6.5 - The Rate Law: Reactant Concentration and Rate
Rate Law

is a mathematical relationship between the concentration of the reactant(s) and the rate of reaction that is
determined empirically (recall: Methods of Measuring Reaction Rates)

The rate of a reaction will always be proportional to the product of the initial concentrations of the reactants, where
these concentrations are raised to some exponential values.
For the general reaction:
a A + b B  products
The rate law can be expressed as:
r  [A]m[B]n
And the rate law equation can be written as:
where:
r = k [A]m[B]n
k is a rate constant, determined empirically and valid only for a specific reaction at a specific temperature
m and n are determined empirically and can any real number value, including fractions or zero
The meaning of the exponents in the rate law equation, m and n

The exponents describe the mathematical dependence of the rate on the initial reaction rate.

They are called the individual orders of reaction

The sum of the individual orders of reaction for each reactant is called the overall order of reaction
The meaning of the rate law constant, k

The magnitude of the rate constant indicates the speed of a reaction.

A small reaction rate indicates a slow reaction and a large reaction rate indicates a fast reaction
How Rates Depend on Concentration Change and Order of Reaction
Concentration
Change
x1
x 2 (doubling)
x 3 (tripling)
Order of Reaction
0
1
2
3
10 = 1
20 = 1
30 = 1
11 = 1
21 = 2
31 = 3
12 = 1
22 = 4
32 = 9
13 = 1
23 = 8
33 = 27
In other words:

If a reaction is first order with respect to a reactant then:
o
doubling the concentration of that reactant will result in the rate being multiplied by 2 (2 1)
o
tripling the concentration of that reactant will result in the rate being multiplied by 3 (31)

If a reaction is second order with respect to a reactant then:
o
doubling the concentration of that reactant will result in the rate being multiplied by 4 (2 2)
o
tripling the concentration of that reactant will result in the rate being multiplied by 9 (32)

If a reaction is zero order with respect to a reactant then:
o
doubling the concentration of that reactant will result in the rate being multiplied by 0 (2 0)
o
tripling the concentration of that reactant will result in the rate being multiplied by 0 (30)
o
i.e. the rate does not depend on the concentration of this reactant
Example 1
A series



of experiments is performed for the system:
When the initial concentration of A is doubled,
When the initial concentration of B is doubled,
When the initial concentration of C is doubled,
2A +3B + C  D + 2E
the rate increases by a factor of four
the rate is doubled
there is no effect on rate.
a)
What is the order of reaction with respect to each reactant? What is the overall order of reaction?
b)
Write an expression for the rate law equation.
Example 2
The decomposition of SO2Cl2 is known to be first order with respect to SO 2Cl2:
SO2Cl2 (g)  SO2 (g) + Cl2 (g)
If the initial rate of SO2Cl2 consumption is 3.0 x 10-3 mol/L·s when the initial concentration of SO2Cl2 is 0.25 mol/L, what
would the rate be if another experiment were performed in which the initial concentration of SO 2Cl2 were 0.50 mol/L?
Example 3
Consider the decomposition of dinitrogen pentoxide:
2 N2O5  2 NO2 + O2
Trial #
1
2
[N2O5]0 (mol/L)
0.40
0.80
a)
What is the order of reaction with respect to N 2O5?
b)
Write the rate law equation for this reaction.
c)
Calculate the value of k.
Initial Rate (mol/L·s)
2.1 x 10-4
4.2 x 10-4
Example 4
Consider the following reaction:
Trial #
1
2
3
A2 + 2 B  2 AB
[A2]0 (mol/L)
0.10
0.20
0.10
[B]0 (mol/L)
0.10
0.10
0.20
Initial Rate (mol/L·s)
3 x 10-4
6 x 10-4
3 x 10-4
a)
What is the order of reaction with respect to each reactant? What is the overall order of reaction?
b)
Write the rate law equation for this reaction.
c)
Calculate the value of k.
Example 5
The table below shows the experimental data obtained for the reaction: 2 A + B + 2 C  3 X
Trial #
1
2
3
4
[A]0 (mol/L)
0.10
0.20
0.10
0.20
[B]0 mol/L)
0.10
0.10
0.30
0.10
[C]0 (mol/L)
0.10
0.10
0.10
0.20
Initial (mol/L·s)
3.0 x 10 -4
1.2 x 10 -3
3.0 x 10 -4
2.4 x 10 -3
a)
What is the order of reaction with respect to each of the reactants? What is the overall order of reaction?
b)
Write the rate law equation for this reaction.
c)
Calculate a value for the rate constant.
d)
Calculate the rate of production of X when [A] = [B] = [C] = 0.40 mol/L.