2.2: Reaction Rate Law
- Page ID
- 101146
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Take the reaction we used as an example before: \(A + 2B → 3C + D\)
The general form for reaction rate law is
| \(r=k_{r}[A]^a[B]^b\) |
For gas cases, we can use partial pressure
\[r=k_{r}p_{A}^a p_{B}^b\]
The rate constant \(k_{r}\) 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,
\[2 N_{2}O_{5} ⇌ 4 NO_{2} + O_{2}\]
Say the rate law is found to be directly proportional to the concentration of \(N_{2}O_{5}\), we can express the rate law by\(^{[1]}\):
\[r = k_{r} [N_{2}O_{5}]\]
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:
\[H_{2(g)} + Br_{2(g)} → 2 HBr_{(g)}\]
Complicated rate law:
Rate Law vs. Equilibrium Constant
Be careful not to confuse equilibrium constant expressions with rate law expressions. The expression for \(K_{eq}\) 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 \(2 N_{2}O_{5} ⇌ 4 NO_{2} + O_{2}\) is given below:
\[K_{eq}=\frac{[NO_{2}]^4[O_{2}]}{[N_{2}O_{5}]^2}\]
In contrast, the expression for the rate law generally bears no relation to the reaction equation and must be determined experimentally. \(^{[1]}\)
Reaction Rate Law Units
Reaction rate (r) is generally expressed in units of concentration over time (e.g. \(\frac{mol}{L·s}\), \(\frac{kPa}{min}\), \(\frac{mol}{m^3·h}\) ).
This means the rate constant \(k_{r}\) needs to be such that r is expressed in units of concentration over time.
For the following example, what are the units for the reaction rate constant (\(k_{r}\))?
\[r=k_{r}*p_{A}*p_{B}^2\]
with p in Pa and time in seconds
Solution
Add example text here.
Since r is expressed in concentration over time, the units of r are \(\frac{Pa}{s}\).
\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].