Question

Write the rate laws of the following elementary reactions.

$\begin{array}{l}\left(a\right){\mathbf{CH}}_{\mathbf{3}}\mathbf{NC}\left(g\right)\mathbf{\to }{\mathbf{CH}}_{\mathbf{3}}\mathbf{CN}\left(g\right)\\ \left(b\right){\mathbf{O}}_{\mathbf{3}}\left(g\right)\mathbf{+}\mathbf{NO}\left(g\right)\mathbf{\to }{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{NO}}_{\mathbf{2}}\left(g\right)\\ \left(C\right){\mathbf{O}}_{\mathbf{3}}\left(g\right)\mathbf{\to }{\mathbf{O}}_{\mathbf{2}}\mathbf{+}\mathbf{O}\left(g\right)\\ \left(d\right){\mathbf{O}}_{\mathbf{3}}\left(g\right)\mathbf{+}\mathbf{O}\left(g\right)\mathbf{\to }\mathbf{2}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\\ \left(e\right){}_{\mathbf{6}}{}^{\mathbf{14}}\mathbf{C}\mathbf{\to }{}_{\mathbf{7}}{}^{\mathbf{14}}\mathbf{N}\mathbf{+}\mathbf{\beta particle}\left(\mathrm{nucleardecay}\right)\end{array}$

Short answer

$\begin{array}{l}\left(a\right)rate=K\left[C{H}_{3}NC\right]\\ \left(b\right)rate=K\left[O_3\right]\left[NO\right]\\ \left(c\right)rate=K\left[O_3\right]\\ \left(d\right)rate=K\left[O_3\right]\left[O\right]\\ \left(e\right)rate=K\left[{}_6{}^{14}C\right]\end{array}$

Step-by-step solution

Understanding the rate law expression for elementary reaction.

The rate law expression for any elementary reaction

$\begin{array}{l}\mathbf{a}\mathbf{A}\mathbf{+}\mathbf{b}\mathbf{B}\mathbf{\to }\mathbf{c}\mathbf{C}\mathbf{+}\mathbf{d}\mathbf{D}\\ \mathbf{R}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{=}\mathbf{K}{\left[A\right]}^{\mathbf{a}}{\left[B\right]}^{\mathbf{b}}\end{array}$

(a) Writing rate law expression for the given reaction.

The elementary reaction:

$\begin{array}{l}C{H}_{3}NC\left(g\right)\to C{H}_{3}CN\left(g\right)\\ Rate=K\left[C{H}_{3}NC\right]\end{array}$

(b) Writing rate law expression for the given reaction.

The elementary reaction:

$\begin{array}{l}{O}_3\left(g\right)+NO\left(g\right)\to O_2\left(g\right)+N{O}_2\left(g\right)\\ Rate=K\left[O_3\right]\left[NO\right]\end{array}$

(c) Writing rate law expression for the given reaction.

The elementary reaction:

$\begin{array}{l}{O}_3\left(g\right)\to O_2+O\left(g\right)\\ Rate=K\left[O_3\right]\end{array}$

(d) Writing rate law expression for the given reaction.

The elementary reaction:

$\begin{array}{l}{O}_3\left(g\right)+O\left(g\right)\to 2O_2\left(g\right)\\ Rate=K\left[O_3\right]\left[O\right]\end{array}$

(e) Writing rate law expression for the given reaction.

The elementary reaction:

$\begin{array}{l}{}_6{}^{14}C\to {}_7{}^{14}N+\beta particle\\ Rate=K\left[{}_6{}^{14}C\right]\end{array}$