Chapter 11, Problem 116QRT

(a)

Interpretation Introduction

Interpretation:

The rate constant for the decomposition of cyclobutane to ethylene at $900K$ 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 cyclobutane concentration after two hours at $850K$ 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.

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

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

Where,

    ${\left[A\right]}_t$ is the final concentration of the reactant

    ${\left[A\right]}_0$ is the initial concentration of the reactant

    $k$ is the rate constant

    $t$ is the time