12 Reaction Rate Law
Learning Objectives
By the end of this section, you should be able to:
Define reaction rate law and reaction rate constant (k)
Reaction rate law Definition: The relationship between the rate of reaction and the concentration of reactants.
The rate law is usually proportional to the concentrations of reactants raised to a certain power:
Take the reaction we used as an example before: [latex]A + 2B → 3C + D[/latex]
The general form for reaction rate law is
| [latex]r=k_{r}[A]^a[B]^b[/latex] |
For gas cases, we can use partial pressure
[latex]r=k_{r}p_{A}^a p_{B}^b[/latex]
The rate constant [latex]k_{r}[/latex] is independent of species concentration but generally dependent on temperature.
For example, let’s look at the rate of the gas-phase decomposition of dinitrogen pentoxide,
[latex]2 N_{2}O_{5} ⇌ 4 NO_{2} + O_{2}[/latex]
Say the rate law is found to be directly proportional to the concentration of [latex]N_{2}O_{5}[/latex], we can express the rate law by[latex]^{[1]}[/latex]:
[latex]r = k_{r} [N_{2}O_{5}][/latex]
Reaction rate laws can be complicated and may tell us about the mechanism of the reactions. For example, consider the reaction between hydrogen and bromine:
Simple stoichiometry:
[latex]H_{2(g)} + Br_{2(g)} → 2 HBr_{(g)}[/latex]
Complicated rate law:
[latex]r = \frac{k_{a}[H_{2}][Br_{2}]^{3/2}}{[Br_{2}]+k_{b}[HBr]}[/latex]
Rate Law vs. Equilibrium Constant
Be careful not to confuse equilibrium constant expressions with rate law expressions. The expression for [latex]K_{eq}[/latex] can always be written by inspecting the balanced reaction equation, and often contains a term for each species of the reaction (raised to the power of its coefficient) whose concentration changes during the reaction. The equilibrium constant for the reaction [latex]2 N_{2}O_{5} ⇌ 4 NO_{2} + O_{2}[/latex] is given below:
[latex]K_{eq}=\frac{[NO_{2}]^4[O_{2}]}{[N_{2}O_{5}]^2}[/latex]
In contrast, the expression for the rate law generally bears no relation to the reaction equation and must be determined experimentally. [latex]^{[1]}[/latex]
Reaction Rate Law Units
Reaction rate (r) is generally expressed in units of concentration over time (e.g. [latex]\frac{mol}{L·s}[/latex], [latex]\frac{kPa}{min}[/latex], [latex]\frac{mol}{m^3·h}[/latex] ).
This means the rate constant [latex]k_{r}[/latex] needs to be such that r is expressed in units of concentration over time.
Exercise: Rate Constant Units
For the following example, what are the units for the reaction rate constant ([latex]k_{r}[/latex])?
[latex]r=k_{r}*p_{A}*p_{B}^2[/latex]
with p in Pa and time in seconds
Solution
Since r is expressed in concentration over time, the units of r are [latex]\frac{Pa}{s}[/latex].
\begin{align*}
\frac{Pa}{s}& = k_{r}*Pa*Pa^2 \\
k_{r}& =\frac{1}{Pa^2s}
\end{align*}
References
[1] Chemistry LibreTexts. 2020. The Rate Law. [online] Available at: <https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Rate_Laws/The_Rate_Law> [Accessed 23 April 2020].
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