Ramendra C Mukerjee Solutions for Chapter: Chemical Kinetics, Exercise 1: PROBLEMS

A certain reaction is of the first order. After $540$ seconds, $32·5\%$ of the reactant remains.

$\left(\mathrm{a}\right)$ Calculate the rate constant. $\left(\mathrm{b}\right)$ How long would it require for $25\%$ of the reactant to be decomposed?

Two reactions have identical values for energy of activation. Does this ensure that they will have the same rate constant if they run at the same temperature?

The rate of the haemoglobin $\left(\mathrm{Hb}\right)$-carbon monoxide reaction, 

$4\mathrm{Hb}+3\mathrm{CO}\to {\mathrm{Hb}}_4(\mathrm{CO}{)}_3$

has been studied at $20°\mathrm{C}$. Concentrations are expressed in $\mathrm{\mu } \mathrm{mole}/\mathrm{L}.$ 

(a) Calculate the rate constant for the reaction.
(b) Calculate the rate of the reaction at the instant when,

$\left[\mathrm{Hb}\right]=1.50$ and $\left[\mathrm{CO}\right]=0.60 \mathrm{\mu } \mathrm{mole}/\mathrm{L}$

A first order reaction, is $50\%$ complete in $30 \min$ at $27°\mathrm{C}$ and in $10 \min$ at $47°\mathrm{C}$. Calculate the reaction rate constant at $27°\mathrm{C}$ and the energy of activation of the reaction in $\mathrm{kJ}/\mathrm{mole}$.

The decomposition of arsine $\left({\mathrm{AsH}}_3\right)$ into arsenic and hydrogen is a first-order reaction. The decomposition was studied at constant volume and at a constant temperature. The pressures at different times are as follows:

$$\begin{gathered} \mathrm{t} \left(\mathrm{h}\right): 0 5.5 6.5 8 \\ \mathrm{p} \left(\mathrm{atm}\right): 0.9654 1.06 1.076 1.1 \end{gathered}$$

Calculate the velocity constant.

The rate constant of the first order reaction, that is, the decomposition of ethylene oxide into ${\mathrm{CH}}_4$ and $\mathrm{CO}$ may be described by the following equation:

$\mathrm{logk} \left(\mathrm{in} {\mathrm{s}}^{-1}\right)=14.34-\frac{1.25\times {10}^4}{\mathrm{T}}$

Find energy of activation $\mathrm{in} (\mathrm{kJ}/\mathrm{mol})$.

Report your answer up to two decimal places.

The rate constant of the first-order reaction, i.e., the decomposition of ethylene oxide into ${\mathrm{CH}}_4$ and $\mathrm{CO}$, may be described by the following equation.

$\log \mathrm{k} \left({\mathrm{s}}^{-1}\right)=14·34-\frac{1·25\times {10}^4}{\mathrm{T}}$

$\text{ [Hint: Compare the given equation with }\log \mathrm{k}=\log \mathrm{A}-\frac{{\mathrm{E}}_{\mathrm{a}}}{2·303 \mathrm{RT}}$]

(in terms of ${10}^{-5}$. Round off to the second decimal).

For a homogeneous gaseous reaction $\mathrm{A}\to \mathrm{B}+\mathrm{C}+\mathrm{D}$, the initial pressure was ${\mathrm{p}}^{\mathrm{o}}$, while the pressure after time $\mathrm{t}$ was $\mathrm{p}$. Derive an expression for the rate constant $\mathrm{k}$, in terms of ${\mathrm{p}}^{\mathrm{o}}, \mathrm{p}$ and $\mathrm{t}$.