jee main chemistry important questions | Chemical Kinetics jee main questions FREE

Q 11 :

A molecule undergoes two independent first-order reactions whose respective half-lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is _______ min. (Nearest integer) [2023]

(2)

$K_{1} = \frac{\ln 2}{12}, K_{2} = \frac{\ln 2}{3}$

$K = K_{1} + K_{2} = \frac{\ln 2}{12} + \frac{\ln 2}{3}$

$\frac{\ln 2}{t} = \frac{\ln 2}{12} + \frac{\ln 2}{3} \Rightarrow \frac{1}{t} = \frac{1}{12} + \frac{1}{3}$

$\frac{1}{t} = \frac{5}{12} \Rightarrow t = \frac{12}{5} = 2 min$

Q 12 :

$t_{87.5}$ 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) [2023]

(3)

$a_{t} = a_{0} \times \frac{12.5}{100} = \frac{a_{0}}{8} (87.5 % completion)$

$a_{0} \overset{t_{1 / 2}}{\to} a_{0 / 2} \overset{t_{1 / 2}}{\to} a_{0 / 4} \overset{t_{1 / 2}}{\to} \frac{a_{0}}{8}$

$t_{87.5} = 3 t_{1 / 2}$ $∴$ $x = 3$

Q 13 :

$A (g) \to 2 B (g) + C (g)$ is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ______ mm Hg. (Nearest integer) [2023]

(2200)

$\begin{matrix} A (g) & ⟶ & 2 B (g) & + & C (g) \\ t = 0800 & - & - \\ t = (10 min) & 800 - P & 2 P & P \end{matrix}$

$P_{T} = 800 - P + 2 P + P$

$= 800 + 2 P = 1600$

So $P = 400 mm$

So $t_{1 / 2} = 10 min$

Given time = 30 min.

So for 1st order reaction $C_{t} = \frac{C_{0}}{{(2)}^{n}}$

$n = \frac{t}{t_{1 / 2}} = \frac{30}{10} = 3$ ; $n =$ number of half life

$C_{t} = \frac{800}{{(2)}^{3}} = 100 mm of Hg$

So After 30 minutes, $P = 700 mm$

$P_{A} = 800 - 700 = 100,$ $P_{B} = 1400,$ $P_{C} = 700$

$P_{T}$ of reaction mixture $= 100 + 1400 + 700 = 2200 mm of Hg$

Q 14 :

For the zero order reaction A → B + S, initial concentration of A is 0.1 M. If [A] = 0.08 M after 10 minutes, then half life period is.

(25)

$t_{\frac{1}{2}} = \frac{a_{0}}{2 k}$

Q 15 :

$t_{100 %}$ 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? [2026]

$t_{100 %} = {(t_{1 / 2})}^{2}$ and $t_{100 %} = {(t_{1 / 2})}^{- \infty}$
$t_{100 %} = 2 t_{1 / 2}$ and $t_{100 %} = {(t_{1 / 2})}^{\infty}$
$t_{100 %} = 2 t_{1 / 2}$ and $t_{100 %} = {(2 t_{1 / 2})}^{2}$
$t_{100 %} = {(t_{1 / 2})}^{\infty}$ and $t_{100 %} = 2 t_{1 / 2}$

1

2

3

4

(2)

For a zero order reaction :

$t_{100 %} = \frac{a_{0}}{k} and t_{1 / 2} = \frac{a_{0}}{2 k}$

Thus $t_{100 %} = 2 t_{1 / 2}$

For a first order reaction :

$t_{100 %} = \infty and t_{1 / 2} = \frac{0.693}{k}$

Thus $t_{100 %} = {(t_{1 / 2})}^{\infty}$

Q 16 :

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

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 $N_{2} O_{5}$ is an example of the above reaction.

E. In is valid for the above reaction.

Choose the correct answer from the options given below: [2026]

A and B only
A, B and C only
A, B, D and E only
C and D only

1

2

3

4

(1)

For an $n^{th}$ order reaction, units of rate constant are : ${({mol L}^{- 1})}^{1 - n} s^{- 1}$ . As given in question units of rate constant are ${mol}^{- 1} {Ls}^{- 1}$ . Comparing the two, $n = 2$ i.e. the reaction is a second order reaction.

Rate of reaction, $r = k {[X]}^{2}$ and thus if [X] is increased 4 times rate becomes 16 times. Statement C, D and E are true for first order reaction.

Q 17 :

Consider the first order reaction $R \to P$ . The fraction of molecules decomposed in the given first order reaction can be expressed as [2026]

$1 - e^{k_{1} t}$
$1 + e^{k_{1} t}$
$1 + e^{- k_{1} t}$
$1 - e^{- k_{1} t}$

1

2

3

4

(4)

For a first order reaction, concentration of reactants ( $a_{t}$ ) at a given time $t$ is given by $a_{t} = a_{0} e^{- k t}$

Fraction of molecules decomposed at time $t$

$= \frac{a_{0} - a_{t}}{a_{0}} = \frac{a_{0} - a_{0} e^{- k t}}{a_{0}} = 1 - e^{- k t}$

Q 18 :

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? [2026]

The order of all the three reactions is same.
The rate constant of reaction 3 is larger than the rate constant of reaction 2 if the order of reaction is same for both.
The SI unit of rate constant of reaction 1 is $s^{- 1}$ .
Thermal decomposition of HI on gold surface is an example of reaction 2.

1

2

3

4

(2)

(1) For a zero-order reaction: ${[R]}_{t} = {[R]}_{0} - k t$ . Curve 1 is thus a zero-order reaction. Curves (2) and (3) are not zero order reactions.

(2) As [R] falls more sharply for 3 than for 2, rate constant for 3 is more than that of 2 for same order reaction.

(3) For a zero-order reaction (curve 1), unit of rate constant is ${mol L}^{- 1} s^{- 1}$ .

(4) The thermal decomposition of HI on gold surface is an example of zero order reaction.

Q 19 :

First order gas phase reaction

$A \to B + C$

$p_{i} = initial pressure of gas A$ ,

$p_{t} = total pressure of the reaction mixture at time t$

Expression of rate constant ( $k$ ) is [2026]

$\frac{1}{t} \ln \frac{p_{i}}{2 p_{i} - p_{t}}$
$\frac{1}{t} \ln \frac{2 p_{i}}{p_{i} - p_{t}}$
$\frac{1}{t} \ln \frac{p_{i}}{3 p_{i} - 2 p_{t}}$
$\frac{1}{t} \ln \frac{3 p_{i}}{4 p_{i} - p_{t}}$

1

2

3

4

(1)

$\begin{array}{lcccc} A & \to & B & + \\ t = 0 (press.) & p_{i} & 0 \\ t = t (press.) & p_{i} - p & p \end{array} \begin{matrix} C \\ 0 \\ p & total = p_{i} + p = p_{t} \end{matrix}$

$p = p_{t} - p_{i}$

Rate constant $k$ for a first order reaction is

$k = \frac{1}{t} \ln \frac{p_{i}}{p_{i} - p} = \frac{1}{t} \ln \frac{p_{i}}{p_{i} - (p_{t} - p_{i})} = \frac{1}{t} \ln \frac{p_{i}}{2 p_{i} - p_{t}}$

Q 20 :

For a first order reaction A $\to$ B

t/min [A]/M

0 0.6500

$x$ 0.0650

20 0.00065

$x =$ _______ min. (Nearest integer) [2026]

(7)

For a first order reaction:

$k = \frac{2.303}{t} \log \frac{{[A]}_{o}}{{[A]}_{t}}$

For $t = x min$

$k = \frac{2.303}{x} \log \frac{0.65}{0.065}$

$k = \frac{2.303}{x} \log 10$ $\dots (I)$

For $t = 20 min$

$k = \frac{2.303}{20} \log \frac{0.65}{0.00065}$

$k = \frac{2.303}{20} \log 1000$ $\dots (II)$

Equating I and II

$\frac{2.303}{x} \log 10 = \frac{2.303}{20} \log 1000$

$\frac{2.303}{x} \times 1 = \frac{2.303}{20} \times 3$

$x = 6.67 ≃ 7$

Q 21 :

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) [2026]

(46)

For a first order reaction :

$k = \frac{2.303}{t} \log \frac{{[A]}_{_{0}}}{{[A]}_{t}}$

For $t = t_{1 / 2}$

$k = \frac{2.303}{t_{1 / 2}} \log \frac{{[A]}_{0}}{{[A]}_{0} / 2}$

$k = \frac{2.303}{t_{1 / 2}} \log 2$ $\dots (I)$

For $t = t_{99 %}$

$k = \frac{2.303}{t_{99 %}} \log \frac{{[A]}_{0}}{0.01 {[A]}_{0}}$

$k = \frac{2.303}{t_{99 %}} \log 100$ $\dots (II)$

Equating I and II

$\frac{2.303}{t_{99 %}} \log 100 = \frac{2.303}{t_{1 / 2}} \log 2$

$\frac{2.303}{t_{99 %}} \times 2 = \frac{2.303}{t_{1 / 2}} \times 0.3010$

$t_{99 %} = 6.6445 t_{1 / 2}$

$= 6.6445 \times 6.93 min = 46.05 min$

Q 22 :

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) [2026]

(25)

Equal percentage of reaction occurs in equal time interval for a first order reaction.

$100 \overset{t_{1 / 2} = 3 h}{\to} 50 \overset{t_{1 / 2} = 3 h}{\to} 25$

Topic Question Set

Q 11 :

A molecule undergoes two independent first-order reactions whose respective half-lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is _______ min. (Nearest integer) [2023]

Q 13 :

$A (g) \to 2 B (g) + C (g)$ is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ______ mm Hg. (Nearest integer) [2023]

Q 14 :

For the zero order reaction A → B + S, initial concentration of A is 0.1 M. If [A] = 0.08 M after 10 minutes, then half life period is.

Q 17 :

Consider the first order reaction $R \to P$ . The fraction of molecules decomposed in the given first order reaction can be expressed as [2026]

Q 18 :

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? [2026]

Q 19 :

First order gas phase reaction

$A \to B + C$

$p_{i} = initial pressure of gas A$ ,

$p_{t} = total pressure of the reaction mixture at time t$

Expression of rate constant ( $k$ ) is [2026]

Q 20 :

For a first order reaction A $\to$ B

t/min [A]/M

0 0.6500

$x$ 0.0650

20 0.00065

$x =$ _______ min. (Nearest integer) [2026]

Q 21 :

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) [2026]

Q 22 :

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) [2026]

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 11 : A molecule undergoes two independent first-order reactions whose respective half-lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is _______ min. (Nearest integer) [2023]

Q 12 : t87.5 is the time required for the reaction to undergo 87.5% completion and t50 is the time required for the reaction to undergo 50% completion. The relation between t87.5 and t50 for a first-order reaction is t87.5=x×t50. The value of x is _______. (Nearest Integer) [2023]

Q 13 : A(g)→2B(g)+C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ______ mm Hg. (Nearest integer) [2023]

Q 14 : For the zero order reaction A → B + S, initial concentration of A is 0.1 M. If [A] = 0.08 M after 10 minutes, then half life period is.

Q 15 : t100% is the time required for the 100% completion of the reaction while t1/2 is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between t100% and t1/2 for zero and first order reactions respectively? [2026]

Q 17 : Consider the first order reaction R→P. The fraction of molecules decomposed in the given first order reaction can be expressed as [2026]

Q 18 : 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? [2026]

Q 19 : First order gas phase reaction A→B+C pi=initial pressure of gas A, pt=total pressure of the reaction mixture at time t Expression of rate constant (k) is [2026]

Q 20 : For a first order reaction A → B t/min [A]/M 0 0.6500 x 0.0650 20 0.00065 x= _______ min. (Nearest integer) [2026]

Q 21 : 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) [2026]

Q 22 : Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with t1/2 = 3 hour. The percentage of sucrose remaining after 6 hours is _______ (Nearest integer) (Given: log 2 = 0.3010 and log 3 = 0.4771) [2026]

Want Us to Email you About Special Offers & Updates?

Q 11 :

A molecule undergoes two independent first-order reactions whose respective half-lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is _______ min. (Nearest integer) [2023]

Q 13 :

$A (g) \to 2 B (g) + C (g)$ is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ______ mm Hg. (Nearest integer) [2023]

Q 14 :

For the zero order reaction A → B + S, initial concentration of A is 0.1 M. If [A] = 0.08 M after 10 minutes, then half life period is.

Q 17 :

Consider the first order reaction $R \to P$ . The fraction of molecules decomposed in the given first order reaction can be expressed as [2026]

Q 18 :

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? [2026]

Q 19 :

First order gas phase reaction

$A \to B + C$

$p_{i} = initial pressure of gas A$ ,

$p_{t} = total pressure of the reaction mixture at time t$

Expression of rate constant ( $k$ ) is [2026]

Q 20 :

For a first order reaction A $\to$ B

t/min [A]/M

0 0.6500

$x$ 0.0650

20 0.00065

$x =$ _______ min. (Nearest integer) [2026]

Q 21 :

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) [2026]

Q 22 :

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) [2026]