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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 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 __________.

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 \( 2 = 0.3010 \))

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 ________ \( \text{kJ mol}^{-1} \).

\( t_{87.5} \) 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)

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.

\( \mathrm{A} \rightarrow \mathrm{B} \)
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]

\( \text{KClO}_3 + 6\text{FeSO}_4 + 3\text{H}_2\text{SO}_4 \rightarrow \text{KCl} + 3\text{Fe}_2(\text{SO}_4)_3 + 3\text{H}_2\text{O} \)
The above reaction was studied at \( 300 \, \text{K} \) by monitoring the concentration of \( \text{FeSO}_4 \) in which initial concentration was \( 10 \, \text{M} \) and after half an hour became \( 8.8 \, \text{M} \). The rate of production of \( \text{Fe}_2(\text{SO}_4)_3 \) is ______ \( \times 10^{-6} \, \text{mol L}^{-1} \text{s}^{-1} \). (Nearest integer)

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

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:

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: \( \log 2 = 0.3010 \), \( \log 3 = 0.4771 \), \( \log 5 = 0.6989 \))

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) [\( \log 5 = 0.698 \), \( \log 7 = 0.845 \), \( \log 2 = 0.301 \)]

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

Choose the correct option:

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 ____.

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: \( \ln 10 = 2.3 \) ; \( \log 2 = 0.3 \))

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 \( -\dfrac{E_a}{R} \)

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)