Chemical Kinetics

$\ce{A -> products}$ (First order reaction).

Three sets of experiment were performed for a reaction under similar experimental conditions.

Run 1 $\Rightarrow$ 100 mL of 10 M solution of reactant A

Run 2 $\Rightarrow$ 200 mL of 10 M solution of reactant A

Run 3 $\Rightarrow$ 100 mL of 10 M solution of reactant A + 100 mL of $\ce{H2O}$ added.

The correct variation of rate of reaction is

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

$\ce{X -> Y}$    $k_1 = 10^{6}\,e^{\frac{-30000}{T}}$

$\ce{P -> Q}$    $k_2 = 10^{4}\,e^{\frac{-24000}{T}}$

Given : $\ln 10 = 2.303$

• (A)Factor $\mathrm{e}^{-\mathrm{Ea}/\mathrm{RT}}$ 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$^\circ$C doubles the rate of reaction.
• (D)Plot of log k vs $\dfrac{1}{\mathrm{T}}$ gives a straight line with slope $= -\dfrac{\mathrm{Ea}}{\mathrm{R}}$.

The half life of the reaction is ‘x' min.

x = min. (Nearest integer)

Given above is the concentration vs time plot for a dissociation reaction : $\ce{A -> nB}$.

Based on the data of the initial phase of the reaction (initial 10 min), the value of n is .

• (I)$\ce{A -> products}$.
• (II)$\ce{5Br^- (aq) + BrO3^- (aq) + 6H^+ (aq) -> 3Br2 (aq) + 3H2O}$ ($l$)

$\ce{A -> D}$ is an endothermic reaction occurring in three steps (elementary).

(i) $\ce{A -> B}$ $\Delta H_\mathrm{i} = +$ve

(ii) $\ce{B -> C}$ $\Delta H_\mathrm{ii} = -$ve

(iii) $\ce{C -> D}$ $\Delta H_\mathrm{iii} = -$ve

Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of $\ce{A -> D}$ ?

At 27$^\circ$C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol$^{-1}$. The logarithm ratio of $\dfrac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is ….

(Consider that the frequency factor for both the reactions is same)

The half-life of $^{65}$Zn is 245 days. After x days, 75% of original activity remained. The value of x in days is . (Nearest integer)

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

An organic compound undergoes first order decomposition. The times taken for decomposition to $\left(\dfrac{1}{8}\right)^{\mathrm{th}}$ and $\left(\dfrac{1}{10}\right)^{\mathrm{th}}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively.

What is the value of $\dfrac{t_{1/8}}{t_{1/10}}\times 10$ ?

($\log 2 = 0.3$)

$\ce{A -> B}$ (first reaction)

$\ce{C -> D}$ (second reaction)

Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is $\times 10^{-1}$ hour$^{-1}$ (nearest integer).

For reaction $\ce{A -> P}$, rate constant $k = 1.5\times10^{3}$ s$^{-1}$ at 27$^\circ$C. If activation energy for the above reaction is 60 kJ mol$^{-1}$, then the temperature (in $^\circ$C) at which rate constant, $k = 4.5\times10^{3}$ s$^{-1}$ is . (Nearest integer)

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

• (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 $\ce{N2O5}$ is an example of the above reaction.
• (E)  is valid for the above reaction.

Consider the following gas phase reaction being carried out in a closed vessel at 25$^\circ$C.

$\ce{2A(g) -> 4B(g) + C(g)}$

Consider the first order reaction $\ce{R -> P}$.

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 ?

First order gas phase reaction

$\ce{A -> B + C}$

$p_\mathrm{i}$ = initial pressure of gas A, $p_\mathrm{t}$ = 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 : $\log 2 = 0.3010$)

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 $\log 3 = 0.4771$)

Decomposition of a hydrocarbon follows the equation $k = (5.5\times10^{11}\ \mathrm{s^{-1}})\ e^{\frac{-28000\,\mathrm{K}}{T}}$. The activation energy of reaction is kJ mol$^{-1}$. (Nearest Integer)

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

Given below are two statements :

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

Statement I : When Ea $= 12.6$ kcal/mol, the room temperature rate constant is doubled by a 10$^\circ$C increase in temperature (298 K to 308 K)

Statement II : For a first order reaction $\ce{A -> B}$,

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

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