Chapter 17, Problem 17D.1BE

(i)

Interpretation Introduction

Interpretation:

The Arrhenius parameters for the gas-phase decomposition of cyclobutane, ${\text{C}}_{\text{4}}{\text{H}}_{\text{8(g)}}\stackrel{}{\to }{\text{2C}}_{\text{2}}{\text{H}}_{\text{4(g)}}$ are $\text{A = 4}{\text{.00×10}}^{\text{15}}{\text{s}}^{\text{-1}}{\text{ and E}}_{\text{a}}{\text{=261kJmol}}^{\text{-1}}$, $\text{T = 293K}$  then the half-life of cyclobutane has to be calculated

Concept Introduction:

Arrhenius Equation:

The temperature dependence characteristics of reaction is normally expressed mathematically by introducing two parameters, one representing the intercept and the other the slop of the straight line of a so-called ‘Arrhenius plot’ of $\text{ln k}$, against $\text{1/T}$ and writing the Arrhenius equation.

    $\text{lnk = lnA - }\frac{{\text{E}}_{\text{a}}}{\text{RT}}$

A is the parameter obtained from the intercept of the line at $\text{1/T = 0}$ is called the frequency factor.  The parameter ${\text{E}}_{\text{a}}$ is called the activation energy.  The two quantities are collectively known as Arrhenius parameters.

Figure.1

If the activation energy of a reaction is known, the value of a rate constant ${\text{k}}_{\text{2}}$ at a temperature ${\text{T}}_{\text{2}}$ can be predicted from its value ${\text{k}}_1$ at another temperature ${\text{T}}_1$

That is:

    $\ln \left(\frac{{\text{k}}_{\text{2}}}{{\text{k}}_{\text{1}}}\right)\text{=}\frac{{\text{E}}_{\text{a}}}{\text{R}}\left[\frac{\text{1}}{{\text{T}}_{\text{1}}}\text{-}\frac{\text{1}}{{\text{T}}_{\text{2}}}\right]$

(ii)

Interpretation Introduction

Interpretation:

The Arrhenius parameters for the gas-phase decomposition of cyclobutane, ${\text{C}}_{\text{4}}{\text{H}}_{\text{8(g)}}\stackrel{}{\to }{\text{2C}}_{\text{2}}{\text{H}}_{\text{4(g)}}$ are $\text{A = 4}{\text{.00×10}}^{\text{15}}{\text{s}}^{\text{-1}}{\text{ and E}}_{\text{a}}{\text{=261kJmol}}^{\text{-1}}$, $\text{T = 723 K}$ then the half-life of cyclobutane has to be calculated

Concept Introduction:

Arrhenius Equation:

The temperature dependence characteristics of reaction is normally expressed mathematically by introducing two parameters, one representing the intercept and the other the slop of the straight line of a so-called ‘Arrhenius plot’ of $\text{ln k}$, against $\text{1/T}$ and writing the Arrhenius equation.

    $\text{lnk = lnA - }\frac{{\text{E}}_{\text{a}}}{\text{RT}}$

A is the parameter obtained from the intercept of the line at $\text{1/T = 0}$ is called the frequency factor.  The parameter ${\text{E}}_{\text{a}}$ is called the activation energy.  The two quantities are collectively known as Arrhenius parameters.

Figure.1

If the activation energy of a reaction is known, the value of a rate constant ${\text{k}}_{\text{2}}$ at a temperature ${\text{T}}_{\text{2}}$ can be predicted from its value ${\text{k}}_1$ at another temperature ${\text{T}}_1$

That is:

    $\ln \left(\frac{{\text{k}}_{\text{2}}}{{\text{k}}_{\text{1}}}\right)\text{=}\frac{{\text{E}}_{\text{a}}}{\text{R}}\left[\frac{\text{1}}{{\text{T}}_{\text{1}}}\text{-}\frac{\text{1}}{{\text{T}}_{\text{2}}}\right]$