You can't simply look at an overall reaction and know the associated rate law. Instead you must measure it in the lab.
The easiest way to do this is to run a series of experiments with different initial conditions. Since the rate of a reaction can vary with time, we compare the very initial rate of the reaction. This also avoids any complications with changes in rate due to backwards reactions.
By changing the initial concentrations, we can see what concentrations affect the rate and in what way. For example for the reaction
\[\rm{NO_2(g) + CO(g) \rightarrow NO(g) + CO_2(g)}\]
we might run three different experiments with different concentrations of the reactant gases.
| Experiment | Initial NO2 conc. (M) | Initial CO conc. (M) | Initial Rate (M s-1) |
| 1 | 5.0 x 10-4 | 1.6 x 10-2 | 2.8 x 10-9 |
| 2 | 5.0 x 10-4 | 3.2 x 10-2 | 2.8 x 10-9 |
| 3 | 1.5 x 10-3 | 3.2 x 10-2 | 2.5 x 10-8 |
The concentration dependence of the rate can be determined by comparing the different experiments. For example the difference between experiments #1 and #2 is that the CO concentration has been doubled in the 2nd experiment. Looking at the initial rate measured, it is clear that it is the same in both experiments. Thus the rate is independent of CO concentration. We would say the rate is zeroth order in CO. The NO2 dependence can be determined by comparing experiments #2 and #3. Here the NO2 concentration has been increased by a factor of 3 in the third experiment compared to the second. This increases the initial rate. If we compare the initial rate from experiment 3 to experiment 2, we see that the rate has increased by a factor of nine. Since we increase the concentration by 3 and the rate increase by 9 we know the rate is dependent on the NO2 concentration squared. Or we would say the reaction is second order in NO2. Finally, we could also say this rate is second order overall.
We could also determine a value for the rate constant since we now know the rate law
\[\rm{rate = k[NO_2]^2}\]
We know the initial rate and the concentration of NO2, so we could choose the data points from any of our experiments and plug them in to solve for k. Using the data from the first experiment, we see that
\[k = {2.8 x 10^{-9} M s^{-1} \over (5.0 x 10^{-4} M)^2} = 0.011 M^{-1} s^{-1}\]
Knowing this reaction is second order in NO2 gives us some insight into the mechanism. Specifically we know that it must involve some bimolecular step that involves a collision between two NO2 molecules. We care about rate laws because they give us insight into the mechanism of the reaction.
© 2013 mccord/vandenbout/labrake