M K Verma Solutions for Chapter: Chemical Kinetics, Exercise 1: TOPICWISE QUESTIONS

Assuming gas-phase decomposition of dimethyl ether follows $1^{\mathrm{st}}$ order kinetics:

${\mathrm{CH}}_3-\mathrm{O}-{\mathrm{CH}}_3 \left(g\right)\to {\mathrm{CH}}_4 \left(g\right)+{\mathrm{H}}_2 \left(g\right)+\mathrm{CO} \left(g\right)$ 

The reaction is carried out in a constant volume container at $500°\mathrm{C}$ and has a half-life $14.5 \min$. Initially, only dimethyl ether is present at a pressure of $0.4 \mathrm{atm}$. The total pressure of the system after $12 \min$ is: (given $\log \left(1.8\right) = 0.249$)

A sample contains $0.1 \mathrm{g}-\mathrm{atom}$ of radioactive isotope ${}_{\mathrm{z}}{}^{\mathrm{A}} \mathrm{X} \left({\mathrm{t}}_{1/2}=5 \text{days}\right).$ The number of atoms which will decay during the eleventh day is $[{\mathrm{N}}_{\mathrm{A}}=$Avogadro's number, $\mathrm{antilog} \left(0.66\right)=4.6]$

Addition of a catalyst at $300 \mathrm{K}$ increases the rate of a chemical reaction by a factor of $36$. By how many $\mathrm{kJ}$ the activation energy of the catalysed pathway is less than the activation energy of the original pathway approximately $\left(\log \left(6\right)=0.78 \mathrm{and} \mathrm{R}=8.3 \mathrm{J} {\mathrm{k}}^{-1}{\mathrm{mol}}^{-1}\right)$.

A first order reaction is $50\%$ completed in $20$ minutes at $27°\mathrm{C}$ and in $5$ minutes at $47°\mathrm{C}.$ The energy of activation of the reaction is

The increase in the rate constant of a reaction when its temperature is increased from $298 \mathrm{K} \mathrm{to} 308 \mathrm{K}$ is nearly: $\left({\mathrm{E}}_{\mathrm{a}}=12.68 \mathrm{kcal} {\mathrm{mol}}^{-1}, \log 2=0.302\right)$

The reaction $\mathrm{A} \left(\mathrm{g}\right)+\mathrm{B} \left(\mathrm{g}\right)\rightleftharpoons \mathrm{C} \left(\mathrm{g}\right)+\mathrm{D} \left(\mathrm{g}\right)$ is elementary $2^{\mathrm{nd}}$ order reaction opposed by elementary secondary order reaction. When started with equimolar amounts of $\mathrm{A}$ and $\mathrm{B},$ at equilibrium, it is found that the concentration of $\mathrm{A}$ is twice that of $\mathrm{C} .$ Specific rate constant for forward reaction is $2\times {10}^{-3} {\mathrm{mol}}^{-1} {\sec }^{-1}.$ The specific rate constant for backward reaction is

Two reactions proceed at $25°\mathrm{C}$ at the same rate. The temperature coefficient of the first reaction is $2$ and that of the second reaction is $3$, then the ratio of rates $\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)$ of these reactions at $95°\mathrm{C}$ is (${\mathrm{r}}_1$ & ${\mathrm{r}}_2$ are rates of first and second reaction respectively).

The half-life period of a third-order reaction is found to be one hour when started with a concentration of $0.3 \mathrm{mol}/\mathrm{l}$ of reactant. If started with $0.1 \mathrm{moles}$, concentration the half-life period in hours will be: