chemical kinetics

1. Chemical Kinetics (Pt. 3)
Determining the Rate Law
with the Method of Initial
Rates
By Shawn P. Shields, Ph.D.
This work is licensed by Shawn P. Shields-Maxwell under a Creative CommonsAttribution-NonCommercial-ShareAlike 4.0
International License.

2. Reaction Rate and Concentration
The rate of a chemical reaction
depends on the concentration of
the reactants.

3. Comparing the Instantaneous Rate and the
Average Rate
The slope of a
line tangent to
the curve at any
point is the
instantaneous
rate at that
time.
The average rate
is also shown.

4. Initial Instantaneous Rate of Reaction
We can measure
the initial
instantaneous
rate of
reaction to
determine the
rate law for a
given reaction.

5. The (differential) Rate Law
A rate law shows the mathematical relationship
between the reaction rate and the concentrations
of reactants.
The exponents tell the order (dependence) of the
reaction with respect to each reactant.
For the reaction A + B C
The (differential) rate law is
Rate = k [A]n [B]m

6. General Form of the Rate Law
For the reaction A + B C
Where the rate law is
Rate = k [A]n [B]m
n is the “order” of A
m is the “order” of B
k is the “rate constant”
The overall reaction order can be found by adding
the exponents on the reactants in the rate law.

7. Determining the Orders in the Rate Law
For the reaction A + B C
The generalized rate law is
Rate = k [A]n [B]m
We can find the numerical values for n and m
using a data set collected from an “Initial Rates
Experiment”.
We can also calculate the rate constant, k, after
we have determined n and m

8. A Sample Data Set from an “Initial Rates Experiment”
Expt [A]0 [B]0 Observed
rate (M/s)
1 0.01 0.20 5
2 0.02 0.20 10
3 0.04 0.20 20
4 0.20 0.03 15
5 0.20 0.06 30
Concentrations (known)
For the reaction A + B C

9. Determining the Orders for the Rate Law
Perform these steps for each reactant in the reaction.
Step 1: Identify two experiments where one reactant is
held at a constant concentration while the other is varied.
Step 2: Determine the amount the concentration was
changed by, i.e., “doubled, tripled, etc.
Step 3; Determine how the initial rate of reaction changed.
(2, 4, etc.)
Step 4: Find the relationship between the change in rxn
rate and the change in concentration of the reactant.

10. Example: Find the Order of A
Expt [A]0 [B]0 Observed
rate (M/s)
1 0.01 0.20 5
2 0.02 0.20 10
3 0.04 0.20 20
4 0.20 0.03 15
5 0.20 0.06 30

11. Finding the Orders in the Rate Law
For reactant A:
Step 1: Expts 1 and 2 vary A and keep B constant.
Step 2: Reactant A was doubled in concentration
Step 3: The rate of reaction doubled.
Step 4: Find the relationship between the change in
rxn rate and the change in concentration of the
reactant.
What happened to the rxn rate? 𝟐 = (𝟐)𝐧 𝟐 = (𝟐)𝐧 n = 1

12. Determine the Order of B
Expt [A]0 [B]0 Observed
rate (M/s)
1 0.01 0.20 5
2 0.02 0.20 10
3 0.04 0.20 20
4 0.20 0.03 15
5 0.20 0.06 30

13. Finding the Orders in the Rate Law
For reactant B:
Step 1: Expts 4 and 5 vary B and keep A constant.
Step 2: Reactant B was doubled in concentration
Step 3; The rate of reaction doubled
Step 4: Make this statement true:
𝟐 = (𝟐)𝒎 𝟐 = (𝟐)𝒎 m = 1

14. Could we have used Experiments 1 and 3 to
Determine the Order of A instead? Yes!
Expt [A]0 [B]0 Observed
rate (M/s)
1 0.01 0.20 5
2 0.02 0.20 10
3 0.04 0.20 20
4 0.20 0.03 15
5 0.20 0.06 30

15. Finding the Orders in the Rate Law
(using Expts 1 and 3)
For reactant A…what if we had chosen Expts 1 & 3?
Step 2: Reactant A was quadrupled in concentration
Step 3; The rate of reaction quadrupled
Step 4: Make this statement true:
𝟒 = (𝟒)𝒏 𝟒 = (𝟒)𝒏 n = 1
Same answer!

16. Calculating the Rate Constant k using
Experimental Data
After we have determined the order of
each reactant (n and m),
we can use any one of the experiments
in our data set to calculate k.

17. Calculating the Rate Constant k using
Experimental Data
Step 1: Choose one experiment and plug in the
concentrations for the reactants (A and B)
from the table.
Step 2: Plug in the associated initial rate for
that experiment, along with n and m.
Step 3: Solve for the rate constant k,
including units!

18. Calculating the Rate Constant k using
Experimental Data
Choose Experiment 3: [A] = 0.04 [B] = 0.20
Rate = 20 M/s
Step 2: Plug in the associated initial rate for
that experiment, along with n and m.
𝑅𝑎𝑡𝑒 = 𝑘 𝐴 1 𝐵 1
20 𝑀/𝑠 = 𝑘 0.04 1 0.20 1
Step 3: Solve for the rate constant k, including
units!
k = 2500 M-1s-1

19. More examples will be posted separately
Next up:
The First-Order
Integrated Rate Law (Pt 4)