Chem 2 - Chemical Kinetics III - Determining the Rate Law with the Method of Initial Rates

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 Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Reaction Rate and Concentration

The rate of a chemical reaction depends on the concentration of the reactants.

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.

Initial Instantaneous Rate of Reaction

We can measure the initial instantaneous rate of reaction to determine the rate law for a given reaction.

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

General Form of the Rate Law

For the reaction A + B C

Where the rate law isRate = k [A]n [B]m

n is the “order” of A m is the “order” of Bk is the “rate constant”

The overall reaction order can be found by adding the exponents on the reactants in the rate law.

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

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

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.

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 0.20 204 0.20 0.03 155 0.20 0.06 30

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? n = 1

Determine the Order of B

Expt [A]0 [B]0 Observed rate (M/s)

1 0.01 0.20 52 0.02 0.20 103 0.04 0.20 204 0.20 0.03 15

5 0.20 0.06 30

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:

m = 1

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 0.20 103 0.04 0.20 20

4 0.20 0.03 155 0.20 0.06 30

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:

n = 1

Same answer!

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.

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!

Calculating the Rate Constant k using Experimental Data

Choose Experiment 3: [A] = 0.04 [B] = 0.20

Rate = 20 M/sStep 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!

k = 2500 M-1s-1

More examples will be posted separately

Next up:

The First-Order Integrated Rate Law (Pt 4)