Chapter DY, Problem 7PQ

Interpretation Introduction

Interpretation:

The half-life for the first order conversion of cyclobutane to ethylene, ${\text{C}}_{\text{4}}{\text{H}}_{\text{8(g)}}\stackrel{}{\to }{\text{2C}}_{\text{2}}{\text{H}}_{\text{4(g)}}$ is $\text{22}\text{.7s}$ at a particular temperature.  Then the time in seconds that are needed for the partial pressure of cyclobutane to decrease from $\text{100 mm Hg}$ to $\text{10 mm Hg}$ has to be calculated.

Concept Introduction:

Half-life is given by the equation,

    $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{k-rate constant}\end{array}$

Equation relating the rate constant and partial pressure is:

    $\begin{array}{l}{\text{ln[P]}}_{\text{t}}{\text{=-kt+ln[P]}}_{\text{o}}\\ {\text{[P]}}_{\text{t}}\text{=partial pressure at time 't' }\\ {\text{[P]}}_{\text{o}}\text{=initial pressure}\end{array}$