Reaction Order and Rate Constant Units

Reaction Order and Rate Constant Units

In some of our examples, the reaction orders in the rate law happen to be the same as the coefficients in the chemical equation for the reaction. This is merely a coincidence and very often not the case.

Rate laws may exhibit fractional orders for some reactants, and negative reaction orders are sometimes observed when an increase in the concentration of one reactant causes a decrease in reaction rate. A few examples illustrating these points are provided:

\(\begin{array}{}\\ {\text{NO}}_{2}+\text{CO}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{NO}+{\text{CO}}_{\text{2}}\phantom{\rule{3em}{0ex}}\text{rate}=k\left[{\text{NO}}_{2}\right]^{2}\\ {\text{CH}}_{3}\text{CHO}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CH}}_{4}+\text{CO}\phantom{\rule{3em}{0ex}}\text{rate}=k\left[{\text{CH}}_{3}\text{CHO}\right]^{2}\\ {\text{2N}}_{2}{\text{O}}_{5}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2NO}}_{2}+{\text{O}}_{\text{2}}\phantom{\rule{2em}{0ex}}\text{rate}=k\left[{\text{N}}_{2}{\text{O}}_{5}\right]\\ {\text{2NO}}_{2}+{\text{F}}_{2}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2NO}}_{2}\text{F}\phantom{\rule{3em}{0ex}}\text{rate}=k\left[{\text{NO}}_{2}\right]\phantom{\rule{0.2em}{0ex}}\left[{\text{F}}_{2}\right]\\ {\text{2NO}}_{2}\text{Cl}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2NO}}_{2}+{\text{Cl}}_{2}\phantom{\rule{3em}{0ex}}\text{rate}=k\left[{\text{NO}}_{2}\text{Cl}\right]\end{array}\)

It is important to note that rate laws are determined by experiment only and are not reliably predicted by reaction stoichiometry.

Reaction orders also play a role in determining the units for the rate constant k. In second example from the previous lesson, a second-order reaction, we found the units for k to be \(\text{L}\phantom{\rule{0.2em}{0ex}}{\text{mol}}^{-1}\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1},\) whereas in the last example from the previous lesson, a third order reaction, we found the units for k to be mol⁻² L²/s. More generally speaking, the units for the rate constant for a reaction of order \(\left(m+n\right)\) are \({\text{mol}}^{1\text{−}\left(m\text{+}n\right)}\phantom{\rule{0.2em}{0ex}}{\text{L}}^{\left(m\text{+}n\right)-1}\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}.\) The table below summarizes the rate constant units for common reaction orders.

Note that the units in the table can also be expressed in terms of molarity (M) instead of mol/L. Also, units of time other than the second (such as minutes, hours, days) may be used, depending on the situation.