Chemical Kinetics · JEE Main previous year questions

Consider the following statements related to temperature dependence of rate constants. Identify the correct statements. A. The Arrhenius equation holds true only for an elementary homogenous reaction. B. The unit of $A$ is same as that of $k$ in Arrhenius equation. C. At a given temperature, a low activation energy means a fast reaction. D. A and $\mathrm{Ea}$ as used in Arrhenius equation depend on temperature. E. When $\mathrm{Ea}\gg \mathrm{RT}$, A and $\mathrm{Ea}$ become interdependent. Choose the correct answer from the options given below:

1. A.A, C and D Only
2. B.B, D and E Only
3. C.B and C Only
4. D.A and B Only

$$\begin{array}{cc}[\mathrm{A}{]}_0/\mathrm{mol}{\mathrm{L}}^{-1}& {\mathrm{t}}_{1/2}/\min \\ 0.100& 200\\ 0.025& 100\end{array}$$ For a given reaction $\mathrm{R}\to \mathrm{P}$, ${\mathrm{t}}_{1/2}$ is related to $[\mathrm{A}{]}_0$ as given in table. Given: $\log 2=0.30$ Which of the following is true? A. The order of the reaction is $1/2$. B. If $[\mathrm{A}{]}_0$ is $1\mathrm{M}$ , then ${\mathrm{t}}_{1/2}$ is $200\sqrt{10}\min$ C. The order of the reaction changes to $1$ if the concentration of reactant changes from $0.100\mathrm{M}$ to $0.500\mathrm{M}$. D. ${\mathrm{t}}_{1/2}$ is $800\min$ for $[\mathrm{A}{]}_0=1.6\mathrm{M}$ Choose the correct answer from the options given below:

1. A.A and C Only
2. B.A, B and D Only
3. C.A and B Only
4. D.C and D Only

1. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are true

Consider a complex reaction taking place in three steps with rate constants ${\mathrm{k}}_1,{\mathrm{k}}_2$ and ${\mathrm{k}}_3$ respectively. The overall rate constant $k$ is given by the expression $k=\sqrt{\frac{{\mathrm{k}}_1{\mathrm{k}}_3}{{\mathrm{k}}_2}}$. If the activation energies of the three steps are $60$, $30$ and $10\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ respectively, then the overall energy of activation in $\mathrm{kJmo}{\mathrm{l}}^{-1}$ is ____ . (Nearest integer)

1. A.
2. B.
3. C.
4. D.

Consider the following first order gas phase reaction at constant temperature $\mathrm{A}(\mathrm{g})\to 2B(\mathrm{g})+\mathrm{C}(\mathrm{g})$ If the total pressure of the gases is found to be $200\mathrm{torr}$ after $23\sec$. and $300\mathrm{torr}$ upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ____ $\times 10^{-2}{\mathrm{s}}^{-1}$ (nearest integer) [Given : ${\log }_{10}(2)=0.301$]

Consider the following reaction $$\mathrm{A}+\mathrm{B}\to \mathrm{C}$$ The time taken for A to become $1/4^{\mathrm{th}}$ of its initial concentration is twice the time taken to become $1/2$ of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis. The overall order of the reaction is ____.

Consider the two different first order reactions given below $\text{A}+\text{B}\to \text{C}$ (Reaction 1) $\text{P}\to \text{Q}$ (Reaction 2) The ratio of the half life of Reaction 1 : Reaction 2 is $5:2$ If $t_1$ and $t_2$ represent the time taken to complete $2/3^{\text{rd}}$ and $4/5^{\text{th}}$ of Reaction 1 and Reaction 2 , respectively, then the value of the ratio $t_1:t_2$ is ________ $\times 10^{-1}$ (nearest integer). [Given : ${\log }_{10}(3)=0.477$ and ${\log }_{10}(5)=0.699$]

Consider the following single step reaction in gas phase at constant temperature. $$2{\mathrm{A}}_{(g)}+{\mathrm{B}}_{(g)}\to {\mathrm{C}}_{(g)}$$ The initial rate of the reaction is recorded as $r_1$ when the reaction starts with $1.5\mathrm{atm}$ pressure of A and $0.7\mathrm{atm}$ pressure of B. After some time, the rate $r_2$ is recorded when the pressure of C becomes $0.5\mathrm{atm}$. The ratio $r_1:r_2$ is ____ $\times 10^{-1}$. (Nearest integer)

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. $$\mathrm{A}+\mathrm{B}\underset{\mathrm{Step}3}{\stackrel{\mathrm{Step}1}{\rightleftharpoons }}\mathrm{C}\stackrel{\mathrm{Step}2}{\to }\mathrm{P}$$ Some details of the above reactions are listed below. $$\begin{array}{lll}\text{Step}& {\text{Rate constant (sec}}^{-1})& {\text{Activation energy (kJ mol}}^{-1})\\ 1& {\mathrm{k}}_1& 300\\ 2& {\mathrm{k}}_2& 200\\ 3& {\mathrm{k}}_3& \mathrm{E}{\mathrm{a}}_3\end{array}$$ If the overall rate constant of the above transformation (k) is given as $\mathrm{k}=\frac{{\mathrm{k}}_1{\mathrm{k}}_2}{{\mathrm{k}}_3}$ and the overall activation energy (${\mathrm{E}}_{\mathrm{a}}$) is $400\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, then the value of $\mathrm{E}{\mathrm{a}}_3$ is ____ $\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ (nearest integer)

Consider the following reaction, the rate expression of which is given below $\text{A}+\text{B}\to \text{C}$ $\text{rate}=\text{k}[\text{A}{]}^{1/2}[\text{B}{]}^{1/2}$ The reaction is initiated by taking $1\text{ M}$ concentration of A and B each. If the rate constant ($\text{k}$) is $4.6\times 10^{-2}{\text{ s}}^{-1}$, then the time taken for A to become $0.1\text{ M}$ is ________ sec. (nearest integer)

The ratio of $\frac{{}^{14}\mathrm{C}}{{}^{12}\mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${}^{14}\mathrm{C}$ is $5730\text{ years}$, the age of wood sample is ________ years.

The following data were obtained during the first order thermal decomposition of a gas A at constant volume : $\mathrm{A}(\mathrm{g})\to 2B(\mathrm{g})+\mathrm{C}(\mathrm{g})$ | S.No. | Time /s | Total pressure /(atm) | | :--- | :--- | :--- | | 1. | 0 | 0.1 | | 2. | 115 | 0.28 | The rate constant of the reaction is ________ $\times 10^{-2}{\text{ s}}^{-1}$ (nearest integer)

Integrated rate law equation for a first order gas phase reaction is given by (where ${\mathrm{P}}_{\mathrm{i}}$ is initial pressure and ${\mathrm{P}}_{\mathrm{t}}$ is total pressure at time $t$) (Take the reaction to be of the type $\mathrm{A}(\mathrm{g})\to \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$.)

1. A.$k=\frac{2.303}{t}\times \log \frac{P_i}{(2P_i-P_t)}$
2. B.$\mathrm{k}=\frac{2.303}{\mathrm{t}}\times \log \frac{(2{\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{t}})}{{\mathrm{P}}_{\mathrm{i}}}$
3. C.$k=\frac{2.303}{t}\times \frac{P_i}{(2P_i-P_t)}$
4. D.$\mathrm{k}=\frac{2.303}{\mathrm{t}}\times \log \frac{2{\mathrm{P}}_{\mathrm{i}}}{(2{\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{t}})}$

The rate of a first order reaction is $0.04{\text{ mol L}}^{-1}{\text{ s}}^{-1}$ at 10 minutes and $0.03{\text{ mol L}}^{-1}{\text{ s}}^{-1}$ at 20 minutes after initiation. Half life of the reaction is _________ minutes. (Given $\log 2=0.3010,\log 3=0.4771$)

For a reaction taking place in three steps at same temperature, overall rate constant $\mathrm{K}=\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_3}$. If $\mathrm{E}{\mathrm{a}}_1,\mathrm{E}{\mathrm{a}}_2$ and $\mathrm{E}{\mathrm{a}}_3$ are 40, 50 and $60\text{ kJ/mol}$ respectively, the overall Ea is _________ $\text{kJ/mol}$.

The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is _________ $\times 10^{-2}$. (Given antilog $0.2006=1.587$)

Consider the following data for the given reaction $2{\text{HI}}_{(\text{g})}\to {\text{H}}_{2(\text{g})}+{\text{I}}_{2(\text{g})}$ | | 1 | 2 | 3 | | :--- | :--- | :--- | :--- | | ${\text{HI (mol L}}^{-1}\text{)}$ | $0.005$ | $0.01$ | $0.02$ | | ${\text{Rate (mol L}}^{-1}{\text{s}}^{-1}\text{)}$ | $7.5\times 10^{-4}$ | $3.0\times 10^{-3}$ | $1.2\times 10^{-2}$ | The order of the reaction is ________.

Time required for completion of $99.9\%$ of a First order reaction is _______ times of half life ($t_{1/2}$) of the reaction.

$t_{87.5}$ is the time required for the reaction to undergo $87.5\%$ completion and $t_{50}$ is the time required for the reaction to undergo $50\%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5}=x\times t_{50}$ The value of $x$ is ___________. (Nearest integer)

$\mathrm{A}(\mathrm{g})\to 2\mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. The initial pressure of the system was found to be $800\text{ mm Hg}$ which increased to $1600\text{ mm Hg}$ after $10\text{ min}$. The total pressure of the system after $30\text{ min}$ will be ___________ mm Hg. (Nearest integer)

The reaction $2\mathrm{NO}+{\mathrm{Br}}_2\to 2\mathrm{NOBr}$ takes places through the mechanism given below: $\mathrm{NO}+{\mathrm{Br}}_2\rightleftharpoons {\mathrm{NOBr}}_2\text{ (fast)}$ ${\mathrm{NOBr}}_2+\mathrm{NO}\to 2\mathrm{NOBr}\text{ (slow)}$ The overall order of the reaction is __________.

A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is ___________ min. (Nearest integer)

The number of incorrect statement/s from the following is _________ A. The successive half lives of zero order reactions decreases with time. B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction C. Order and molecularity of a chemical reaction can be a fractional number D. The rate constant units of zero and second order reaction are ${\text{mol L}}^{-1}{\text{ s}}^{-1}$ and ${\text{mol}}^{-1}{\text{ L s}}^{-1}$ respectively