Kinetics :  Sample Rate Calculations

Rate Laws

For each of the following, determine the rate law of the reaction and find the value of the rate constant (k) with proper units.

1) 2 O3 O2

 Experiment # Initial [O3] (M) Initial Rate (M/sec) 1 2.00 0.500 2 4.00 1.000 3 6.00 1.500

First, set up a generic rate law:

rate = k[A]X

Next, create a ratio with the rate laws for 2 experiments:

Simplify and solve for x:

The reaction is first order with respect to [O3] because the exponent was calculated to be 1.

Now we can write the rate law and solve for k by plugging in values for the rate and the [O3] from a single experiment:

2) N2O42 NO2

 Experiment. # Initial [N2O4 ] (M) Initial Rate (M/sec) 1 0.50 0.050 2 1.00 0.200 3 1.50 0.450

3)  Xe + 3 F2XeF6
 Experiment. # Initial [Xe] (M) Initial [F2] (M) Initial Rate (M/sec) 1 0.50 0.25 0.00156 2 1.50 1.00 0.05625 3 0.75 0.25 0.0032 4 1.50 0.25 0.01406 5 0.50 1.00 0.00625

The rate law includes the concentrations of all the reactants:

rate = k[Xe]X[F2]Y

Therefore, we must solve for both X and Y separately.
First choose two experiments in which the initial [F2] are the same and set up a ratio with these experiments:

The [F2] cancel each other out ,and the equation simplifies to find that X = 2. The reaction is second order with respect to [Xe].

Next, we do the same to solve for Y.  Choose two experiments in which the initial [Xe] are the same and set up a ratio.

The [Xe] cancel each other out, and the equation simplifies to find that Y = 1.  The reaction is first order with respect to [F2].

Now we can write the rate law:

* The reaction is first order with respect to F2 and second order with respect to Xe.

Now we have to solve for k:

Next:  "Collision Molecular Theory"