For our two experiments we are considering the same reaction,
| Experiment # | Initial [NO2] | Initial Rate (M/min) |
| 1 | 0.350 M | 3.4 x 10-2 |
| 2 | 0.700 M | 1.5 x 10-1 |
From our data when we doubled the initial concentration of NO2(g) the rate increased by a factor of four. Had we tripled the initial concentration of NO2(g) the initial rate would have increased by a factor of nine. From this knowledge we could write a relationship between the initial rate and the initial concentration of NO2(g);
To complete our rate law we include a rate constant.
Where k is call the rate constant for a reaction. The rate constant represents the basic tendency of a reaction to go rapidly; a large 'k' means a fast reaction for a given concentration of reactants, and a small 'k' means the reaction goes more slowly for the same reactant concentrations.
The expression;
We can calculate the rate constant, k, if we know the instanteous rate of the reaction at a given concentration. That is;
Substituting the initial rate and the initial concentration from Experiment #1 above;
0.302 M-1*min-1 = k
In the rate expression the exponent is referred to as the order of the reaction. According to the rate law, which was experimentally determined the exponent is 2 and we say the reaction is second order. The exponent can have integer values of 0, 1, 2 or 3 and fractional values like 1/2 or 3/2. The order of a reaction is defined as the sum of the exponents of the concentration terms in the rate equation. Order is purely an experimental parameter and describes what is observed about the rate equation rather than implying anything about the mechanism of the reaction.