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# Rate equations

Rate of reaction equations, year 12 A level

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### Rate equations

1. 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. 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. 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. 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. 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. 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. 7. Graphical representations of first order reactions
8. 8. Graphical representations of first order reactions
9. 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. 10. Graphical representations of second order reactions
11. 11. Graphical representations of second order reactions
12. 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. 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. 14. Graphical representations of zero order reactions
15. 15. Graphical representations of zero order reactions
16. 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. 17. Comparing graphs of reactions
18. 18. 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.
19. 19. 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:
20. 20. Bromate(v) and bromide reaction
21. 21. Bromate(v) and bromide reaction
22. 22. Bromate(v) and bromide reaction
23. 23. 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.