Chemical Kinetics (23rd Nov) - Live Session

$The forward rate constant for the elementary$
$reversible gaseous reaction$
$C_{2} H_{6} ⇌ 2 {CH}_{3} is 1.57 x 10^{- 3} s^{- 1} at 100 K$
$What is the rate constant for thebackward reaction$
$at this temperature if 10^{- 4} moles of {CH}_{3} and 10$
$moles of C_{2} H_{6} are present in a 10 liter vessel at$
$equilibrium .$
1.   $1.57 x 10^{9} L {mol}^{- 1} s^{- 1}$
2.   $1.57 x 10^{10} L {mol}^{- 1} s^{- 1}$
3.   $1.57 x 10^{11} L {mol}^{- 1} s^{- 1}$
4.   $1.57 x 10^{7} L {mol}^{- 1} s^{- 1}$

$The kinetic data for the given reaction$
$A (g) + 2 B (g) \overset{k}{\to} c (g) is provided in$
$the following table for three$
$experiments at 300 K$

Ex. No.	[A/M]	[B/M]	Initial rate ( $M s e c^{- 1}$ )
1.	0.01	0.01	$6.930 x 10^{- 6}$
2.	0.02	0.01	$1.386 x 10^{- 6}$
3.	0.02	0.01	$1.386 x 10^{- 5}$

$In another experiment starting with initial$
$concentration of 0.5 and 1 M respectively$
$for A and B at 300 K, find the rate of$
$raction after 50 minutes from start of$
$experiment (in M / \sec) .$

1.   $6.93 x 10^{- 4}$ M/sec
2.   $0.25 x 10^{- 7}$ M/sec
3.   $4.33 x 10^{- 5}$ M/sec
4.   $3.46 x 10^{- 4}$ M/sec

$The reaction A (g) + 2 B (g) \overset{}{\to} C (g) is$
$an elementary reaction . In an experiment$
$involving this reaction, the initial partial$
$pressures of A and B are P_{A} = 0.40 atm$
$and P_{B} = 1.0 atm respectively .$
$When P_{C} = 0.3 atm, the rate of the reaction$
$relative to the initial rate is :$
1.   $\frac{1}{12}$
2.   $\frac{1}{50}$
3.   $\frac{1}{25}$
4.   $None of these$

$Two first order reaction have half - lives in$
$the ratio 8 : 1 . Calculate the ratio of time$
$intervals t_{1} : t_{2} . The time t_{1} and t_{2} are the$
$time period for (\frac{1}{4}) th and (\frac{3}{4}) th completion .$
1. 1 : 0.301
2. 0.125 : 0.602
3. 1 : 602
4. None of these

$Reaction A + B \overset{}{\to} C + D follows rate$
$law, r = k {[A]}^{1 / 2} {[B]}^{1 / 2} starting with 1 M pof$
$A and B each . what is the time taken for$
$concentration of A become 0.1 M ?$
$[Given k = 2.303 x 10^{- 2} \sec^{- 1}] .$
1. 10 sec
2. 100 sec
3. 1000 sec
4. 434 sec

$For the two reactions I : A \overset{}{\to} B; II : C \overset{}{\to} D$
$following graph is obtained .$

Which of the following is true:
a.   $If [B] = [A] then at that time [B] < [D]$
b.   $If [C] = [A] then at that time [B] < [D]$
c.   ${(t_{100 %})}_{reaction I} : {(t_{100 %})}_{reaction II}$
d.   $[A] = [C] at t = \frac{\sqrt{3}}{4} \min .$

1. a,b
2.a,b,c
3.c,d
4. a,d

$The reaction A (g) \overset{}{\to} B (g) + 2 C (g) is$
$a first order reaction with rate constant$
$2.772 x 10^{- 3} s^{- 1} . Starting with 0.1 mole$
$of A in 2 liter vessel, find the concentration$
$of A after 250 \sec when the reaction is$
$allowed to take place at constant pressure$
$at 300 K .$
1. 0.0125 M
2. 0.025 M
3. 0.05 M
4. None of these

$For a first order homogeneous gaseous$
$reaction, A \overset{}{\to} 2 B + C If the total$
$pressure after time t was P_{t} and after long$
$time (t \overset{}{\to} \infty) was P_{\infty} then k in terms$
$of P_{t}, P_{\infty} and t is :$
1.   $k = \frac{2.303}{t} \log (\frac{P_{\infty}}{P_{\infty} - P_{t}})$
2.   $k = \frac{2.303}{t} \log (\frac{2 P_{\infty}}{P_{\infty} - P_{t}})$
3.   $k = \frac{2.303}{t} \log (\frac{2 P_{\infty}}{3 (P_{\infty} - P_{t})})$
4.   $None of these$

$A (aq) \overset{}{\to} B (aq) + C (aq) is a first order reaction . Time t \infty moles of reagent n_{1} n_{2} Reaction progress is measure with help of titration of reagent' R' . If all A, B, and C reacted with reagent and have' n' factors [n factor; eq . wt . = \frac{mol . wt .}{n}] in the ratio of 1 : 2 : 3 with the reagent . The k in terms of t, n_{1}, and n_{2} is :$
1.   $k = \frac{1}{t} In (\frac{n_{2}}{n_{2} - n_{1}})$
2.   $k = \frac{1}{t} In (\frac{2 n_{2}}{n_{2} - n_{1}})$
3. $k = \frac{1}{t} In (\frac{4 n_{2}}{n_{2} - n_{1}})$
4.   $k = \frac{1}{t} In (\frac{4 n_{2}}{5 (n_{2} - n_{1})})$

10.

The gaseous decomposition reaction, A(g) 2B(g) + C(g) is observed to first order over the excess of liquid water at $25 ° C$ It is found that after 10 minutes the total pressure of the system is 188 torr and after a very long time, it is 388 torr. The rate constant of the reaction $(in {hr}^{- 1})$ is :
[Given : vapour pressure of $H_{2} O$ at $25 °$ is 28 torr (In 2 = 0.7, In 3 = 1.1, In 10 = 2.3)]
1. 0.02
2. 1.2
3. 0.2
4. None of these

11.

$The reaction, Sucrose \overset{H^{+}}{\to} Glucose + Fructose, takes place at a certain temperature while the volume of solution is maintained at I litre . At time zero the initial rotation of the mixture is 34 ° . After 30 minutes the total rotation of solution is 19 ° and after a very long time, the total rotation is - 11 ° C . Find the time when the solution was optically inactive .$

1. 135 min
2. 103.7 min
3. 38.7 min
4. 45 min

12.

$A gaseous compound A reacts by three$
$independent first - order processes$
$(as shown in the figure) with rate$
$constant$
$2 x 10^{- 3}$
$3 x 10^{- 3}$
$and$
$1.93 x 10^{- 3} \sec^{- I}$
$for products$
$B, C, and D respectively . If initially pure$
$A was taken in a closed container with$
$P = 8 atm, then the partial pressure$
$of B (in atm) after 100 \sec from the$
$start of experiment .$

1. 0.288
2. 0.577
3. 1.154
4. None of these

13.

$A copmound a dissociate by two parallel first order paths at certain temperature A (g) \overset{k_{1} (\min^{- 1})}{\to} 2 B (g) k_{1} = 6.93 x 10^{- 3} \min^{- 1} A (g) \overset{k_{1} (\min^{- 1})}{\to} C (g) k_{2} = 6.93 x 10^{- 3} \min^{- 1} The reaction started with 1 mole of pure of' a' in 1 liter closed container with initial pressure 2 atm . What id the pressure (in atm) developed in container after 50 minutes from start of experiment ?$

1. 1.25
2. 0.75
3. 1.50
4. 2.50

14.

For the given hypothetical elementary parallel reaction,

Initially, only 2 moles of A are present. The total no. of moles of A, B, and C at the end of 75% reaction are:
1. 2
2. 3
3. 4
4. 3.5

15.

A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in presence of a catalyst at the same rate with same frequency factor, the temperature required is 400 K the activation energy of the reaction, if the catalyst lowers the activation energy barrier by 16 kJ/mol is:
1. 100 kJ/mol
2. 80 kJ/mol
3. 60 kJ/mol
4. None of th above

16.

$Consider the reaction .$

$The rate constant for two parallel reactions were found to be 10^{- 2} {dm}^{3} {mol}^{- 1} s^{- 1} and 4 x 10^{- 2} {dm}^{3} {mol}^{- 1} s^{- 1} . If the corresponding energies of activation of the parallel reaction are 100 and 120 K J / mol respecctively, the net energy of activation (E_{a}) of A is$
1. 100 kJ/mol
2. 120 kJ/mol
3. 116 kJ/mol
4. 220 kJ/mol

17.

$A reaction takes place in various steps . The rate constant for first, second, third, and fifth step are k_{1}, k_{2}, k_{3} and k_{5} respectively . The overall rate constant is given by k = \frac{k_{2}}{k_{3}} {(\frac{k_{1}}{k 5})}^{1 / 2} If activation energy are 40, 60, 50, and 10 kJ / mol respectively, the overall energy of activation (kJ / mol) is :$
1. 10
2. 20
3. 25
4. None of the above

18.

$For reaction A \overset{}{\to} B, the rate constant k_{1} = A_{1} e^{- E_{a_{1}} / (RT)} and for the reaction X \to y, the rate constant k_{2} = A_{2} e^{- E_{a_{2}} / (RT)} . If A_{1} = 10^{8} A_{2} = 10^{10} a n d E_{a_{1}} = 600 cal / mol, E_{a_{2}} = 1800 cal / mol, then the temperature at which k_{1} = k_{2} is (given : R = 2 cal / K - mol)$
1.   $1600 K$
2.   $1200 x 4.606 K$
3.   $\frac{1200}{4.606} K$
4.   $\frac{600}{4.606} K$

19.

$For first - order parallel reaction k_{1} and k_{2} are 4 and 2 \min^{- 1} respectively at 300 K . If the activation energies for the formation of B and C are respectively 30, 000 and 38, 314 J / mol respectively . The temperature at which B and C will be obtained in the equimolar ratio is :$

1. 757.48 K
2. 378.74 K
3. 600.91 K
4. None of the above

20.

$The folowing mechanism has been$
$proposed for the exothermic catalyzed$
$complex reaction$
$A + B \underset{fast}{\overset{slow}{⇌}} IAB \overset{k_{1}}{\to} AB + I \overset{k_{2}}{\to} P + A$
$If k_{1} is much smaller than k_{2}, the most$
$suitable qualitative plot of potential$
$energy (P . E .) versus$
$reaction co - ordinate (R . C .) for$
$the above reaction$
1.
2.
3.
4.

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