Chemical Kinetics — JEE Main PYQs

Consider the reaction $\mathrm{aX \rightarrow bY}$, for which the rate constant at 30°C is $1 \times 10^{-3}$ mol$^{-1}$ L s$^{-1}$. Which of the following statements are true ?

A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times.

B. The reaction is a second order reaction.

C. The half-life period is independent of the concentration of X.

D. Decomposition of $\mathrm{N_2O_5}$ is an example of the above reaction.

E. [Figure: straight-line increasing plot of $\ln \frac{[R_0]}{[R]}$ versus time] is valid for the above reaction.

Choose the correct answer from the options given below :

Consider the following gas phase reaction being carried out in a closed vessel at 25°C.

$$\mathrm{2A(g) \longrightarrow 4B(g) + C(g)}$$

time (min)	total pressure of the system (mm Hg)
30	300
$\infty$	600

The pressure of C(g) at 30 minutes time interval would be __________ mm Hg. (nearest integer)

Consider the first order reaction $\mathrm{R \rightarrow P}$. The fraction of molecules decomposed in the given first order reaction can be expressed as

Consider the given graph showing variation of reactant concentration with time.

Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

[Figure: graph of [R] (mol L$^{-1}$) vs t/s, all three curves starting from $[R]_0$; curve 1 decreases linearly, curves 2 and 3 decay exponentially with curve 3 falling fastest]

For a first order reaction A $\rightarrow$ B

t/min	[A]/M
0	0.6500
x	0.0650
20	0.00065

$x =$ ____________ min. (Nearest integer)

First order gas phase reaction

$\mathrm{A \rightarrow B + C}$

$p_i$ = initial pressure of gas A, $p_t$ = total pressure of the reaction mixture at time $t$

Expression of rate constant ($k$) is

If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be ________ minutes.

(Given : $\log 2 = 0.3010$)

For a reaction $\mathrm{A \rightarrow P}$ at T K, the half life ($t_{1/2}$) is plotted as a function of initial concentration $[A]_0$ of A as given below.

[Figure: straight-line plot through the origin of $t_{1/2}/\mathrm{s}$ (y-axis) versus $[A]_0/\mathrm{mol\ L^{-1}}$ (x-axis); at $[A]_0 = 4 \times 10^{-3}$ the half life is 240 s, and at $[A]_0 = 1.5 \times 10^{-3}$ the half life is $x$]

The value of $x$ in the given figure is ________ s (Nearest integer)

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $\mathrm{t_{1/2}}$ = 3 hour. The percentage of sucrose remaining after 6 hours is _____. (Nearest integer)

(Given : log 2 = 0.3010 and log 3 = 0.4771)

Decomposition of a hydrocarbon follows the equation $k = (5.5 \times 10^{11}\ \mathrm{s^{-1}})\ e^{\frac{-28000\ \mathrm{K}}{T}}$. The activation energy of reaction is ________ kJ mol$^{-1}$. (Nearest Integer)

Given : $R = 8.3\ \mathrm{J\ K^{-1}\ mol^{-1}}$

Given below are two statements :

$\mathrm{R} = 8.314\ \mathrm{J\,K^{-1}\,mol^{-1}}$ and 1 cal = 4.2 J

Statement I : When $\mathrm{E_a} = 12.6$ kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K)

Statement II : For a first order reaction A $\rightarrow$ B,

[Figure: graph of $\mathrm{t_{1/2}}$/s (y-axis) versus $\mathrm{[A]_0}$/mol L$^{-1}$ (x-axis) shown as a straight line rising through the origin]

Here $\mathrm{[A]_0}$ is the initial concentration of A and $\mathrm{t_{1/2}}$ is half life of reaction.

In the light of the above statements, choose the correct answer from the options given below :

For the reaction A $\rightarrow$ products.

[Figure: straight-line plot of $\dfrac{t_{1/2}}{\text{min}}$ versus $[A]_0/\mathrm{mol\ L^{-1}}$ through the origin, slope = 76.92 (appropriate units)]

The concentration of A at 10 minutes is __________ $\times 10^{-3}\ \mathrm{mol\ L^{-1}}$ (nearest integer). The reaction was started with 2.5 $\mathrm{mol\ L^{-1}}$ of A.

Reactant A converts to product D through the given mechanism (with the net evolution of heat) :

$\mathrm{A \rightarrow B}$ \quad slow; \quad $\Delta H = +\text{ve}$

$\mathrm{B \rightarrow C}$ \quad fast; \quad $\Delta H = -\text{ve}$

$\mathrm{C \rightarrow D}$ \quad fast; \quad $\Delta H = -\text{ve}$

Which of the following represents the above reaction mechanism ?

For the reaction $\mathrm{A \rightarrow B}$ the following graph was obtained. The time required (in seconds) for the concentration of A to reduce to $2.5\ \mathrm{g\ L^{-1}}$ (if the initial concentration of A was $50\ \mathrm{g\ L^{-1}}$) is __________. (Nearest integer)

Given : $\log 2 = 0.3010$

[Figure: concentration of A/(g L$^{-1}$) vs time/s — exponential decay curve starting at 50, passing through about 30 at 5 s, 20 at 10 s, and 10 at about 25 s]

In a reaction A + B $\rightarrow$ C, initial concentrations of A and B are related as $[A]_0 = 8[B]_0$. The half lives of A and B are 10 min and 40 min, respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same ?

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 Ea as used in Arrhenius equation depend on temperature. E. When Ea >> RT, A and Ea become interdependent.

Choose the correct answer from the options given below:

Half life of zero order reaction A $\rightarrow$ product is 1 hour, when initial concentration of reactant is $2.0\ \mathrm{mol\ L^{-1}}$. The time required to decrease concentration of A from 0.50 to $0.25\ \mathrm{mol\ L^{-1}}$ is :

Consider the following plots of log of rate constant k (log k) vs $\frac{1}{\mathrm{T}}$ for three different reactions. The correct order of activation energies of these reactions is :

[Figure: log k vs 1/T plot showing three straight lines labelled 1, 2 and 3 — line 1 has a moderately steep negative slope, line 2 is the steepest (nearly vertical), and line 3 is nearly flat with a shallow negative slope]

Reaction $\mathrm{A(g) \rightarrow 2B(g) + C(g)}$ is a first order reaction. It was started with pure A

t/min	Pressure of system at time t/mm Hg
10	160
$\infty$	240

Which of the following option is incorrect?

A person's wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay (r) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?

[Given: N = No. of bacteria, t = time, bacterial growth follows 1$^{st}$ order kinetics.]

$\mathrm{A(g) \rightarrow B(g) + C(g)}$ is a first order reaction.

Time	$t$	$\infty$
$\mathrm{p_{system}}$	$\mathrm{p_t}$	$\mathrm{p_\infty}$

The reaction was started with reactant A only. Which of the following expression is correct for rate constant $k$ ?

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2$ (s), respectively. The ratio $t_1/t_2$ will be:

Which of the following statement is not true for radioactive decay ?

$$\mathrm{A} \rightarrow \mathrm{B}$$

The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48\ \mathrm{kJ\ mol^{-1}}$ and the frequency factor is $10^{20}$, the time required for $50\%$ molecules of A to become B is ________ picoseconds (nearest integer). $[\mathrm{R} = 8.314\ \mathrm{J\ K^{-1}\ mol^{-1}}]$

Consider the given figure and choose the correct option :

[Figure: energy vs reaction coordinate diagram — the curve rises from Reactant to a peak labelled Activated complex, then falls to Product; $E_1$ marks the drop from the peak down to the product level and $E_2$ the gap between the product and reactant levels, the product level lying above the reactant level]

For the thermal decomposition reaction of $\mathrm{N_2O_5(g)}$ mentioned below, at constant volume, the following table can be created.

$$\mathrm{2N_2O_5(g) \rightarrow 2N_2O_4(g) + O_2(g)}$$

S.No.	Time (s)	Total pressure (atm)
1	0	0.6
2	100	'x'

$x =$ _____ $\times 10^{-3}$ atm (nearest integer)

(Given : rate constant for the reaction is $4.606 \times 10^{-2}\ \mathrm{s^{-1}}$.)

Which of the following graphs most appropriately represents a zero order reaction ?

For a reaction, $\mathrm{N_2O_{5(g)} \to 2NO_{2(g)} + \frac{1}{2}O_{2(g)}}$ in a constant volume container, no products were present initially. The final pressure of the system when 50% of reaction gets completed is

Given below are two statements :

Statement (I): [Figure: a plot of $t_{1/2}$ (y-axis) versus $[R]_0$ (x-axis) shown as a horizontal straight line] is valid for a first order reaction.

Statement (II): [Figure: a plot of $\log\frac{[R]}{[R]_0}$ (y-axis) versus time (x-axis) shown as a straight line through the origin with slope $= \frac{k}{2.303}$] is valid for a first order reaction.

In the light of the above statements, choose the correct answer from the options given below :

Consider a complex reaction taking place in three steps with rate constants $k_1$, $k_2$ and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k = \sqrt{\dfrac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are 60, 30 and $10\ \mathrm{kJ\ mol^{-1}}$ respectively, then the overall energy of activation in $\mathrm{kJ\ mol^{-1}}$ is _______. (Nearest integer)

For a given reaction $\mathrm{R \to P}$, $t_{1/2}$ is related to $[\mathrm{A}]_0$ as given in table.

$[\mathrm{A}]_0/\mathrm{mol\ L^{-1}}$	$t_{1/2}/\mathrm{min}$
0.100	200
0.025	100

Given: $\log 2 = 0.30$

Which of the following is true?

A. The order of the reaction is $\frac{1}{2}$.

B. If $[\mathrm{A}]_0$ is 1M, then $t_{1/2}$ is $200\sqrt{10}$ min

C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M.

D. $t_{1/2}$ is 800 min for $[\mathrm{A}]_0 = 1.6$ M

Choose the correct answer from the options given below:

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth?

Where N - Number of Bacteria at any time, $N_0$ - Initial number of Bacteria.

Consider an elementary reaction

$$A(g) + B(g) \to C(g) + D(g)$$

If the volume of reaction mixture is suddenly reduced to $\dfrac{1}{3}$ of its initial volume, the reaction rate will become $'x'$ times of the original reaction rate. The value of $x$ is :

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.

$$\mathrm{A + B \underset{Step\ 3}{\overset{Step\ 1}{\rightleftharpoons}} C \xrightarrow{Step\ 2} P}$$

Some details of the above reactions are listed below.

Step	Rate constant (sec$^{-1}$)	Activation energy (kJ mol$^{-1}$)
1	$k_1$	300
2	$k_2$	200
3	$k_3$	$Ea_3$

If the overall rate constant of the above transformation (k) is given as $k = \dfrac{k_1 k_2}{k_3}$ and the overall activation energy ($E_a$) is 400 kJ mol$^{-1}$, then the value of $Ea_3$ is ________ kJ mol$^{-1}$ (nearest integer)

Consider the following reaction, the rate expression of which is given below

$$\mathrm{A + B \rightarrow C}$$

$$\text{rate} = k\,[\mathrm{A}]^{1/2}\,[\mathrm{B}]^{1/2}$$

The reaction is initiated by taking 1 M concentration of A and B each. If the rate constant (k) is $4.6 \times 10^{-2}\ \mathrm{s^{-1}}$, then the time taken for A to become 0.1 M is ________ sec. (nearest integer)

During Kinetic study of reaction $2A + B \rightarrow C + D$, the following results were obtained :

	A [M]	B [M]	initial rate of formation of D
I	0.1	0.1	$6.0 \times 10^{-3}$
II	0.3	0.2	$7.2 \times 10^{-2}$
III	0.3	0.4	$2.88 \times 10^{-1}$
IV	0.4	0.1	$2.40 \times 10^{-2}$

Based on above data, overall order of the reaction is ________.

Consider the following single step reaction in gas phase at constant temperature.

$$\mathrm{2A_{(g)} + B_{(g)} \rightarrow C_{(g)}}$$

The initial rate of the reaction is recorded as $r_1$ when the reaction starts with 1.5 atm pressure of A and 0.7 atm pressure of B. After some time, the rate $r_2$ is recorded when the pressure of C becomes 0.5 atm. The ratio $r_1 : r_2$ is ________ $\times 10^{-1}$. (Nearest integer)

Time required for 99.9% completion of a first order reaction is _________ times the time required for completion of 90% reaction.(nearest integer)

Consider the two different first order reactions given below

$\mathrm{A + B \to C}$ (Reaction 1)

$\mathrm{P \to Q}$ (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 $\frac{2}{3}^{\mathrm{rd}}$ and $\frac{4}{5}^{\mathrm{th}}$ 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 reaction

$\mathrm{A + B \rightarrow C}$

The time taken for A to become $1/4^{th}$ 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 __________.

For a reaction $\mathrm{A} \xrightarrow{K_1} \mathrm{B} \xrightarrow{K_2} \mathrm{C}$

If the rate of formation of B is set to be zero then the concentration of B is given by :

Given below are two statements : Statement I : The rate law for the reaction $\mathrm{A + B \rightarrow C}$ is rate $(r) = k[\mathrm{A}]^2[\mathrm{B}]$. When the concentration of both A and B is doubled, the reaction rate is increased "$x$" times. Statement II : [Figure: linear plot of concentration of R versus time, starting at $[\mathrm{R_0}]$ and decreasing with slope $= -K$] The figure is showing "the variation in concentration against time plot" for a "$y$" order reaction. The Value of $x + y$ is ________.

Consider the following first order gas phase reaction at constant temperature

$$\mathrm{A(g) \rightarrow 2B(g) + C(g)}$$

If the total pressure of the gases is found to be 200 torr after 23 sec. and 300 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 : $\log_{10}(2) = 0.301$]

The ratio of $\frac{\mathrm{^{14}C}}{\mathrm{^{12}C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of $\mathrm{^{14}C}$ is 5730 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 :

$$\mathrm{A(g) \rightarrow 2B(g) + C(g)}$$

S.No.	Time/s	Total pressure/(atm)
1.	0	0.1
2.	115	0.28

The rate constant of the reaction is ________ $\times 10^{-2}\ \mathrm{s^{-1}}$ (nearest integer)

Consider the following data for the given reaction

$$\mathrm{2\,HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}}$$

	1	2	3
$\mathrm{HI\ (mol\ L^{-1})}$	0.005	0.01	0.02
$\mathrm{Rate\ (mol\ L^{-1}s^{-1})}$	$7.5 \times 10^{-4}$	$3.0 \times 10^{-3}$	$1.2 \times 10^{-2}$

The order of the reaction is ________.

For a reaction taking place in three steps at same temperature, overall rate constant $K = \frac{K_1 K_2}{K_3}$. If $E_{a_1}$, $E_{a_2}$ and $E_{a_3}$ are 40, 50 and 60 kJ/mol respectively, the overall $E_a$ is ______ kJ/mol.

The rate of First order reaction is 0.04 $\mathrm{mol\ L^{-1}\ s^{-1}}$ at 10 minutes and 0.03 $\mathrm{mol\ L^{-1}\ s^{-1}}$ at 20 minutes after initiation. Half life of the reaction is ________ minutes. (Given log2 = 0.3010, log3 = 0.4771)

$\mathrm{NO_2}$ required for a reaction is produced by decomposition of $\mathrm{N_2O_5}$ in $\mathrm{CCl_4}$ as by equation

$$\mathrm{2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}}$$

The initial concetration. of $\mathrm{N_2O_5}$ is 3 mol L$^{-1}$ and it is 2.75 mol L$^{-1}$ after 30 minutes.

The rate of formation of $\mathrm{NO_2}$ is $\mathrm{x \times 10^{-3}}$ mol L$^{-1}$ min$^{-1}$, value of x is _______. (nearest integer)

Integrated rate law equation for a first order gas phase reaction is given by

(where $\mathrm{P_i}$ is initial pressure and $\mathrm{P_t}$ is total pressure at time $t$)

$r = k\,[\mathrm{A}]$ for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is ________ minutes.