Reaction order
• Rate = k[A]m[B]n
• m and n are called reaction orders
• The overall reaction order is m + n
• When order: = 0 = zero order
= 1 = first order
= 2 = second order
1
Reaction order
• Order is an experimental quantity
• Order need bear no relationship to the balanced
equation
• 2H2O2(aq) → 2H2O(l) + O2(g)
• Rate = k[H2O2]
• Rate is directly proportional to concentration of H2O2
• Rate = k[H2O2]1 (FIRST ORDER REACTION)
2
Reaction order
• But what if you plot Rate vs conc (as in lecture 1) and you do not
get a straight line?
• Then plot Rate vs [conc]2
• If it is now a straight line then it is a SECOND ORDER REACTION
• 2NO2(g) → 2NO(g) + O2(g)
• Rate = k[NO2]2
• Example of where the reaction order is the same as stoichiometric
coefficient in the balanced equation
3
Reaction order
• Consider the reaction:
NH4+(aq) + NO2-(aq) → N2(g) + 2H2O(l)
• Rate = k[NH4+][NO2-]
• That is, the rate is dependent on the concentration
of NH4+ and on NO2• The rate law is first order in NH4+ and first order in
NO2-: it is second order overall
4
• Question: A reaction was found to be third
order in A. Increasing the concentration of A
by a factor of 3 will cause the reaction rate to
(a) remain constant
(b) increase by a factor of 27
(c) increase by a factor of 9
(d) triple
(e) decrease by a factor of the cube root of 3
Question: The rate law for the reaction of NO(g) with Cl2(g) is
given by: Rate = k[NO]2[Cl2]. Which of the following
statements is correct?
(a) This reaction is first order with respect to NO and third order
overall.
(b) This reaction is first order with respect to Cl2 and third order
overall.
(c) This reaction is first order with respect to Cl2 and second
order overall.
(d) This reaction is second order with respect to NO and second
order overall.
(e) It never rains in Cork.
Units of rate coefficient
• First order reaction eg Rate = k[A]1
• Since rate is the change in concentration with time then the
units of rate are mol L-1 s-1 (M s-1)
• Units of rate = (units of rate coefficient)(units of
concentration)
• Units of rate coefficient = units of rate / units of concentration
• Units of rate coefficient = M s-1 / M = s-1
7
Units of rate coefficient
• Second order reaction eg Rate = k[A]2
• Since rate is the change in concentration with time then the
units of rate are mol L-1 s-1 (M s-1)
• Units of rate = (units of rate coefficient)(units of
concentration)2
• Units of rate coefficient = units of rate / (units of
concentration)2
• Units of rate coefficient = M s-1 / M2 = M-1 s-1
8
Units of rate coefficient
• What are the units of a zero order reaction?
9
Using Rates to Determine Rate Laws
• The rate law for any chemical reaction must be determined
experimentally
• To determine the rate law you must determine reaction orders
• Zero order – changing concentration of the reactant will have no
effect on rate
• First order – changing concentration of the reactant will
produce proportional changes in the rate
• Second order - doubling concentration of the reactant increases
the rate by a factor of 4. (tripling concentration causes the rate to
be increased by a factor of 32 = 9)
The initial rate of a reaction was measured for several different starting
concentrations of A and B, and the results are as follows:
Using these data, determine (a) the rate law for the reaction; (b) the
magnitude of the rate constant; (c) the rate of the reaction when [A] = 0.050M
and [B] = 0.100 M.
Solution
Analyze: We are given a table of data that relates concentrations of
reactants with initial rates of reaction and asked to determine (a) the
rate law, (b) the rate constant, and (c) the rate of reaction for a set of
concentrations not listed in the table.
Plan: (a) We assume that the rate law has the following
form: Rate = k[A]m[B]n so we must use the given data to
deduce the reaction orders m and n. We do so by
determining how changes in the concentration change the
rate. (b) Once we know m and n, we can use the rate law and
one of the sets of data to determine the rate constant k. (c)
Now that we know both the rate constant and the reaction
orders, we can use the rate law with the given concentrations
to calculate rate.
Solve: (a) As we move from experiment 1 to experiment 2, [A] is held
constant and [B] is doubled. Thus, this pair of experiments shows how [B]
affects the rate, allowing us to deduce the order of the rate law with
respect to B. Because the rate remains the same when [B] is doubled, the
concentration of B has no effect on the reaction rate. The rate law is
therefore zero order in B (that is, n = 0)
In experiments 1 and 3, [B] is held constant so they show how [A] affects
rate. Holding [B] constant while doubling [A] increases the rate fourfold.
This result indicates that rate is proportional to [A]2 (that is, the reaction is
second order in A). Hence the rate law is
This rate law could be reached in a more formal way by taking the ratio of
the rates from two experiments:
This rate law could be reached in a more formal way by taking the ratio
of the rates from two experiments:
Using the rate law, then, we have
2n equals 1 only if n = 0
We can deduce the value of m in a similar fashion:
Using the rate law gives
Because 2m = 4, we conclude that m = 2
(b) Using the rate law and the data from experiment 1, we have
(c) Using the rate law from part (a) and the rate constant from part (b),
we have
Because [B] is not part of the rate law, it is irrelevant to the rate,
provided that there is at least some B present to react with A.
Check: A good way to check our rate law is to use
the concentrations in experiment 2 or 3 and see if
we can correctly calculate the rate. Using data
from experiment 3, we have
Thus, the rate law correctly reproduces the data, giving
both the correct number and the correct units for the
rate.
PRACTICE EXERCISE
The following data were measured for the reaction of nitric oxide with
hydrogen:
(a) Determine the rate law for this reaction. (b) Calculate the rate
constant. (c) Calculate the rate when [NO] = 0.050 M and [H2] =
0.150 M.
Answers: (a) rate = k[NO]2[H2], (b) k = 1.2 M-2s-1, (c) = 4.5 x 10-4 M/s
Question: Select the rate law that corresponds to the data shown for the
following reaction.
A+B→C
Experiment
1
2
3
4
(a) Rate = k[B]4
(b) Rate = k[A][B]3
(c) Rate = k[A]2[B]2
(d) Rate = k[B]3
(e) Rate = k[B]
[A] (M)
0.012
0.024
0.024
0.012
[B] (M)
0.035
0.070
0.035
0.070
Initial Rate (M s-1)
0.10
0.80
0.10
0.80
Question: Consider the following kinetic data collected at the very
beginning of a reaction:
Run Initial [A] Initial [B] Initial [C] Initial Rate
(mol/L) (mol/L-s)
(mol/L)
(mol/L)
---------------------------------------------------------------------------1
0.10
0.10
0.10
1.40 x 104
2
0.20
0.10
0.10
1.12 x 105
3
0.20
0.20
0.10
2.24 x 105
4
0.20
0.20
0.20
8.96 x 105
Which of the following is an appropriate expression for the rate law?
a) Rate = k[A]8[B]2[C]4
b) Rate = k[A]3[B][C]2
c) Rate = k[A]2[B][C]2
d) Rate = k[A]2[B][C]