If a graph of concentration of reactant is plotted
against time for a first order reaction the so called
half life for the reagent is the same wherever it is
measured on the graph and is given by t½ = 0.69/k

7. Graphical representations of first order reactions

8. Graphical representations of first order reactions

9. Second order reactions
 In a second order reaction the rate of reaction is
proportional to the concentration of the reactant
squared.
 If the concentration of the reactant doubles the rate
is four times faster.
 Rate = k [A]2

10. Graphical representations of second order reactions

11. Graphical representations of second order reactions

12. Zero order reactions
 A reaction is zero order if a change in concentration
of the reagent does not change the rate of the
reaction.
 Rate = k [A]0
 Since [A]0 = 1 Rate =k (a constant)
 It may seem strange that zero order reactions exist
because we assume that reaction rates are
concentration dependent, however they can occur
when the reagents react slowly to form an
intermediate which then react quickly to form the
products.

13. Zero order reactions
 An example of a zero order reaction is the nitration
of methylbenzene. The methylbenzene reacts with
nitronium ions formed from nitric acid. The creation
of the NO2
+ ions form slowly but then react
immediately with the methylbenzene.

14. Graphical representations of zero order reactions

15. Graphical representations of zero order reactions

16. Predicting the rate expression
 It is not possible to predict the rate expression from
a balanced equation. This is because reactions can
take place through several different steps and the
rate is determined by the slowest step (called the rate
determining step).
 Example: decomposition of ozone –
 Step 1 O 3 = O 2 + O (fast)
 Step 2 O 3 + O = 2O 2 (slow)
 So - Rate = k [O] [O 3]

17. Comparing graphs of reactions

27. Order of reaction from initial reaction rates
 If a series of experiment are conducted using
different initial concentrations for the different
reagents then the order of reaction for each reagent
can be determined.

28. Bromate(v) and bromide reaction
 The reaction is:
 BrO 3
- + 5Br- + 6H+ = 3Br 2 + 3H 2 + 3H2O
 A series of three experiments produced the following
results:

29. Bromate(v) and bromide reaction

30. Bromate(v) and bromide reaction

31. Bromate(v) and bromide reaction

32. Bromate(v) and bromide reaction
 The overall rate equation becomes:
 Rate = k[BrO 3
- ] [Br- ] [H+ ]2
 The value of k could be determined from any of the
experimental results.