Chemical kinetics practice · Hard

A two step mechanism has been suggested for the reaction of nitric oxide and bromine:

$\begin{aligned} & \mathrm{NO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons \mathrm{NOBr}_2(\mathrm{~g}) \\ & \mathrm{NOBr}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \rightarrow 2 \mathrm{NOBr}(\mathrm{g}) \end{aligned}$

Observed rate law is, rate $=k[\mathrm{NO}]^2\left[\mathrm{Br}_2\right]$. Hence, rate determining step is

Mathematical expression for ${t_{1/4}}$ i.e., when ${\left( {1/4} \right)^{th}}$ reaction is over following first order kinetics can be given by

The acid catalysed reaction of acetic acid with ethanol:

$\mathrm{CH}_3 \mathrm{COOH}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} \rightarrow \mathrm{CH}_3 \mathrm{COOC}_2 \mathrm{H}_5 +\mathrm{H}_2 \mathrm{O}$

follows the rate law $-\frac{\mathrm{d}\left[\mathrm{CH}_3 \mathrm{COOH}\right]}{\mathrm{d} t}=K\left[\mathrm{H}^{+}\right]\left[\mathrm{CH}_3 \mathrm{COOH}\right] \left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]$ $=K^{\prime} \left[\mathrm{CH}_3 \mathrm{COOH}\right] \left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]$. When $\left[\mathrm{CH}_3 \mathrm{COOH}\right]_0=\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]_0=0.2 \mathrm{~M}$ and $\mathrm{pH}=3,$ the half-life for the reaction is 50 minutes. The value of true rate constant, $K$, of the reaction is

A radioactive substance decays $20 \%$ in $10 \mathrm{~min}$. If at the start, there are $5 \times 10^{20}$ atoms present, after what time will the number of atoms be reduced to $5 \times 10^{17}$ atoms?

The slope of Arrhenius plot $\left( {\ln \,k\,\mathrm{v/s}\frac{1}{T}} \right)$ of first order reaction is $- 5 \times {10^3}K.$ The value of ${E_a}$ of the reaction is.
Choose the correct option for your answer.
[Given $R = 8.314\mathrm{ J}{\mathrm{K}^{ - 1}}\mathrm{ mo}{\mathrm{l}^{ - 1}}$]

For a homogeneous gaseous reaction $\mathrm{A} \longrightarrow 3 \mathrm{B}$, if pressure after time $\mathrm{t}$ was $\mathrm{P}_{\mathrm{t}}$ and after completion of reaction, pressure was $\mathrm{P}_{\infty}$ then select correct relation

Select the incorrect statement :

Correct statements in the following are

a) In $\mathrm{Hg}_{(t)}+\mathrm{Cl}_{2(g)} \rightarrow \mathrm{HgCl}_{2(s)}$, the rate of disappearance of any of the reactants is same as the rate of appearance of the product

b) In $2 \mathrm{HI}_{(g)} \rightarrow \mathrm{H}_{2(g)}+\mathrm{I}_{2(g)}$, the rate of consumption of $\mathrm{HI}$ is half of rate of formation of $\mathrm{H}_2$ or $\mathrm{I}_2$

c) In $\underset{(a q)}{5 \mathrm{Br}^{-}}+\underset{(\mathrm{aq})}{\mathrm{BrO}_3^{-}}+\underset{(\mathrm{aq})}{6 \mathrm{H}^{+}} \rightarrow \underset{(\mathrm{aq})}{3 \mathrm{Br}_2}+3 \mathrm{H}_2 \mathrm{O}(\mathrm{I})$, the rate of consumption of $\mathrm{Br}^{-}(\mathrm{aq})$ is 1.66 times to the rate of a formation of $\mathrm{Br}_2$

Naturally occurring potassium consists of $0.01 \%$ of $40 \mathrm{~K}$ which has a half-life of $1.28 \times 10^9 \mathrm{yr}$. Activity of $1.00 \mathrm{~g}$ sample of $\mathrm{KCl}$ is

The rate of a reaction double when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be $(R = 8.314\,\,\,\mathrm{J}{\mathrm{K}^{ - \mathrm{1}}}\mathrm{mo}{\mathrm{l}^{ - \mathrm{1}}}\,\,\,\,\mathrm{and}\,\,\,\log 2 = 0.301)$

The order of the reaction $\mathrm{A} \rightarrow \text{products}$ is $0.5 .$ The time for complete reaction $T$ and time for $50 \%$ reaction, $t_{1 / 2}$ will be related as

What is order with respect to A, B, C, respectively

$\begin{array}{cccccccccccccccccccc} {[{\text{A}}]}&{[{\text{B}}]}&{[{\text{C}}]}&{{\text{Rate(M/sec)}}} \\ {{\text{0}}{\text{.2}}}&{{\text{0}}{\text{.1}}}&{{\text{0}}{\text{.02}}}&{{\text{8}}.{\text{08}} \times {\text{1}}{{\text{0}}^{{\text{ - 3}}}}} \\ {{\text{0}}{\text{.1}}}&{{\text{0}}{\text{.2}}}&{{\text{0}}{\text{.02}}}&{{\text{2}}.{\text{01}} \times {\text{1}}{{\text{0}}^{{\text{ - 3}}}}} \\ {{\text{0}}{\text{.1}}}&{{\text{1}}{\text{.8}}}&{{\text{0}}{\text{.18}}}&{{\text{6}}.{\text{03}} \times {\text{1}}{{\text{0}}^{{\text{ - 3}}}}} \\ {{\text{0}}{\text{.2}}}&{{\text{0}}{\text{.1}}}&{{\text{0}}{\text{.08}}}&{{\text{6}}.{\text{464}} \times {\text{1}}{{\text{0}}^{{\text{ - 2}}}}} \end{array}$

For the first-order reaction with $C_0$ as the initial concentration and $C$ at time $t,\left(C_0-C\right)=$

The half-life for the first-order decomposition of nitramide $\mathrm{NH}_4 \mathrm{NO}_2(\mathrm{aq}) \rightarrow \mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}({l})$ is 123 minutes at $27^{\circ} \mathrm{C}$. If $200 \mathrm{~ml}$ of $0.02 \mathrm{~M}$ $\mathrm{NH}_4 \mathrm{NO}_2$ solution is allowed to decompose, then how long must the reaction proceed to produce $49.26 \mathrm{~ml}$ of 'wet' $\mathrm{N}_2 \mathrm{O}(\mathrm{g})$ measured at $27^{\circ} \mathrm{C}$ and $785 \mathrm{~mm} \mathrm{~Hg}?$ The vapour pressure of water at $27^{\circ} \mathrm{C}$ is $25 \mathrm{~mm} \mathrm{~Hg}$.

A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table.

Time ( days ) % Reactant remaining 0 100 2 50 4 39 6 25 8 21 10 18 12 15 14 12.5 15 10 $\;\;\begin{array}{llllllllllllllllllll} {\mathbf{Time}\mathrm{ }\left( {\mathbf{days}} \right)\;\;\;\;\;\% \mathrm{ }\mathbf{Reactant}\mathrm{ }\mathbf{remaining}}\\ {\;\;\;\;\;\;0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;100}\\ {\;\;\;\;\;2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;50}\\ {\;\;\;\;\;4\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;39}\\ {\;\;\;\;\;6\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;25}\\ {\;\;\;\;\;8\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;21}\\ {\;\;\;\;10\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;18}\\ {\;\;\;\;12\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;15}\\ {\;\;\;\;14\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;12.5}\\ {\;\;\;\;15\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;10} \end{array}$
Which one of following best describes the order and the half-life of the reaction?

Reaction order Half-life (days)

For the consecutive first-order reactions $\mathrm{A} \xrightarrow{K_{\mathrm{1}}}\mathrm{B} \xrightarrow{K_2} \mathrm{C}, \mathrm{B}$ is in steady state. What will be the concentration of $\mathrm{C}$ at this stage? At $t=0,[\mathrm{A}]=[\mathrm{A}]_0$ and $[\mathrm{B}]=[\mathrm{C}]=0$.

For the consecutive first-order reactions: ${A} \xrightarrow{K_1} {B} \xrightarrow{K_2} {C},$
in what condition, $[{C}]=\left[{A}_0\right] .\left(1-e^{-K_1 t}\right)?$

Rate constant of the following reaction is $1.0 \times 10^{-5} \mathrm{~s}^{-1}$.

$2 \mathrm{~N}_2 \mathrm{O}_5 \longrightarrow 2 \mathrm{~N}_2 \mathrm{O}_4+\mathrm{O}_2$

At a time when $\left[\mathrm{N}_2 \mathrm{O}_5\right]=0.2 \mathrm{~mol} \mathrm{~L}^{-1}$, average rate of the reaction

The reaction of hydrogen and iodine monochloride is given as:

${H}_2({~g})+2 {ICl}({g}) \longrightarrow 2 {HCl}({g})+{I}_2({~g})$

The reaction is of first order with respect to ${H}_2({~g})$ and ${ICI}({g})$, following mechanisms were proposed.

Mechanism A:

${H}_2({~g})+2 {ICl}({g}) \longrightarrow 2 {HCl}({g})+{I}_2({~g})$

Mechanism B:

$\begin{aligned} & {H}_2({~g})+{ICl}({g}) \longrightarrow {HI}({g}) ; \text { slow } \\ & {HI}({g})+{ICl}({g}) \longrightarrow {HCl}({g})+{I}_2({~g}) ; \text { fast } \end{aligned}$

Which of the above mechanism(s) can be consistent with the given information about the reaction?

Half-life of two samples is 0.1 and 0.8 s. Their respective concentration is 400 and 50 respectively.

The order of reaction is

For a reaction scheme, $A\xrightarrow{{{k_1}}}B\xrightarrow{{{k_2}}}C,$ if the rate of formation of $B$ is set to be zero then the concentration of B is given by

Two radio isotopes ${P}$ and ${Q}$ of atomic mass 10 and 20 respectively are mixed in equal amount by mass. After 20 days, their weight ratio $\frac{{W}_{{P}}}{{W}_{{Q}}}$ is found to be $1: 4$. Isotope ${Q}$ has a half-life of 10 days. The half-life of isotope ${P}$ is:

For the first-order parallel reactions $\mathrm{A} \xrightarrow{K_1} \mathrm{B}$ and $\mathrm{A} \xrightarrow{K_2} \mathrm{C}, K_1=8 \mathrm{~min}^{-1}$ and $K_2=2 \mathrm{~min}^{-1}$ at $300 \mathrm{~K}.$ If the activation energies for the formation of $\text{B}$ and $\text{C}$ are $20$ and $28.314 \mathrm{~kJ} / \mathrm{mol},$ respectively, then find the temperature at which $\text{B}$ and $\text{C}$ will be obtained in $2: 1$ mole ratio. $(\ln 2=0.7)$

The rate constant of a first order reaction at $27^\circ \,C$ is ${10^{ - 3}}\,\mathrm{mi}{\mathrm{n}^{ - 1}}$. The temperature coefficient of this reaction is 2. What is the rate constant (in $\mathrm{mi}{\mathrm{n}^{ - 1}}$) at $17^\circ \,C$ for this reaction?