Chemical Kinetics · JEE Main previous year questions

1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true

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

First order gas phase reaction $\text{A}\to \text{B}+\text{C}$ $p_i=$ initial pressure of gas $\text{A}$, $p_t=$ total pressure of the reaction mixture at time $t$ Expression of rate constant $(\text{k})$ is

1. A.$\frac{1}{t}\ln \frac{p_i}{2p_i-p_t}$
2. B.$\frac{1}{t}\ln \frac{2p_i}{p_i-p_t}$
3. C.$\frac{1}{t}\ln \frac{p_i}{3p_i-2p_t}$
4. D.$\frac{1}{t}\ln \frac{3p_i}{4p_i-p_t}$

If the half life of a first order reaction is $6.93\text{ minutes}$ then the time required for completion of $99\%$ of the reaction will be _______ minutes . (Given : $\log 2=0.3010$)

Consider the first order reaction $\mathrm{R}\to \mathrm{P}$. The fraction of molecules decomposed in the given first order reaction can be expressed as

1. A.$1-e^{k_{1}t}$
2. B.$1+e^{k_{1}t}$
3. C.$1+e^{-k_{1}t}$
4. D.$1-e^{-k_{1}t}$

For a first order reaction $\mathrm{A}\to \mathrm{B}$ $$\begin{array}{ll}t/\min & [\mathrm{A}]/\mathrm{M}\\ 0& 0.6500\\ x& 0.0650\\ 20& 0.00065\end{array}$$ $x=$ ____ $\min$. (Nearest integer)

$t_{100\%}$ 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 ?

1. A.$t_{100\%}=(t_{1/2}{)}^2$ and $t_{100\%}=(t_{1/2}{)}^{-\infty }$
2. B.$t_{100\%}=2t_{1/2}$ and $t_{100\%}=(t_{1/2}{)}^{\infty }$
3. C.$t_{100\%}=2t_{1/2}$ and $t_{100\%}=(2t_{1/2}{)}^2$
4. D.$t_{100\%}=(t_{1/2}{)}^{\infty }$ and $t_{100\%}=2t_{1/2}$

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

1. A.A and B Only
2. B.A, B and C Only
3. C.A, B, D and E Only
4. D.C and D Only

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

1. A.30
2. B.9
3. C.3
4. D.0.9

$\text{A}\to \text{B}$ (first reaction) $\text{C}\to \text{D}$ (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 ________ $\times 10^{-1}{\text{ hour}}^{-1}$ (nearest integer).

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

1. A.1.741
2. B.0.1741
3. C.17.41
4. D.3.482

Observe the following reactions at $T(\text{K})$. I. $\text{A}\to \text{products}$. II. $5{\text{Br}}^{-}(\text{aq})+{\text{BrO}}_3^{-}(\text{aq})+6{\text{H}}^{+}(\text{aq})\to 3{\text{Br}}_2(\text{aq})+3{\text{H}}_2\text{O}(\text{l})$ Both the reactions are started at 10.00 am . The rates of these reactions at 10.10 am are same. The value of $-\frac{\Delta [{\text{Br}}^{-}]}{\Delta t}$ at 10.10 am is $2\times 10^{-4}{\text{ mol L}}^{-1}{\text{ min}}^{-1}$. The concentration of A at 10.10 am is $10^{-2}{\text{ mol L}}^{-1}$. What is the first order rate constant (in ${\text{min}}^{-1}$ ) of reaction $I$ ?

1. A.$4\times 10^{-3}$
2. B.$2\times 10^{-3}$
3. C.$10^{-3}$
4. D.$10^{-2}$

$\mathrm{A}\to$ product (First order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions: Run $1\Rightarrow 100\mathrm{mL}$ of 10 M solution of reactant A Run $2\Rightarrow 200\mathrm{mL}$ of 10 M solution of reactant A Run $3\Rightarrow 100\mathrm{mL}$ of 10 M solution of reactant $\mathrm{A}+100\mathrm{mL}$ of ${\mathrm{H}}_2\mathrm{O}$ added. The correct variation of rate of reaction is

1. A.Run $1=$ Run $2=$ Run 3
2. B.Run $3<$ Run $1<$ Run 2
3. C.Run $1<$ Run $2<$ Run 3
4. D.Run $3<$ Run $1=$ Run 2

The temperature at which the rate constants of the given below two gaseous reactions become equal is ____ K. (Nearest integer) $\mathrm{X}⟶\mathrm{Y},{\mathrm{k}}_1=10^6{e}^{\frac{-30000}{\mathrm{T}}}$ $\mathrm{P}⟶\mathrm{Q},{\mathrm{k}}_2=10^4{e}^{\frac{-24000}{\mathrm{T}}}$ Given : $\ln 10=2.303$

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 $20\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. If ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are the rate constants of first and second reaction respectively at 300 K , then $\ln \frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}$ will be ____. (nearest integer) $\left[\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}\right]$

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is : $C{H}_{3}Br+N{u}^{-}⟶C{H}_{3}Nu+B{r}^{-}$

1. A.$Cl{O}_4^{-}>C{H}_{3}CO{O}^{-}>O{H}^{-}>Ph{O}^{-}$
2. B.$O{H}^{-}>Ph{O}^{-}>C{H}_{3}CO{O}^{-}>Cl{O}_4^{-}$
3. C.$C{H}_{3}CO{O}^{-}>Ph{O}^{-}>O{H}^{-}>Cl{O}_4^{-}$
4. D.$Ph{O}^{-}>O{H}^{-}>C{H}_{3}CO{O}^{-}>Cl{O}_4^{-}$

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

1. A.$6.9\times 10^{-4}$
2. B.$6.9\times 10^{-3}$
3. C.$6.9\times 10^{-1}$
4. D.$6.9\times 10^{-2}$

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 $t_2$ (s), respectively. The ratio $t_1/t_2$ will be:

1. A.$\frac{4}{3}$
2. B.$\frac{3}{2}$
3. C.$\frac{3}{4}$
4. D.$\frac{2}{3}$

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

1. A.$(n-m)$
2. B.$2^{(n-m)}$
3. C.$\frac{1}{2^{m+n}}$
4. D.$(m+n)$

1. A.${\text{Ea}}_2>{\text{Ea}}_1>{\text{Ea}}_3$
2. B.${\text{Ea}}_1>{\text{Ea}}_3>{\text{Ea}}_2$
3. C.${\text{Ea}}_3>{\text{Ea}}_2>{\text{Ea}}_1$
4. D.${\text{Ea}}_1>{\text{Ea}}_2>{\text{Ea}}_3$

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

1. A.$0.5\text{ hour}$
2. B.$15\text{ min}$
3. C.$60\text{ min}$
4. D.$4\text{ hour}$

In a reaction $A+B\to C$, initial concentrations of $A$ and $B$ are related as $[A{]}_0=8[B{]}_0$. 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?

1. A.$20\min$
2. B.$40\min$
3. C.$80\min$
4. D.$60\min$