D13.4 Effect of Concentration: Rate Laws
When we previously learned about elementary reactions that make up the steps in a multi-step reaction mechanism, we discussed how each type of elementary reaction showed unique dependence on concentrations of reactants. The overall reaction also has a specific dependence on concentrations of various reaction species, as well as a rate constant that is unique to itself (and usually differs from the rate constants of the individual elementary reactions in its mechanism).
Rate laws or rate equations are mathematical expressions that relate the rate of a chemical reaction to the concentrations of reactants (and sometimes products or catalysts). Often the rate of reaction is proportional to some power of the concentration of a substance involved in the reaction:
In the rate law, k is the rate constant, which is independent of concentrations but depends on temperature. Each exponent, m, n, or p, defines the order of a reaction with respect to the concentration of each reactant, [A], [B], or [C]. It is the power to which a concentration must be raised to correctly calculate the rate. For example, if m = 1, the reaction is first-order with respect to [A]; if n = 2, the reaction is second-order with respect to [B]; if p = 0, the reaction is zeroth-order with respect to [C], which means that the rate of the reaction is not affected by the concentration of C, because [C]0 = 1. The overall reaction order is the sum of the individual orders, m + n + p + … Reaction orders are usually positive integers, although they can be fractions or negative numbers.
Activity: Order of a Reaction and Rate Law
An experiment shows that the following reaction:
NO2(g) + CO(g) ⟶ NO(g) + CO2(g)
is second-order in NO2 and zeroth-order in CO at 100 °C. What is the rate law for this reaction?
Write in your notebook, then left-click here for an explanation.
The rate law has the form:
rate = k[NO2]m[CO]n
The reaction is second-order in NO2; thus m = 2. The reaction is zeroth-order in CO; thus n = 0. The rate law is:
rate = k[NO2]2[CO]0 = k[NO2]2
The rate of reaction is solely dependent on the concentration of NO2. When we consider reaction mechanisms later on, we will explain how a reactant’s concentration can have no effect on reaction rate.
In a transesterification reaction, a triglyceride reacts with an alcohol to form an ester and glycerol. Many students learn about the reaction between methanol and ethyl acetate as a sample reaction:
CH3OH + CH3COOCH2CH3 ⟶ CH3COOCH3 + CH3CH2OH
The rate law for this reaction, under certain conditions, is determined to be:
rate = k[CH3OH]
Determine the order of reaction with respect to methanol and ethyl acetate; also determine the overall order of reaction.
Write in your notebook, then left-click here for an explanation.
Reaction Order and Rate Constant Units
It is often true that, as in the last activity, the reaction orders in the rate law are different from the coefficients in the overall chemical equation for the reaction. It is important to note that rate laws must be determined experimentally and are not reliably predicted by reaction stoichiometry. As we will learn later, this experimentally determined rate law is an important piece of information when verifying the validity of a proposed reaction mechanism.
Because an elementary reaction describes exactly the reaction that is occurring, it is possible to determine the order of an elementary reaction solely by looking at the reaction equation. This is true for all elementary reactions but only for elementary reactions.
- For a unimolecular elementary reaction, the reaction is overall first-order:
A ⟶ products rate = k[A]
- For a bimolecular elementary reaction, the reaction is overall second-order:
A + B ⟶ products rate = k[A][B]2 A ⟶ products rate = k[A]2
Exercise: Rate Law for a Reaction
Reaction orders play a role in determining the units for the rate constant—the units for k are whatever is needed so that substituting into the rate law expression affords the appropriate units for the rate.
The units for the rate constant for common reaction orders are summarized below.
| Overall Reaction Order (m+n+…) | Units of k (M1-(m+n+…)s-1) |
|---|---|
| zeroth |  |
| first |  |
| second |  |
| third |  |
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