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Consider the reaction \( a\mathrm{X} \rightarrow b\mathrm{Y} \), for which the rate constant at \( 30^\circ \text{C} \) is \( 1 \times 10^{-3} \, \text{mol}^{-1} \, \text{L} \, \text{s}^{-1} \). Which of the following statements are true?

A. When concentration of ‘\( \mathrm{X} \)’ 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 \( \mathrm{X} \).

D. Decomposition of \( \mathrm{N}_2\mathrm{O}_5 \) is an example of the above reaction.

E. is valid for the above reaction versus time.

Choose the correct answer from the options given below:

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) \( \big[ \, R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \, \big] \)

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)

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: \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( R = 8.3 \, \mathrm{J}\,\mathrm{K}^{-1}\,\mathrm{mol}^{-1} \), \( \ln 10 = 2.3 \)

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: \( R = 8.3 \, \mathrm{J\, K^{-1}\, mol^{-1}} \)

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:

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)

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 \( \log 3 = 0.4771 \))

10.

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

11.

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

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

12.

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:

13.

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: \( \log 2 = 0.3010 \))

14.

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:

15.

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)

16.

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?

17.

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?

18.

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 \( \dfrac{t_{1/8}}{t_{1/10}} \times 10 \)? (\( \log 2 = 0.3 \))

19.

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

\( \frac{1}{T} \, (\mathrm{K}^{-1}) \)	\( \log_{10} K_p \)
\( 0.05 \)	\( 3.5 \)
\( 0.06 \)	\( 2.5 \)
\( 0.07 \)	\( 1.5 \)

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

20.

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: \( \ln 10 = 2.303 \)

21.

\( t_{100\%} \) 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?

22.

\( \mathrm{A} \rightarrow \) 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:

23.

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______.

24.

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 \( \log 2 = 0.3010 \))

25.

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?

26.

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)

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