Chapter 17, Problem 17.41P

Interpretation Introduction

Interpretation:

The gas phase decomposition of ${\text{CH}}_{\text{3}}\text{CHO}{}_{\text{(g)}}$ is a second order reaction and occurs as follows:

  ${\text{CH}}_{\text{3}}\text{CHO}{}_{\text{(g)}}\to {\text{CH}}_{\text{4}\text{(g)}}\text{+}\text{CO}{}_{\text{(g)}}$

The value of rate constant is $\text{0}\text{.105}{\text{M}}^{\text{-1}}\cdot {\text{s}}^{\text{-1}}$ at ${\text{490}}^{\text{°}}\text{C}$.  The concentration of ${\text{CH}}_{\text{3}}\text{CHO}{}_{\text{(g)}}$ has to be calculated $\text{5}\text{.0}\text{minutes}$ later, if the initial concentration is $\text{0}\text{.012}\text{M}$.

Concept Introduction:

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

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