Chapter 17, Problem 17.46P

Interpretation Introduction

Interpretation:

The decomposition of ${\text{NO}}_{\text{2}\text{(g)}}$ is a second order reaction and is described by the equation:

  $\text{2}{\text{NO}}_2{}_{\text{(g)}}\to \text{2}{\text{NO}}_{\text{(g)}}\text{+}{\text{O}}_2{}_{\text{(g)}}$

The rate constant for the reaction is $\text{0}\text{.54}{\text{M}}^{\text{-1}}\cdot {\text{s}}^{\text{-1}}$ at ${\text{300}}^{\text{°}}\text{C}$.  The value of $\left[{\text{NO}}_{\text{2}}\right]$ has to be calculated after the reaction has run for $\text{2}\text{.0}\text{minutes}$, if the ${\left[{\text{NO}}_2\right]}_{\text{0}}$ is $\text{1}\text{.25}\text{M}$.

Concept Introduction:

In second order reactions, the concentration of $\text{A}$ at any time can be calculated by using the following equation:

  $\begin{array}{l}\frac{\text{1}}{\left[\text{A}\right]}\text{=}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\text{+}\text{kt}\\ \\ \left[\text{A}\right]\text{=}\text{concentration}\text{of}\text{A}\text{at}\text{time,t}\\ \\ {\left[\text{A}\right]}_{\text{0}}\text{=}\text{Initial}\text{concentration}\text{of}\text{A}\\ \\ \text{k}\text{=}\text{Rate}\text{constant}\\ \\ \text{t}\text{=}\text{time}\end{array}$