Embibe Experts Solutions for Chapter: Chemical Kinetics, Exercise 1: JEE Advanced Paper 1 - 2020

For the following reaction $2\mathrm{X}+\mathrm{Y}\stackrel{\mathrm{k}}{\to }\mathrm{P}$ the rate of reaction is $\frac{\mathrm{d}\left[\mathrm{P}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{X}\right]$. Two moles of $\mathrm{X}$ are mixed with one mole of $\mathrm{Y}$ to make $1.0 \mathrm{L}$ of solution. At $50 \mathrm{s}, 0.5$ mole of $\mathrm{Y}$ is left in the reaction mixture. The correct statement(s) about the reaction is(are) $($Use: $\ln 2=0.693)$

Which of the following plots is(are) correct for the given reaction?

($[\mathrm{P}{]}_0$ is the initial concentration of $\mathrm{P}$)

The decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\stackrel{ ∆ }{\to }2{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$ is started in a closed cylinder under the isothermal isochoric condition at an initial pressure of $1 \mathrm{atm}$. After $\frac{\mathrm{Y}}{10}\times {10}^3\mathrm{ }\mathrm{s}$ , the pressure inside the cylinder is found to be $1.45\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{m}$ . If the rate constant of the reaction is $5\times {10}^{-4}{\mathrm{s}}^{-1}$, assuming ideal gas behaviour, the value of $\mathrm{Y}$ is(nearest integer)

For a first order reaction $\mathrm{A}\left(\mathrm{g}\right)\mathrm{ }\to \mathrm{ }2\mathrm{B}\left(\mathrm{g}\right)\mathrm{ }+\mathrm{ }\mathrm{C}\left(\mathrm{g}\right)$ at constant volume and 300 K, the total pressure at the beginning $(\mathrm{t}\mathrm{ }=\mathrm{ }0)$ and at time are $\mathrm{ }{\mathrm{p}}_0\mathrm{ }\mathrm{and}\mathrm{ }{\mathrm{p}}_{\mathrm{t}}$, respectively. Initially, only A is present with concentration $\mathrm{ }{\left[\mathrm{A}\right]}_0$, and  ${\mathrm{t}}_{\frac{1}{3}\mathrm{ }}$ is the time required for the partial pressure of A to reach $1/3^{\mathrm{rd}}$ of its initial value. The correct option(s) is (are)
(Assume that all these gases behave as ideal gases)

Consider the following reversible reaction:

$\mathrm{A} \left(\mathrm{g}\right)+\mathrm{B}\mathrm{ }\left(\mathrm{g}\right)\rightleftharpoons \mathrm{AB} \left(\mathrm{g}\right)$

The activation energy of the backward reaction exceeds that of the forward reaction by $2\mathrm{RT}$ (in $\mathrm{ }{\mathrm{mol}}^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $∆{\mathrm{G}}^{⊝} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ for the reaction at $300 \mathrm{K}$ is ____.

(Given; $\ln \left(2\right)=\mathrm{ }0.7, =\mathrm{ }2500\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\mathrm{ }\mathrm{at}\mathrm{ }300\mathrm{ }\mathrm{K}$ and $\mathrm{G}$ is the Gibbs energy)

In a bimolecular reaction, the steric factor $\mathrm{P}$ was experimentally determined to be $4.5$. The correct option(s) among the following is(are)

${}_{92}{}^{238}\mathrm{U}$ is known to undergo radioactive decay to form ${}_{82}{}^{206}\mathrm{Pb}$ by emitting alpha and beta particles. A rock initially contained $68\times {10}^{-6}\mathrm{g}$ of ${}_{92}{}^{238}\mathrm{U}$. If the number of alpha particles that it would emit during its radioactive decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{Pb}$ in three half-lives is $\mathrm{Z}\times {10}^{18}$, then what is the value of $\mathrm{Z}$?

Consider the kinetic data given in the following table for the reaction $\mathrm{A}+\mathrm{B}+\mathrm{C}\to$ Product.