Chapter 11, Problem 101QRT

(a)

Interpretation Introduction

Interpretation:

The activation energy for the isomerization reaction of cyclopropane to propene has to be calculated.

Concept Introduction:

The temperature dependence of rate constant can be explained through Arrhenius equation.

  $k=A{e}^{\frac{-E_a}{RT}}$

Where $k$ is the rate constant, $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the universal gas constant and $T$ is the temperature.

The logarithmic form of Arrhenius is given below.

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

Where, ${\text{k}}_{\text{1}}$ and ${\text{k}}_{\text{2}}$ are the rate constants at temperature ${\text{T}}_{\text{1}}$ and ${\text{T}}_{\text{2}}$ respectively.

(b)

Interpretation Introduction

Interpretation:

The time taken for the concentration drop from $0.10Mto0.023M$ at ${500}^{o}C$ has to be calculated for the isomerization reaction.

Concept Introduction:

The temperature dependence of rate constant can be explained through Arrhenius equation.

  $k=A{e}^{\frac{-E_a}{RT}}$

Where $k$ is the rate constant, $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the universal gas constant and $T$ is the temperature.

The logarithmic form of Arrhenius is given below.

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

Where, ${\text{k}}_{\text{1}}$ and ${\text{k}}_{\text{2}}$ are the rate constants at temperature ${\text{T}}_{\text{1}}$ and ${\text{T}}_{\text{2}}$ respectively.

The integrated rate law for a first order reaction is given below.

  $\ln {\left[A\right]}_t-\ln {\left[A\right]}_0=-kt$

Where ${\left[A\right]}_{t}and{\left[A\right]}_0$ are the initial and final concentrations of the reactants, and $k$ is the rate constant and $t$ is the time taken to reduce the initial concentration to ${\left[A\right]}_t.$