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JEE Mains | PYQ

The number of given statement/s which is/are correct is ________.
(A) The stronger the temperature dependance 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.

For certain chemical reaction \( X \rightarrow Y \), the rate of formation of product is plotted against the time as shown in the figure. The number of correct statement/s from the following is ______ .

(A) Over all order of this reaction is one
(B) Order of this reaction can’t be determined
(C) In region I and III, the reaction is of first and zero order respectively
(D) In region-II, the reaction is of first order
(E) In region-II, the order of reaction is in the range of \( 0.1 \) to \( 0.9 \).

For the following graphs,

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

Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by \( 20 \, \text{kJ mol}^{-1} \). If \( k_1 \) and \( k_2 \) are the rate constants of first and second reaction respectively at \( 300 \, \text{K} \), then \( \ln \frac{k_2}{k_1} \) will be _________________.
(Nearest integer) \( \big[ \, R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \, \big] \)

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

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

Consider \( \mathrm{A} \xrightarrow{k_1} \mathrm{B} \) and \( \mathrm{C} \xrightarrow{k_2} \mathrm{D} \) are two reactions. If the rate constant \( (k_1) \) of the \( \mathrm{A} \rightarrow \mathrm{B} \) reaction can be expressed by the following equation \( \log_{10} k = 14.34 - \frac{1.5 \times 10^{4}}{T/\mathrm{K}} \) and activation energy of \( \mathrm{C} \rightarrow \mathrm{D} \) reaction \( (E_{a_{2}}) \) is \( \tfrac{1}{5} \)th of the \( \mathrm{A} \rightarrow \mathrm{B} \) reaction \( (E_{a_{1}}) \), then the value of \( (E_{a_{2}}) \) is ________ \( \mathrm{kJ \, mol^{-1}} \). (Nearest Integer)

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

Catalyst \( A \) reduces the activation energy for a reaction by \( 10 \, \text{kJ mol}^{-1} \) at \( 300 \, \text{K} \). The ratio of rate constants, \( \dfrac{k_{T,\ \text{Catalysed}}}{k_{T,\ \text{Uncatalysed}}} \) is \( e^{x} \). The value of \( x \) is ________. [Nearest integer]
[Assume that the pre-exponential factor is same in both the cases. Given \( R = 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \)]

The rate constant for a first order reaction is given by the following equation:
\( \ln K = 33.24 - \frac{2.0 \times 10^{4}K}{T} \).
The Activation energy for the reaction is given by __________ \( \text{kJ mol}^{-1} \). (In Nearest integer)
(Given : \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \) ).

In a reaction \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \), initial concentrations of \( \mathrm{A} \) and \( \mathrm{B} \) are related as \( [\mathrm{A}]_{0} = 8[\mathrm{B}]_{0} \). The half lives of \( \mathrm{A} \) and \( \mathrm{B} \) are \( 10 \, \text{min} \) and \( 40 \, \text{min} \), 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?

A radioactive element has a half life of \( 200 \) days. The percentage of original activity remaining after \( 83 \) days is __________. (Nearest integer)
(Given : antilog \( 0.125 = 1.333 \), antilog \( 0.693 = 4.93 \) )

A reaction has a half life of \( 1 \) min. The time required for \( 99.9\% \) completion of the reaction is ___ min.
[Use : \( \ln 2 = 0.69 \); \( \ln 10 = 2.3 \)]

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

For reaction \( A \rightarrow P \), rate constant \( k = 1.5 \times 10^{3} \, \mathrm{s}^{-1} \) at \( 27^{\circ}\mathrm{C} \)
If activation energy for the above reaction is \( 60 \, \mathrm{kJ}\,\mathrm{mol}^{-1} \), then the temperature (in \( ^{\circ}\mathrm{C} \)) at which rate constant, \( k = 4.5 \times 10^{3} \, \mathrm{s}^{-1} \) is ________. (Nearest integer)
Given: \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( R = 8.3 \, \mathrm{J}\,\mathrm{K}^{-1}\,\mathrm{mol}^{-1} \), \( \ln 10 = 2.3 \)

For a reversible reaction \( A \rightleftharpoons B \), the \( \Delta H_{\text{forward reaction}} = 20 \,\text{kJ mol}^{-1} \). The activation energy of the uncatalyzed forward reaction is \( 300 \,\text{kJ mol}^{-1} \). When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at \( 27^\circ \text{C} \) is found to be same as that of the uncatalyzed reaction at \( 327^\circ \text{C} \). The activation energy of the catalysed backward reaction is ________ \( \text{kJ mol}^{-1} \).

Consider the two different first order reactions given below
\( \mathrm{A + B \rightarrow C} \) \( \text{(Reaction 1)} \)
\( \mathrm{P \rightarrow Q} \) \( \text{(Reaction 2)} \)
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 \( \dfrac{2}{3} \)rd and \( \dfrac{4}{5} \)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 \( \log_{10}(5) = 0.699 \)]

Decomposition of a hydrocarbon follows the equation \( k = (5.5 \times 10^{11} \text{ s}^{-1}) e^{\frac{-28000 \text{ K}}{\text{T}}}\). The activation energy of the reaction is ________ \( \mathrm{kJ\, mol^{-1}} \). (Nearest Integer)
Given: \( R = 8.3 \, \mathrm{J\, K^{-1}\, mol^{-1}} \)

At \( 345 \,\mathrm{K} \), the half life for the decomposition of a sample of a gaseous compound initially at \( 55.5 \,\mathrm{kPa} \) was \( 340 \,\mathrm{s} \). When the pressure was \( 27.8 \,\mathrm{kPa} \), the half life was found to be \( 170 \,\mathrm{s} \). The order of the reaction is ____________. [integer answer]

The following data were obtained during the first order thermal decomposition of a gas A at constant volume: \( \mathrm{A(g)} \rightarrow 2\mathrm{B(g)} + \mathrm{C(g)} \)

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

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

Given below are two statements:
\( R = 8.314\ \mathrm{J\,K^{-1}\,mol^{-1}} \) and \( 1\ \mathrm{cal} = 4.2\ \mathrm{J} \)
Statement-I: When \( Ea = 12.6\ \mathrm{kcal/\,mol} \), the room temperature rate constant is doubled by a \( 10^\circ \mathrm{C} \) increase in temperature (\( 298\ \mathrm{K} \) to \( 308\ \mathrm{K} \)).
Statement-II: For a first order reactions \( \mathrm{A \rightarrow B} \),

Here \( [A]_0 \) is the initial concentration of \( \mathrm{A} \) and \( t_{1/2} \) is half-life of reaction.
In the light of the above statements, choose the correct answer from the options given below:

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 \( E_a \) as used in Arrhenius equation depend on temperature.
(E) When \( E_a \>>> RT \), \( A \) and \( E_a \) become interdependent. 
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 \(\displaystyle k = \sqrt{\frac{k_1 k_3}{k_2}} \). If the activation energies of the three steps are \( 60 \), \( 30 \) and \( 10 \) \( \text{kJ mol}^{-1} \) respectively, then the overall energy of activation in \( \text{kJ mol}^{-1} \) is ________. (Nearest integer)

For a first order reaction, the ratio of the time for \( 75\% \) completion of a reaction to the time for \( 50\% \) completion is __________. (Integer answer)

For a reaction \( \mathrm{A} \xrightarrow{k_{1}} \mathrm{B} \xrightarrow{k_{2}} \mathrm{C} \) If the rate of formation of \( \mathrm{B} \) is set to be zero then the concentration of \( \mathrm{B} \) is given by:

For kinetic study of the reaction of iodide ion with \( \mathrm{H_2O_2} \) at room temperature:
(a) Always use freshly prepared starch solution
(b) Always keep the concentration of sodium thiosulphate solution less than that of \( \mathrm{KI} \) solution
(c) Record the time immediately after the appearance of blue colour.
(d) Record the time immediately before the appearance of blue colour
(e) Always keep the concentration of sodium thiosulphate solution more than that of \( \mathrm{KI} \) solution.
Choose the correct answer from the options given below:

Assuming \( 1 \, \mu \text{g} \) of trace radioactive element X with a half life of \( 30 \, \text{years} \) is absorbed by a growing tree. The amount of X remaining in the tree after \( 100 \, \text{years} \) is __________ \( \times 10^{-1} \, \mu \text{g} \).
[Given \( \ln 10 = 2.303 \) ; \( \log 2 = 0.30 \)]

At \( 27^\circ \mathrm{C} \) in presence of a catalyst, activation energy of a reaction is lowered by \( 10 \, \mathrm{kJ \, mol^{-1}} \). The logarithm of ratio of \( \dfrac{k(\text{catalysed})}{k(\text{uncatalysed})} \) is……
(Consider that the frequency factor for both the reactions is same)

For a certain first order reaction \( 32\% \) of the reactant is left after \( 570 \, \text{s} \). The rate constant of this reaction is _______ \( \times 10^{-3} \, \text{s}^{-1} \), (Round off to the Nearest Integer).
[Given : \( \log_{10} 2 = 0.301 \), \( \ln 10 = 2.303 \)]

\( \text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g) \)
In the above first order reaction the concentration of \( \text{PCl}_5 \) reduces from initial concentration \( 50 \, \text{mol L}^{-1} \) to \( 10 \, \text{mol L}^{-1} \) in \( 120 \) minutes at \( 300 \, \text{K} \). The rate constant for the reaction at \( 300 \, \text{K} \) is \( x \times 10^{-2} \, \text{min}^{-1} \). The value of \( x \) is __________ . [Given \( \log 5 = 0.6989 \) ]

\( t_{87.5} \) 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)

For a given reaction \( R \rightarrow P \), \( t_{1/2} \) is related to \( [A]_{0} \) as given in table. [Given : \( \log 2 = 0.30 \)]
Which of the following is true?

For a reaction, given below is the graph of \( \ln k \) vs \( \dfrac{1}{T} \). The activation energy for the reaction is equal to ________ \( \text{cal mol}^{-1} \). (nearest integer)
(Given: \( R = 2 \, \text{cal K}^{-1} \text{ mol}^{-1} \))

For the reaction \( \text{A} \rightarrow \text{B} \) the following graph was obtained. The time required (in seconds) for the concentration of \( \text{A} \) to reduce to \( 2.5 \, \text{g L}^{-1} \) (if the initial concentration of \( \text{A} \) was \( 50 \, \text{g L}^{-1} \)) is ________. (Nearest integer)
Given: \( \log 2 = 0.3010 \).

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 \( 1^{\text{st}} \) order kinetics.]

Decomposition of \( A \) is a first order reaction at \( T(\mathrm{K}) \) and is given by \( \mathrm{A(g) \rightarrow B(g) + C(g)} \). In a closed \( 1 \, \mathrm{L} \) vessel, \( 1 \, \mathrm{bar} \) \( \mathrm{A(g)} \) is allowed to decompose at \( T(\mathrm{K}) \). After \( 100 \) minutes, the total pressure was \( 1.5 \, \mathrm{bar} \). What is the rate constant \( \left(\mathrm{in}\ \mathrm{min}^{-1}\right) \) of the reaction? \( (\log 2 = 0.3) \)

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with \( t_{1/2} = 3 \) hour. The percentage of sucrose remaining after \( 6 \) hours is ________ (Nearest integer)
(Given : \( \log 2 = 0.3010 \) and \( \log 3 = 0.4771 \))

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

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

For a first order reaction \( A \rightarrow B \)

\( x \) = ________ \( \text{min}. \) (Nearest integer)

Consider the given figure and choose the correct option:

\( \mathrm{A} \rightarrow \mathrm{B} \)
The above reaction is of zero order. Half-life of this reaction is \( 50 \, \mathrm{min} \). The time taken for the concentration of \( \mathrm{A} \) to reduce to one-fourth of its initial value is \( \_\_\_\_\_ \, \mathrm{min} \). [Nearest integer]

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

Consider the following data for the given reaction
\( 2\text{HI}(g) \rightarrow \text{H}_2(g) + \text{I}_2(g) \)

The order of the reaction is __________.

For the given first order reaction
\( \mathrm{A \to B} \)
the half life of the reaction is \( 0.3010\,\text{min} \). The ratio of the initial concentration of reactant to the concentration of reactant at time \( 2.0\,\text{min} \) will be equal to ________. (Nearest integer)

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: \( \log 2 = 0.3010 \))

The inactivation rate of viral preparation is proportional to the amount of virus. In the first minute after preparation, \( 10\% \) of the virus is inactivated. The rate constant for viral inactivation is ______ \( \times 10^{-3} \, \text{min}^{-1} \). (Nearest integer). [Use: \( \ln 10 = 2.303 \); \( \log_{10} 3 = 0.477 \); property of logarithm: \( \log x^{y} = y \log x \) ]

\( \mathrm{A(g)} \rightarrow 2\mathrm{B(g)} + \mathrm{C(g)} \) 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 that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is:
\( 2\mathrm{K_2Cr_2O_7} + 8\mathrm{H_2SO_4} + 3\mathrm{C_2H_6O} \rightarrow 2\mathrm{Cr_2(SO_4)_3} + 3\mathrm{C_2H_4O_2} + 2\mathrm{K_2SO_4} + 11\mathrm{H_2O} \)
If the rate of appearance of \( \mathrm{Cr_2(SO_4)_3} \) is \( 2.67 \, \text{mol} \, \text{min}^{-1} \) at a particular time, the rate of disappearance of \( \mathrm{C_2H_6O} \) at the same time is ____________ \( \text{mol} \, \text{min}^{-1} \). (Nearest integer)

$2\text{NO}\text{ (g)} + \text{Cl}_2\text{ (g)} \rightleftharpoons 2\text{NOCl}\text{(s)}$
This reaction was studied at \( -10^\circ \mathrm{C} \) and the following data was obtained.

\( [\mathrm{NO}]_0 \) and \( [\mathrm{Cl_2}]_0 \) are the initial concentrations and \( r_0 \) is the initial reaction rate.
The overall order of the reaction is ____________. (Round off to the Nearest Integer).

For a chemical reaction \( A \rightarrow B \), it was found that concentration of \( B \) is increased by \( 0.2 \, \mathrm{mol\,L^{-1}} \) in \( 30 \, \mathrm{min} \). The average rate of the reaction is _______ \( \times 10^{-1} \, \mathrm{mol\,L^{-1}\,h^{-1}} \). (in nearest integer)

Correct statements regarding Arrhenius equation among the following are:

A.   Factor \( e^{-\frac{E_a}{RT}} \) corresponds to fraction of molecules having kinetic energy less than Ea.

B.     At a given temperature, lower the Ea, faster is the reaction.

C.   Increase in temperature by about 10°C doubles the rate of reaction.

 D.  plot of \( \log k \) vs \( \frac{1}{T} \) gives a straight line with slope \(= -\frac{E_{\text{a}}}{R}\)

 Choose the correct answer from the options given below:

A student has studied the decomposition of a gas \( \mathrm{AB}_3 \), at \( 25^\circ \mathrm{C} \). He obtained the following data.

The order of the reaction is:

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

The rate constants for decomposition of acetaldehyde have been measured over the temperature range \( 700 \) — \( 1000 \) \( \mathrm{K} \). The data has been analysed by plotting \( \ln k \) vs \( \frac{10^3}{T} \) graph. The value of activation energy for the reaction is __________ \( \mathrm{kJ\ mol^{-1}} \). (Nearest integer) (Given: \( R = 8.31\ \mathrm{J\ K^{-1}\ mol^{-1}} \))

For the first order reaction \( \mathrm{A} \longrightarrow \mathrm{B} \), the half life is \(30 \ \mathrm{min}\). The time taken for \(75\%\) completion of the reaction is ______ \( \mathrm{min} \). (Nearest integer) (Given: \( \log 2 = 0.3010 \), \( \log 3 = 0.4771 \), \( \log 5 = 0.6989 \))

Reactant \( A \) converts to product \( D \) through the given mechanism (with the net evolution of heat):
\( A \rightarrow B \) slow; \( \Delta H = +\text{ve} \)
\( B \rightarrow C \) fast; \( \Delta H = -\text{ve} \)
\( C \rightarrow D \) fast; \( \Delta H = -\text{ve} \)
Which of the following represents the above reaction mechanism?

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

For a first reaction \( A \rightarrow B \) , the rate constant, \( k = 5.5 \times 10^{-14} \, \text{s}^{-1} \). The time required for \( 67\% \) completion of reaction is \( x \times 10^{-1} \) times the half life of reaction. The value of \( x \) is ______ (nearest integer) (Given : \( \log 3 = 0.4771 \) )

For the decomposition of azomethane, \( \mathrm{CH_3N_2CH_3(g) \rightarrow CH_3CH_3(g) + N_2(g)} \), a first order reaction, the variation in partial pressure with time at \( 600 \, \text{K} \) is given as:

The half life of the reaction is ________ \( \times 10^{-5} \, \text{s} \). [Nearest intager]

\( r = k[A] \) for a reaction, \( 50\% \) of \( A \) is decomposed in \( 120 \) minutes. The time taken for \( 90\% \) decomposition of \( A \) is ______ minutes.

The reaction \( 2A + B_2 \rightarrow 2AB \) is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of \( 3 \), the rate of the reaction increases by a factor of ________. (Round off to the Nearest Integer)

The equation \( k = (6.5 \times 10^{12}\, \text{s}^{-1}) e^{-26000\, \text{K}/T} \) is followed for the decomposition of compound A.

The activation energy for the reaction is ______ \( \text{kJ} \, \text{mol}^{-1} \). [Nearest integer]

(Given: \( R = 8.314 \, \text{J} \, \text{K}^{-1} \, \text{mol}^{-1} \) )

Given below are two statements:
Statement I: The rate law for the reaction \( \text{A} + \text{B} \rightarrow \text{C} \) is rate \( (r) = k[\text{A}]^{2}[\text{B}] \). When the concentration of both \( \text{A} \) and \( \text{B} \) is doubled, the reaction rate is increased "x" times.
Statement II:

The figure is showing " the variation in concentration against time plot" for a "y" order reaction.

The value of \( x + y \) is __________.

The reaction $\text{A}_2 + \text{B}_2 \rightarrow 2\text{AB}$ follows the mechanism

$\text{A}_2 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \text{A} + \text{A} \quad \text{(fast)}$

$\text{A} + \text{B}_2 \overset{k_2}{\longrightarrow} \text{AB} + \text{B} \quad \text{(slow)}$

$\text{A} + \text{B} \rightarrow \text{AB} \quad \text{(fast)}$

The overall order of the reaction is :

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

\( A \rightarrow B \)
The rate constants of the above reaction at \( 200 \, \text{K} \) and \( 300 \, \text{K} \) are \( 0.03 \, \text{min}^{-1} \) and \( 0.05 \, \text{min}^{-1} \) respectively.
The activation energy for the reaction is _____ \( \text{J} \)
(Nearest integer)
(Given: \( \ln 10 = 2.3 \)
\( R = 8.3 \, \text{J K}^{-1}\text{mol}^{-1} \)
\( \log 5 = 0.70 \)
\( \log 3 = 0.48 \)
\( \log 2 = 0.30 \) )

If compound A reacts with B following first order kinetics with rate constant \( 2.011 \times 10^{-3} \, \mathrm{s^{-1}} \). The time taken by A (in seconds) to reduce from \( 7 \, \mathrm{g} \) to \( 2 \, \mathrm{g} \) will be _______. (Nearest integer) [\( \log 5 = 0.698 \), \( \log 7 = 0.845 \), \( \log 2 = 0.301 \)]

At \( 30^\circ \text{C} \), the half life for the decomposition of \( \mathrm{AB_2} \) is \( 200 \, \text{s} \) and is independent of the initial concentration of \( \mathrm{AB_2} \). The time required for \( 80\% \) of the \( \mathrm{AB_2} \) to decompose is: (Given: \( \log 2 = 0.30 \), \( \log 3 = 0.48 \))

Consider the following reaction that goes from \( A \) to \( B \) in three steps as shown below:

Choose the correct option:

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

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

Consider the following phase reaction being carried out in a closed vessel at \( 25^\circ \text{C} \).
\( 2A(g) \rightarrow 4B(g) + C(g) \)

The pressure of \( C(g) \) at \( 30 \) minutes time interval would be ________ \( \text{mm Hg} \). (nearest integer)

Rate law for a reaction between A and B is given by \( r = k[A]^n[B]^m \) 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 \( \left( \frac{r_2}{r_1} \right) \) is:

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?

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

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

Some details of the above reactions are listed below.

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 \( 400 \, \text{kJ mol}^{-1} \), then the value of \( E_{a3} \) is ______ \( \text{kJ mol}^{-1} \) (nearest integer)

For a given chemical reaction
\( \gamma_{1} A + \gamma_{2} B \rightarrow \gamma_{3} C + \gamma_{4} D \)
Concentration of \( C \) changes from \( 10 \, \text{mmol dm}^{-3} \) to \( 20 \, \text{mmol dm}^{-3} \) in \( 10 \, \text{s} \). Rate of appearance of \( D \) is \( 1.5 \) times the rate of disappearance of \( B \) which is twice the rate of disappearance of \( A \). The rate of appearance of \( D \) has been experimentally determined to be \( 9 \, \text{mmol dm}^{-3}\text{s}^{-1} \). Therefore the rate of reaction is __________ \( \text{mmol dm}^{-3}\text{s}^{-1} \). (Nearest Integer)

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

Which of the following option is incorrect?

Observe the following reactions at \( T(\mathrm{K}) \).
I. \( A \rightarrow \text{products} \).
II. \( 5\,\mathrm{Br^- (aq)} + \mathrm{BrO_3^- (aq)} + 6\,\mathrm{H^+ (aq)} \rightarrow 3\,\mathrm{Br_2 (aq)} + 3\,\mathrm{H_2O (l)} \)

Both the reactions are started at \( 10.00 \) am. The rates of these reactions at \( 10.10 \) am are same. The value of \( -\dfrac{\Delta[\mathrm{Br^-}]}{\Delta t} \) at \( 10.10 \) am is \( 2 \times 10^{-4} \, \mathrm{mol\,L^{-1}\,min^{-1}} \). The concentration of \( A \) at \( 10.10 \) am is \( 10^{-2} \, \mathrm{mol\,L^{-1}} \). What is the first order rate constant (in \( \mathrm{min^{-1}} \)) of reaction I?

An organic compound undergoes first order decomposition. The time taken for decomposition to \( \left( \dfrac{1}{8} \right)^{\text{th}} \) and \( \left( \dfrac{1}{10} \right)^{\text{th}} \) of its initial concentration are \( t_{1/8} \) and \( t_{1/10} \) respectively. What is the value of \( \dfrac{t_{1/8}}{t_{1/10}} \times 10 \)? (\( \log 2 = 0.3 \))

For the first order reaction \( \mathrm{A \rightarrow 2B} \), \( 1 \) mole of reactant \( \mathrm{A} \) gives \( 0.2 \) moles of \( \mathrm{B} \) after \( 100 \) minutes. The half life of the reaction is _______ min. (Round off to the Nearest Integer)
[Use: \( \ln 2 = 0.69 \), \( \ln 10 = 2.3 \) Properties of logarithms: \( \ln x^{y} = y \ln x \); \( \ln \left(\dfrac{x}{y}\right) = \ln x - \ln y] \)

\( [A] \quad\rightarrow [B] \)
Reactant  Product 
If formation of compound \( [B] \) follows the first order of kinetics and after \( 70 \) minutes the concentration of \( [A] \) was found to be half of its initial concentration. Then the rate constant of the reaction is \( x \times 10^{-6} \ \text{s}^{-1} \). The value of \( x \) is _______. (Nearest Integer).

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

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 : \( \ln 10 = 2.303 \) and \( \log 2 = 0.3010 \))

The reaction \( 2\mathrm{NO} + \mathrm{Br}_2 \longrightarrow 2\mathrm{NOBr} \)
Takes places through the mechanism given below:
\(\text{NO} + \text{Br}_2 \Leftrightarrow \text{NOBr}_2\,(\text{fast})\)
 \( \mathrm{NOBr}_2 + \mathrm{NO} \longrightarrow 2\mathrm{NOBr} \) (slow)
The overall order of the reaction is ____.

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below
\( \mathrm{A(g)} \rightleftharpoons \mathrm{B(g)} + \mathrm{C(g)} \)

The magnitude of \( \frac{\Delta H^\circ}{R} \) calculated from the above data is ______. (Nearest integer)

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 \( t_2 \) (\( \text{s} \)), respectively. The ratio \( \frac{t_1}{t_2} \) will be:

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

\( \mathrm{N_2O_{5(g)}} \rightarrow 2\,\mathrm{NO_{2(g)}} + \dfrac{1}{2}\,\mathrm{O_{2(g)}} \) 
In the above first order reaction the initial concentration of \( \mathrm{N_2O_5} \) is \( 2.40 \times 10^{-2} \,\mathrm{mol\,L^{-1}} \) at \( 318 \,\text{K} \). The concentration of \( \mathrm{N_2O_5} \) after \( 1 \) hour was \( 1.60 \times 10^{-2} \,\mathrm{mol\,L^{-1}} \). The rate constant of the reaction at \( 318 \,\text{K} \) is _______ \( \times 10^{-3} \,\mathrm{min^{-1}} \). (Nearest integer)
[Given: \( \log 3 = 0.477, \\ \log 5 = 0.699 \)]

For a chemical reaction \( A + B \rightarrow \text{Product} \), the order is \( 1 \) with respect to \( A \) and \( B \).

What is the value of \( x \) and \( y \)?

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

For a reaction \( \mathrm{A} \rightarrow 2\mathrm{B} + \mathrm{C} \) the half lives are \( 100 \, \text{s} \) and \( 50 \, \text{s} \) when the concentration of reactant \( \mathrm{A} \) is \( 0.5 \) and \( 1.0 \, \text{mol} \, \text{L}^{-1} \) respectively. The order of the reaction is ______________. (Nearest Integer)

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

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

The temperature at which the rate constants of the given below two gaseous reactions become equal is _____ \( \mathrm{K} \). (Nearest integer)

\( \mathrm{X} \rightarrow \mathrm{Y} \quad k_{1} = 10^{6} e^{\frac{-30000}{T}} \)
\( \mathrm{P} \rightarrow \mathrm{Q} \quad k_{2} = 10^{4} e^{\frac{-24000}{T}} \)
Given: \( \ln 10 = 2.303 \)

Consider the following reaction \( \mathrm{A + B \rightarrow C} \).
The time taken for \( \mathrm{A} \) to become $1/4^{\text{th}}$ of its initial concentration is twice the time taken to become \( \tfrac{1}{2} \) of the same. Also, when the change of concentration of \( \mathrm{B} \) 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 ______.

\( t_{100\%} \) is the time required for the \( 100\% \) completion of the reaction while \( t_{1/2} \) is the time required for \( 50\% \) of the reaction to be completed. Which of the following option correctly represents the relation between \( t_{100\%} \) and \( t_{1/2} \) for zero and first order reactions respectively?

\( \mathrm{A} \rightarrow \) product (First order reaction).
Three sets of experiment were performed for a reaction under similar experimental conditions:
Run \( 1 \Rightarrow \) \( 100 \,\text{mL} \) of \( 10 \,\text{M} \) solution of reactant \( \mathrm{A} \)
Run \( 2 \Rightarrow \) \( 200 \,\text{mL} \) of \( 10 \,\text{M} \) solution of reactant \( \mathrm{A} \)
Run \( 3 \Rightarrow \) \( 100 \,\text{mL} \) of \( 10 \,\text{M} \) solution of reactant \( \mathrm{A} + 100 \,\text{mL} \) of \( \mathrm{H_2O} \) added.
The correct variation of rate of reaction is:

For \( \mathrm{A_2 + B_2 \rightleftharpoons
 2AB} \)
\( E_a \) for forward and backward reaction are \( 180 \) and \( 200 \ \mathrm{kJ\,mol^{-1}} \) respectively
If catalyst lowers \( E_a \) for both reaction by \( 100 \ \mathrm{kJ\,mol^{-1}} \). Which of the following statement is correct?

\( \mathrm{NO_2} \) required for a reaction is produced by decomposition of \( \mathrm{N_2O_5} \) in \( \mathrm{CCl_4} \) as by equation \( 2\mathrm{N_2O_{5(g)}} \rightarrow 4\mathrm{NO_{2(g)}} + \mathrm{O_{2(g)}} \).
The initial concentration of \( \mathrm{N_2O_5} \) is \( 3 \, \mathrm{mol\, L^{-1}} \) and it is \( 2.75 \, \mathrm{mol\, L^{-1}} \) after \( 30 \, \text{minutes} \).
The rate of formation of \( \mathrm{NO_2} \) is \( x \times 10^{-3} \, \mathrm{mol\, L^{-1}\, min^{-1}} \), value of \( x \) is _______. (nearest integer).

For a reaction taking place in three steps at same temperature, overall rate constant \( K = \frac{k_1 k_2}{k_3} \). If \( E_{a1}, E_{a2} \) and \( E_{a3} \) are \( 40 \), \( 50 \) and \( 60 \, \mathrm{kJ/mol} \) respectively, the overall \( E_a \) is _________ \( \mathrm{kJ/mol} \).

The number of neutrons and electrons, respectively, present in the radioactive isotope of hydrogen is:

A flask is filled with equal moles of \( A \) and \( B \). The half lives of \( A \) and \( B \) are \( 100 \, \text{s} \) and \( 50 \, \text{s} \) respectively and are independent of the initial concentration. The time required for the concentration of \( A \) to be four times that of \( B \) is ____________ \( \text{s} \). (Given: \( \ln 2 = 0.693 \))

For the reaction \( A \rightarrow \) products.

The concentration of \( A \) at \( 10 \) minutes is ________ \( \times 10^{-3} \, \text{mol L}^{-1} \) (nearest integer) 

Given above is the concentration vs time plot for a dissociation reaction: \( \mathrm{A} \rightarrow n\mathrm{B} \).
Based on the data of the initial phase of the reaction (initial \( 10 \, \text{min} \)), the value of \( n \) is______.

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

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

The half-life of \( ^{65}\mathrm{Zn} \) is \( 245 \, \text{days} \). After \( x \, \text{days} \), \( 75\% \) of original activity remained. The value of \( x \) in \( \text{days} \) is ______. (Nearest integer)
(Given: \( \log 3 = 0.4771 \) and \( \log 2 = 0.3010 \))

The number of incorrect statements 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.

The number of correct statement/s from the following is \( \_\_\_\_\_ \).
I. Larger the activation energy, smaller is the value of the rate constant
II. The higher is the activation energy, higher is the value of the temperature coefficient
III. At lower temperatures, increase in temperature causes more change in the value of \( k \) than at higher temperature
IV. A plot of \( \ln k \) vs \( \dfrac{1}{T} \) is a straight line with slope equal to \( -\dfrac{E_a}{R} \)

A \( \rightarrow \) D is an endothermic reaction occurring in three steps (elementary).
(i) A \( \rightarrow \) B \( \Delta H_i = +\text{ve} \)
(ii) B \( \rightarrow \) C \( \Delta H_{ii} = -\text{ve} \)
(iii) C \( \rightarrow \) D \( \Delta H_{iii} = -\text{ve} \)
Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of A \( \rightarrow \) D?

The activation energy of one of the reactions in a biochemical process is \( 532611 \, \mathrm{J \, mol^{-1}} \). When the temperature falls from \( 310 \, \mathrm{K} \) to \( 300 \, \mathrm{K} \), the change in rate constant observed is \( k_{300} = x \times 10^{-3} k_{310} \). The value of \( x \) is ____________
[Given: \( \ln 10 = 2.3 \)
\( R = 8.3 \, \mathrm{J \, K^{-1} \, mol^{-1}} \) ]

The correct reaction profile diagram for a positive catalyst reaction.

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

For the thermal decomposition of reactant \( \mathrm{AB(g)} \), the following plot is constructed.

The half-life of the reaction is ‘\( x \)’ \( \text{min} \). \( x = \) min ________. (Nearest integer)

The first order rate constant for the decomposition of \( \mathrm{CaCO_3} \) at \( 700 \,\mathrm{K} \) is \( 6.36 \times 10^{-3} \,\mathrm{s^{-1}} \) and activation energy is \( 209 \,\mathrm{kJ\, mol^{-1}} \). Its rate constant (in \( \mathrm{s^{-1}} \)) at \( 600 \,\mathrm{K} \) is \( x \times 10^{-6} \). The value of \( x \) is _______. (Nearest integer)
[Given : \( R = 8.31 \,\mathrm{J\, K^{-1}\, mol^{-1}} \); \( \log 6.36 \times 10^{-3} = -2.19 \), \( 10^{-4.79} = 1.62 \times 10^{-5} \) ]

The following data was obtained for chemical reaction given below at  975 K.

The order of the reaction with respect to \( \mathrm{NO} \) is __________. [Integer answer]

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 the following reaction, the rate expression of which is given below
\( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \)
\( \text{rate} = k[\mathrm{A}]^{1/2}[\mathrm{B}]^{1/2} \)
The reaction is initiated by taking \( 1\,\mathrm{M} \) 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 \( 0.1\,\mathrm{M} \) is __________ sec.

It has been found that for a chemical reaction with rise in temperature by \( 9 \, \mathrm{K} \) the rate constant gets doubled.
Assuming a reaction to be occurring at \( 300 \, \mathrm{K} \), the value of activation energy is found to be _______ \( \mathrm{kJ\,mol^{-1}} \). [nearest integer]
(Given \( \ln 10 = 2.3 \), \( R = 8.3 \, \mathrm{J\,K^{-1}\,mol^{-1}} \) and \( \log 2 = 0.30 \) )

For the reaction \( \mathrm{A} \to \mathrm{B} \), the rate constant \( k \) (in \( \text{s}^{-1} \)) is given by \( \log_{10} k = 20.35 - \frac{(2.47 \times 10^{3})}{T} \).
The energy of activation in \( \text{kJ mol}^{-1} \) is ________. (Nearest integer) [Given: \( R = 8.314 \, \text{J K}^{-1}\text{ mol}^{-1} \)]