Chemical Kinetics

If for a first-order reaction, the value of A and \({E}_{a}\) are \(4\times {10}^{13}{s}^{-1}\)and 98.6 kJ \(mo{l}^{-1}\)respectively, then at what temperature will its half-life be 10 minutes?

For an elementary reaction

\(\mathrm{A}+\mathrm{B}\to \mathrm{C}+\mathrm{D}\)

When volume becomes \(\frac{1}{3}\)rd, rate of reaction becomes

Memory Based Question 28/Jan/25 Evening shift

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 \(\mathrm{Ea}_{1}, \mathrm{Ea}_{2}\) and \(\mathrm{Ea}_{3}\) are \(40,50\) and \(60 \mathrm{~kJ} / \mathrm{mol}\) respectively, the overall \(\mathrm{Ea}\) is ........... \(\mathrm{kJ} / \mathrm{mol}\).

[JEE Main 2024, 29 Jan (Shift 1)]

If for a first-order reaction, the value of A and \({E}_{a}\) are \(4\times {10}^{13}{s}^{-1}\)and 98.6 kJ \(mo{l}^{-1}\)respectively, then at what temperature will its half-life be 10 minutes?

For \({\mathrm{A}}_{2}+{\mathrm{B}}_{2}⇌2\mathrm{AB}\)
\({\mathrm{E}}_{\mathrm{a}}\) for forward and backward reaction are \(180\) and \(200\mathrm{kJ}{\mathrm{mol}}^{-1}\) respectively. If catalyst lowers \({\mathrm{E}}_{\mathrm{a}}\) for both reaction by \(100\mathrm{kJ}{\mathrm{mol}}^{-1}\). Which of the following statement is correct?

[JEE Main 2025, 4 Apr (Shift 1)]

For an elementary reaction

\(\mathrm{A}+\mathrm{B}\to \mathrm{C}+\mathrm{D}\)

When volume becomes \(\frac{1}{3}\)rd, rate of reaction becomes

Memory Based Question 28/Jan/25 Evening shift

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
\(\mathrm{A}+\mathrm{B}\underset{\mathrm{Step}2}{\overset{\mathrm{Step}1}{⇌}}\mathrm{C}\overset{\mathrm{Step}2}{\to }\mathrm{P}\)

Some details of the above reactions are listed below.
Step Rate constant \((se{c}^{-1})\) Activation energy {\(kJmo{l}^{-1}\))
1 \({k}_{1}\) \(300\)
2 \({k}_{2}\) \(200\)
3 \({k}_{3}\) \({\mathrm{Ea}}_{3}\)

If the overall rate constant of the above transformation (k) is given as \(k=\frac{{k}_{1}{k}_{2}}{{k}_{3}}\)and the overall activation energy \(\left({E}_{a}\right)\) is \(400kJmo{l}^{-1}\), then the value of \(E{a}_{3}\) is _______ \(\mathrm{kJ}{\mathrm{mol}}^{-1}\) (nearest integer)

[JEE Main 2024, 4 Apr (Shift 1)]

A drug becomes ineffective when it decomposes to 50 % its concentration. If 16 mg of said drug becomes 4 mg in 12 months, find the time in which drug becomes ineffective given that decomposition of drug follows first order kinetics.

Memory Based Question 29/Jan/25 Evening shift

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 \({\mathrm{E}}_{\mathrm{a}}​\) as used in Arrhenius equation depend on temperature.
E. When \({\mathrm{E}}_{\mathrm{a}}​\) >> RT. A and Ea become interdependent.
Choose the correct answer from the options given below

[JEE Main 2025, 3 Apr (Shift 2)]

The reaction \({A}_{2}+{B}_{2}\to 2AB\) follows the mechanism

\({A}_{2}\overset{{k}_{1}}{\underset{{k}_{-1}}{⇌}}A+A\text{ (fast) }\\ A+{B}_{2}\overset{{k}_{2}}{\to }AB+B\text{ (slow) }\\ A+B\to AB\text{ (fast) }\)

The overall order of the reaction is

Find the order of the reaction

\(\mathrm{A}+\mathrm{B}\to \mathrm{F}\)

if the mechanism of the reaction is given below:
Step 1: \(\mathrm{A}+\mathrm{B}\to \mathrm{D}(\mathrm{slow})\)
Step 2: \(\mathrm{D}\to \mathrm{C}+\mathrm{E}(\mathrm{fast})\)
Step 3: \(\mathrm{C}+\mathrm{E}\to \mathrm{F}(\mathrm{fast})\)

Memory Based Question 29/Jan/25 Morning shift

Rate law for a reaction between A and B is given by \(\mathrm{R}=\mathrm{k}[\mathrm{A}{]}^{\mathrm{n}}[\mathrm{B}{]}^{\mathrm{m}}\)
If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction \(\left(\frac{{\mathrm{r}}_{2}}{{\mathrm{r}}_{1}}\right)\) is

[JEE Main 2025, 4 Apr (Shift 1)]

The reaction \({\mathrm{A}}_{2}+{\mathrm{B}}_{2}\to 2\mathrm{AB}\) follows the mechanism

\({\mathrm{A}}_{2}\overset{{\mathrm{k}}_{1}}{\underset{{\mathrm{k}}_{-1}}{⇌}}\mathrm{A}+\mathrm{A}\text{ (fast) }\)

\(\mathrm{A}+{\mathrm{B}}_{2}\overset{{\mathrm{k}}_{2}}{\to }\mathrm{AB}+\mathrm{B}\text{ (slow) }\)

\(\mathrm{A}+\mathrm{B}\to \mathrm{AB}\text{ (fast) }\)

The overall order of the reaction is

Integrated rate law equaiton for a first order gas phase reaction is given by (where P_i is initial pressure P_t is total pressure at time t)

A drug becomes ineffective when it decomposes to 50 % its concentration. If 16 mg of said drug becomes 4 mg in 12 months, find the time in which drug becomes ineffective given that decomposition of drug follows first order kinetics.

Memory Based Question 29/Jan/25 Evening shift

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

Rate law for a reaction between A and B is given by \(\mathrm{R}=\mathrm{k}[\mathrm{A}{]}^{\mathrm{n}}[\mathrm{B}{]}^{\mathrm{m}}\)
If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction \(\left(\frac{{\mathrm{r}}_{2}}{{\mathrm{r}}_{1}}\right)\) is

[JEE Main 2025, 4 Apr (Shift 1)]

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

[JEE Main 2025, 4 Apr (Shift 2)]

Given below are two statements
Statement I : A catalyst cannot alter the equilibrium constant \(\left({\mathrm{K}}_{\mathrm{C}}\right)\) of the reaction, temperature remaining constant
Statement II : A homogeneous catalyst can change the equilibrium composition of a system temperature remaining constant
In the light of the above statements, choose the correct answer from the options given below.

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

[JEE Main 2025, 4 Apr (Shift 2)]

Integrated rate law equaiton for a first order gas phase reaction is given by (where P_i is initial pressure P_t is total pressure at time t)

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 \({\mathrm{E}}_{\mathrm{a}}​\) as used in Arrhenius equation depend on temperature.
E. When \({\mathrm{E}}_{\mathrm{a}}​\) >> RT. A and Ea become interdependent.
Choose the correct answer from the options given below

[JEE Main 2025, 3 Apr (Shift 2)]

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 \({t}_{2}\), respectively. The ratio \({t}_{1}/{t}_{2}\) will be

[JEE Main 2025, 8 Apr (Shift 1)]

Find the order of the reaction

\(\mathrm{A}+\mathrm{B}\to \mathrm{F}\)

if the mechanism of the reaction is given below:
Step 1: \(\mathrm{A}+\mathrm{B}\to \mathrm{D}(\mathrm{slow})\)
Step 2: \(\mathrm{D}\to \mathrm{C}+\mathrm{E}(\mathrm{fast})\)
Step 3: \(\mathrm{C}+\mathrm{E}\to \mathrm{F}(\mathrm{fast})\)

Memory Based Question 29/Jan/25 Morning shift

Consider the two different first order reactions given below
\(\begin{aligned}& A + B \rightarrow C \text { (Reaction 1) } \\& P \rightarrow Q \text { (Reaction 2) }\end{aligned}\)

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 \(2 / 3^{ rd }\) 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 \(\log _{10}(5)=0.699\) ]

[JEE Main 2024, 06 Apr (Shift 2)]

Consider the two different first order reactions given below
\(\begin{aligned}& A + B \rightarrow C \text { (Reaction 1) } \\& P \rightarrow Q \text { (Reaction 2) }\end{aligned}\)

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 \(2 / 3^{ rd }\) 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 \(\log _{10}(5)=0.699\) ]

[JEE Main 2024, 06 Apr (Shift 2)]

Time required for completion of \(99.9 \%\) of a first order reaction is ............ times of half life (\({\mathrm{t}}_{1/2}\)) of the reaction

[JEE Main 2024, 27 Jan (Shift 2)]

In a reaction \(\mathrm{A}+\mathrm{B}\to \mathrm{C}\), initial concentrations of A and B are related as \([\mathrm{A}{]}_{0}=8[\mathrm{B}{]}_{0}\). 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?

[JEE Main 2025, 3 Apr (Shift 1)]

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

[JEE Main 2025, 22 Jan (Shift 1)]

A sample initially contains only \(\mathrm{U}-238\) isotope of uranium. With time, some of the \(\mathrm{U}-238\) radioactively decays into \(\mathrm{Pb}-206\) while the rest of it remains undisintegrated. When the age of the sample is \(P\times {10}^{8}\) years, the ratio of mass of \(\mathrm{Pb}-206\) to that of \(\mathrm{U}-238\) in the sample is found to be 7. The value of \(\mathbf{P}\) is
[Given: Half-life of \(\mathrm{U}-238\) is \(4.5\times {10}^{9}\) years; \({\log }_{e}2=0.693\) ]

Consider an elementary reaction

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

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

[JEE Main 2025, 28 Jan (Shift 2)]

For \({\mathrm{A}}_{2}+{\mathrm{B}}_{2}⇌2\mathrm{AB}\)
\({\mathrm{E}}_{\mathrm{a}}\) for forward and backward reaction are \(180\) and \(200\mathrm{kJ}{\mathrm{mol}}^{-1}\) respectively. If catalyst lowers \({\mathrm{E}}_{\mathrm{a}}\) for both reaction by \(100\mathrm{kJ}{\mathrm{mol}}^{-1}\). Which of the following statement is correct?

[JEE Main 2025, 4 Apr (Shift 1)]

Consider an elementary reaction

\(\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g})\to \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})\)

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

Consider the following reaction,

\(2{H}_{2}(g)+2NO(g)\to {N}_{2}(g)+2{H}_{2}O(g)\)

which follows the mechanism given below:

\(2\mathrm{NO}\left(\mathrm{g}\right)\underset{{\mathrm{k}}_{-1}}{\overset{{\mathrm{k}}_{1}}{⇌}}{\mathrm{N}}_{2}{\mathrm{O}}_{2}\left(\mathrm{g}\right)\left(\mathrm{fast}\mathrm{equilibrium}\right)\\ {\mathrm{N}}_{2}{\mathrm{O}}_{2}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\left(\mathrm{g}\right)\overset{{\mathrm{k}}_{2}}{\to }{\mathrm{N}}_{2}\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{g}\right)\left(\mathrm{slow}\mathrm{reaction}\right)\\ {\mathrm{N}}_{2}\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\left(\mathrm{g}\right)\overset{{\mathrm{k}}_{3}}{\to }{\mathrm{N}}_{2}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{g}\right)\left(\mathrm{fast}\mathrm{reaction}\right)\\\)
The order of the reaction is

[JEE Advanced 2024, Paper-1]

Drug X becomes ineffective after 50% decomposition. The original concentration of drug in a bottle was 16 mg / mL which becomes 4 mg / mL in 12 months. The expiry time of the drug in months is ______.
Assume that the decomposition of the drug follows first order kinetics

[JEE Main 2025, 29 Jan (Shift 2)]

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 \({t}_{2}\), respectively. The ratio \({t}_{1}/{t}_{2}\) will :

[JEE Main 2025, 8 Apr (Shift 1)]

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

[JEE Main 2024, 6 Apr (Shift 1)]

For the reaction A \(\to\)B , the rate constant k ( in s^-1), is given by log k = 20.35 - \(\frac{(2.47\times {10}^{3})}{\mathrm{T}}\). The energy of activation in kJ/mol is ____. (Nearest integer)

[Given R- 8.314 J/K/mol]

[JEE Main 2021, 31 Aug (Shift 2)]

\({ }_{92}^{238} \mathrm{U}\) is known to undergo radioactive decay to form by \({ }_{82}^{206} \mathrm{~Pb}\) 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 \(\mathrm{Z}\) ?

[JEE Advanced 2020, Paper-1]

If \( 75 \% \) of a first order reaction was completed in 90 minutes, \( 60 \% \) of the same reaction would be completed in approximately how many minutes?

(Take : \( \log 2=0.30 ; \log 2.5=0.40 \) )

[JEE Main 2020, 4 Sep (Shift 1)]

\(N _2 O _5( g ) \rightarrow 2 NO _2( g )+\frac{1}{2} O _2( g )\)

In the above first order reaction the initial concentration of \(N _2 O _5\), is \(2.40 \times 10^{-2} ~mol L ^{-1}\) at \(318 K\). The concentration of \(N _2 O _5\), after 1 hour was \(1.60 \times 10^{-2} ~mol L ^{-1}\). The rate constant of the reaction at \(318 ~K\) is______ \(\times 10^{-3} ~min ^{-1}\). (Nearest integer) [Given: \(\log 3=0.477, \log 5=0.699]\)

[JEE Main 2021, 22 Jul (Shift 2)]

An exothermic reaction X \(\to\) Y has an activation energy 30 kJ mol^–1. If energy change \(\left(△\mathrm{H}\right)\) during the reaction is –20 kJ, then the activation energy for the reverse reaction is.....(kJ)

[JEE Main 2021, 26 Feb (Shift 1)]

The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from \( 27^{\circ} \mathrm{C} \) to \( 42^{\circ} \mathrm{C} \). Its energy of activation in \( \mathrm{J} / \mathrm{mol} \) is........

(Take In \( 5=1.6094 ; \mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \) )

[JEE Main 2020, 4 Sep (Shift 2)]

For a certain reaction, the rate \(=\mathrm{k}[\mathrm{A}{]}^{2}[\mathrm{B}]\), when the initial concentration of A is tripled keeping concentration of B constant, the initial rate would

[NEET 2023]

The number of correct statement/s from the following is_____

(A) Larger the activation energy, smaller is the value of the rate constant.
(B) The higher is the activation energy, higher is the value of the temperature coefficient.
(C) At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature.
(D) A plot of \(\ln kvs\frac{1}{T}\) is a straight line with slope equal to \(-\frac{{E}_{a}}{R}\)

[JEE Main 2023, 24 Jan (Shift 1)]

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 \(mol L ^{-1} s ^{-1}\) and \(mol ^{-1} Ls ^{-1}\) respectively

[JEE Main 2023, 10 Apr (Shift 2)]

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

[JEE Main 2023, 13 Apr (Shift 2)]

For the reaction, \(2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\); the observed rate expression is, rate \(=\mathrm{k}_{\mathrm{f}}[\mathrm{NO}]^2\left[\mathrm{H}_2\right]\).
The rate expression for the reverse reaction is
[JEE Main 2020, 7 Jan (Shift 2)]

For the reaction \(2 A +3 B +\frac{3}{2} C \rightarrow 3 P\), which statement is correct?

[JEE Main 2020, 3 Sep (Shift 2)]

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ' \(k\) ' value of \(3.3 \times 10^{-4} s ^{-1}\) at \(153^{\circ} C\). The time in minutes it takes for the isomerization to proceed \(40 \%\) to completion at this temperature is ___ . (Rounded off to the nearest integer)

[JEE Main 2021, 24 Feb (Shift 2)]

For a certain first-order reaction \(32 \%\) of the reactant is left after \(570 \mathrm{~s}\). The rate constant of this reaction is........ \(\times 10^{-3} \mathrm{~s}^{-1}\)[Given: \(\left.\log _{10} 2=0.301, \ln 10=2.303\right]\)

[JEE Main 2021, 17 Mar (Shift 1)]

\({\mathrm{KClO}}_{3}+6{\mathrm{FeSO}}_{4}+3{\mathrm{H}}_{2}{\mathrm{SO}}_{4}\to \mathrm{KCl}+3{\mathrm{Fe}}_{2}{\left({\mathrm{SO}}_{4}\right)}_{3}+3{\mathrm{H}}_{2}\mathrm{O}\)

The above reaction was studied at \(300 K\) by monitoring the concentration of \(FeSO _4\) in which initial concentration was \(10 ~M\) and after half an hour became \(8.8 ~M\). The rate of production of \(Fe _2\left( SO _4\right)_3\) is___________ \(\times 10^{-6} mol L ^{-1} s ^{-1}\). (Nearest integer)

[JEE Main 2023, 11 Apr (Shift 1)]

For conversion of compound \(A \rightarrow B\), the rate constant of the reaction was found to be \(4.6 \times 10^{-5} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\). The order of the reaction is

[JEE Main 2023, 29 Jan (Shift 2)]

\(A\to B\)

The above reaction is of zero order. Half life of this reaction is 50 min. The time taken for the concentration of A to reduce to one-fourth of its initial value is _________min(Nearest Integer)

[JEE Main 2023, 1 Feb (Shift 2)]

The number of given statement/s which is/are correct is

(A) The stronger the temperature dependence of the rate constant, the higher is the activation energy.

(B) If a reaction has zero activation energy, its rate is independent of temperature.

(C) The stronger the temperature dependence of the rate constant, the smaller is the activation energy.

(D) If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.
[JEE Main 2023, 8 Apr (Shift 1)]

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)

[JEE Main 2023, 10 Apr (Shift 1)]

The first order rate constant for the decomposition of \({\mathrm{CaCO}}_{3}\) at 700 K is \(6.36\times {10}^{-3}{\mathrm{s}}^{-1}\)and activation energy is 209kJ/mol. Its rate constant (in s^-1) at 600 K is \(x\times {10}^{-6}\\\). The value of x is ____. (Nearest integer)

[ Given R = 8.314 J/K/ mol ; log \(6.36\times {10}^{-3}{\mathrm{s}}^{-1}\) = -2.19, \({10}^{-4.79}=1.62\times {10}^{-5}\)]

[JEE Main 2021, 27 Aug (Shift 2)]

The reaction \(2 NO + Br _2 \rightarrow 2 NOBr\) takes places through the mechanism given below

\(NO + Br _2 \Leftrightarrow NOBr _2\) (fast)
\(NOBr _2+ NO \rightarrow 2 NOBr\) (slow)

The overall order of the reaction is

[JEE Main 2023, 12 Apr (Shift 1)]

For a reaction of order \(n\), the unit of the rate constant is:

An organic compound undergoes first order decomposition. If the time taken for the 60% decomposition is 540 s, then the time required for 90% decomposition will be_________ s. (Nearest integer).Given: ln 10=2.3 ; log 2=0.3

Given below are two statements
Statement I : A catalyst cannot alter the equilibrium constant \(\left({\mathrm{K}}_{\mathrm{C}}\right)\) of the reaction, temperature remaining constant
Statement II : A homogeneous catalyst can change the equilibrium composition of a system temperature remaining constant
In the light of the above statements, choose the correct answer from the options given below

[JEE Main 2025, 3 Apr (Shift 1)]

\(t _{87.5}\) 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)

[JEE Main 2023, 13 Apr (Shift 1)]

A first order reaction has the rate constant, \(k =4.6 \times 10^{-3}\) \(s ^{-1}\). The number of correct statement/s from the following is/are____
Given: \(\log 3=0.48\)
(a) Reaction completes in \(1000 ~s\).
(b) The reaction has a half-life of \(500 ~s\).

(c) The time required for \(10 \%\) completion is 25 times the time required for \(90 \%\) completion.
(d) The degree of dissociation is equal to \(\left(1- e ^{- kt }\right)\).
(e) The rate and the rate constant have the same unit.

[JEE Main 2023, 25 Jan (Shift 2)]

The slope of Arrhenius Plot (ln \( \mathrm{K} \mathrm{v} / \mathrm{s} \) 1/T) of first order reaction is \( -5 \times 10^{3} \mathrm{~K} \). The value of \( \mathrm{E}_{\mathrm{a}} \) of the reaction is.

[Given \( \mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \) ]

[NEET 2021]

The rate constant for a first order reaction is \(20 ~min ^{-1}\). The time required for the initial concentration of the reactant to reduce to its \(\frac{1}{32}\) level is______ \(10^{-2} ~min\). (Nearest integer) (Given : \(\ln 10=2.303, \log 2=0.3010)\)

[JEE Main 2023, 31 Jan (Shift 2)]

A sample of milk splits after \(60 \mathrm{~min}\). at \(300 \mathrm{~K}\) and after \(40 \mathrm{~min}\). at \(400 \mathrm{~K}\) when the population of lactobacillus acidophilus in it doubles. The activation energy (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) for this process is closest to____ . (Given, \(\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \ln (2 / 3)=0.4, \mathrm{e}^{-3}=4.0\right)\)

[JEE Main 2020, 9 Jan (Shift 2)]

For the first order reaction \(A\to B\) the half life is \(30 min\). The time taken for 75% completion of the reaction is_________ min. (Nearest Integer).

Given:log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6989

[JEE Main 2023, 25 Jan (Shift 1)]

The rate constant of a reaction increases by five times on increase in temperature from \(\ 27^{\circ} \mathrm{C} \) to \(\ 52^{\circ} \mathrm{C} \). The value of activation energy in \(\ \mathrm{kJ} \mathrm{mol}^{-1} \) is _____(Rounded-off to the nearest integer)
\(\ \left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right] \)

[JEE Main 2019, 10 Jan (Shift 1)]

A and B decompose via first order kinetics with half-lives \( 54.0 \mathrm{~min} \) and \( 18.0 \mathrm{~min} \) respectively. Starting from an equimolar non reactive mixture of \( \mathrm{A} \) and \( \mathrm{B} \), the time taken for the concentration of A to become 16 times that of \( B \) is.................... min (Round off to the nearest Integer)

[JEE Main 2021, 16 Mar (Shift 2)]

The rate of a reaction decreased by \( 3.555 \) times when the temperature was changed from \( 40^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \). The activation energy ( in \( \mathrm{kJ} \mathrm{mol}^{-1} \) ) of the reaction is [to the nearest integer| Take; \( \mathrm{R}-8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \ln 3.555-1.268 \)

[JEE Main 2020, 6 Sep (Shift 2)]

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ' \(\ k\) ' value of \(\ 33 \times 10^{-4} \mathrm{~s}^{-1} \) at \(\ 153^{\circ} \mathrm{C} \). The time in minutes it takes for the isomerization to proceed \(\ 40 \%\) to completion at this temperature is ____ . (Rounded off to the nearest integer)

[JEE Main 2021, 24 Feb (Shift 1)]

A reaction has a half life of \(\mathrm{1 ~min}\). The time required for \(99.9 \%\) completion of the reaction is__________ \(\min\). (Round off to the nearest integer) [Use \(\ln 2=0.69 ; \ln 10=2.3\) ]

[JEE Main 2021, 18 Mar (Shift 2)]

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is:

(Given: In 10 = 2.303 and log 2 = 0.3010)

[JEE Main 2022, 24 Jun (Shift 2)]

\(A\) and \(B\) are two substances undergoing radioactive decay in a container. The half life of \(A\) is \(\mathrm{15 ~min}\) and that of \(B\) is \(\mathrm{5 ~min}\). If the initial concentration of \(B\) is 4 times that of \(A\) and they both start decaying at the same time, time it will take for the concentration of both of them to be same is ......... \(\min\)

[JEE Main 2023, 1 Feb (Shift 1)]