For the general reaction:

aA + bB → cC + dD

we can write the rate law, in terms of reactants, as

Rate = k[A]^m[B]ⁿ

The rate law includes the concentrations of reactants, molarity, and the rate constant, k. The rate constant can have different units depending on the order of the reaction. A reaction has an individual order with “respect to” or “in” each reactant. The reactant exponents, m and n, have nothing to do with the coefficients in the chemical reaction. In fact, the exponents can only be determined experimentally, and they indicate the order with respect to each reactant. The overall order of a reaction can be determined by adding the exponents.

For example, if the rate law is Rate = k[A]²[B], the order with respect to [A] is 2, the order with respect to [B] is 1, and the overall order for the reaction is equal to 3. The reaction is 2^nd order in [A] and 1^st order in [B]. The reaction is third order overall.

For the reaction

A → P

If the rate of reaction doubles when the concentration of A doubles, the rate will depend on [A]¹. The reaction will be first order with respect to A. The units of k would be the reciprocal of time, time^-1. Time can be measured in seconds, minutes, hours, years, etc.

rate = k[A]

If the rate quadruples when the concentration of A is doubled, the rate will depend on [A]². The reaction is second order with respect to [A]. The units of k will be M^-1(time)^-1

rate = k[A]²

If the concentration of A is doubled, and the rate does not change, the rate does not depend on [A], and the reaction is zero order with respect to A. The units of k are in M/time.

rate = k[A]⁰ = k

Recall, that anything to the zero power is equal to 1.

Below, are plots of [A] vs time for a zero order, first order, and second order reaction. Note, the zero order is linear while both first and second order are nonlinear.

Below are plots of the rate, M/s, vs the time for a zero order, first order, and second order reaction. Here we see the rate is constant for a zero order reaction because the rate is not dependent on [A]. The rate vs [A] is linear for a first order reaction because the rate is directly proportional to [A], and nonlinear for a second order reaction because the rate increases exponentially with [A].

The reaction,

2 NO (g) + 2 H₂ (g) → N₂ (g) + 2 H₂O (g)

has the rate law

Rate = k[NO]^2[H₂]

The reaction is second order with respect to NO, first order with respect to H₂, and third order overall. Again, reaction orders are determined from experimental data and not from the balanced equation. We can have both negative and fractional orders.

CH₃CHO (g) → CH₄ (g) + CO(g)     Rate = [CH₃CHO]^3/2

The order with respect to CH₃CHO is 3/2. The overall order of the reaction is 3/2.

In the table below are some reactions and the experimentally determined rate law for each.

Worksheet: Reaction Order and Rate Law

Exercises

Exercise 1. The rate law for the general reaction

aA + bB → cC + dD is Rate = k[A]^m[B]ⁿ. What are the units for k, if the order with respect to [A] is 2 and the order with respect to [B] is 1? The time is measured in hours.

Check Solution to Exercise 1

Exercise 2. Consider the following reaction.

CH₃Br (aq) + OH^– (aq) → CH₃OH (aq) + Br^– (aq)

The order with respect to each of the reactants is first order. The units of time are seconds.

Check Solution to Exercise 2

Exercise 3. Consider the following reaction.

5 Br^– (aq) + BrO₃^– (aq) + 6 H⁺ (aq) → 3 Br₂ (aq) + 3 H₂O (l)

The reaction is first order in Br^–, first order in BrO₃^– and second order in H⁺. The time was measured in seconds. Write the rate law with the appropriate units.

Check Solution to Exercise 3

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