Let's consider the following problem;

The following initial rate data were collected for the reaction

2NO_2(g) + F_2(g) ---> 2NO₂F_(g)

at 100 degrees C.

i) Determine the reaction order for NO_2(g) and F_2(g).

To determine the order with respect to NO_2(g) the ratio of experiments 1 and 2 must be used. Even though the concentration of F_2(g) is not exactly constant, it is to two significant figures.

The ratio of the two experiments can be written as;

Since the rate constant is constant and the concentration of F_2(g) is constant we can cancel both of those terms and substitute for the initial rate and concentration of NO_2(g). We then have;

Reducing the two ratio yields;

4.05 = (4.02)^m

1 = m

So the order of the reaction with respect to NO_2(g) is 1.

To determine the order with respect to F_2(g) the ratio of experiments 1 and 3 can be used. Even though the concentration of NO_2(g) is not exactly constant, it is to two significant figures.

The ratio of the two experiments can be written as;

Since the rate constant is constant and the concentration of NO_2(g) is constant we can cancel both of those terms and substitute for the initial rate and concentration of F_2(g). We then have;

Reducing the two ratio yields;

3.98 = (3.99)ⁿ

1 = m

So the order of the reaction with respect to F_2(g) is 1.

ii) Determine the overall order of the reaction.

The overall order is just the sum of the order of the reaction with respect NO_2(g) and F_2(g). So the overall order is equal to 2.

iii) Write the specific rate law for the reaction.

rate = k[NO_2(g)]¹[F_2(g)]¹

iv) Determine the magnitude and the units for the rate constant of this reaction.

The rate constant can be determined by rearranging the rate law equation from part iii);

Now any of the data from one of the three experiments can be substituted into the above relationship. Substituting the data from Experiment #1 and solving yields;