K L Chugh Solutions for Chapter: Chemical Kinetics, Exercise 8: Follow Up Problems

The rate constants of a reaction at $500 \mathrm{K}$ and $700 \mathrm{K}$ are $0.02{ \mathrm{s}}^{-1}$ and $0.07{ \mathrm{s}}^{-1}$ respectively. Calculate the values of ${\mathrm{E}}_{\mathrm{a}}$ and A.

The first order rate constant for the decomposition of ethyl iodide by the reaction ${\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{I}}_{\left(\mathrm{g}\right)}⟶{\mathrm{C}}_2{\mathrm{H}}_4\left(\mathrm{g}\right)+{\mathrm{HI}}_{\left(\mathrm{g}\right)}$ at $600 \mathrm{K}$ is $1.60\times {10}^{-5}{ \mathrm{s}}^{-1}$. Its energy of activation is $209 \mathrm{kJ}/\mathrm{mol}.$ Calculate the rate constant of the reaction at $700 \mathrm{K}$

Rate constant $\mathrm{k}$ of a reaction varies with temperature according to equation:

$\log \mathrm{k}=$ constant $-\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303\mathrm{R}}·\frac{1}{ \mathrm{T}}$

What is the activation energy for the reaction. When a graph is plotted for $\log \mathrm{k}$ versus $\frac{1}{\mathrm{T}},$ a straight line with a slope $-6670 \mathrm{K}$ is obtained. Calculate energy of activation for this reaction $\left(\mathrm{R}=8.314 {\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}\right)$

If a first order reaction has activation energy of $25000 \mathrm{cal}$ and a frequency factor of $5\times {10}^{12} {\sec }^{-1},$at what temperature will the reaction rate have a half-life of $1$ minute? [Hint. $\mathrm{k}=\frac{0.693}{{\mathrm{t}}_{1/2}}$ for a first order reaction.]

If a first order reaction has activation energy of $25000 \mathrm{cal}$ and a frequency factor of $5\times {10}^{12} {\sec }^{-1},$ at what temperature will the reaction rate have a half-life of $80$ days?

[Hint. $\mathrm{k}=\frac{0.693}{{\mathrm{t}}_{1/2}}$ for a first order reaction.]

The activation energy for a first order reaction is $60 \mathrm{kJ}{ \mathrm{mol}}^{-1}$ in the absence of a catalyst and $50 \mathrm{kJ}{ \mathrm{mol}}^{-1}$ in the presence of a catalyst. How many times will the rate of reaction grow in the presence of the catalyst if the reaction proceeds at $27°\mathrm{C}?$

For a reaction, the energy of activation is zero. What is the value of rate constant at $300 \mathrm{K},$ if $\mathrm{k}=1.6\times {10}^6{ \mathrm{s}}^{-}$ at $280 \mathrm{K}?$

The rate constant for the decomposition of a hydrocarbon is $2.418\times {10}^{-5}{ \mathrm{s}}^{-1}$ at $546 \mathrm{K}.$ If the energy of activation is $179.9 \mathrm{kJ}/\mathrm{mol},$ what will be the value of pre-exponential factor?