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Chemical Kinetics Test - 7

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Chemical Kinetics Test - 7

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Question 1
4 / -1

The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be (Given, R = 8.314 J K^-1 mol^-1, log2 = 0.3010).

A
53.6 kJ mol-1

B
48.6 kJ mol-1

C
58.5 kJ mol^-1

D
60.5 kJ mol^-1

Solution
Question 2
4 / -1

In the following reaction
N₂O N₂+O
k = (5.0 x 10¹¹ L mol^-1s^-1) e ^-29000R/T, E_a (energy o f activation) is

A
5.0 x 10¹¹ kcal mol^-1

B
29000 kcal mol^-1

C
58.0 kcal mol^-1

D
- 29000 kcal mol^-1

Solution

By Arrhenius equation
Question 3
4 / -1

Rate of a reaction can be expressed by Arrhenius equation as k = Ae^-EalRT. In this equation, E_a represents.

A
the energy above which all the colliding molecules will react

B
the energy below which colliding molecules will not react

C
the total energy of the reacting molecules at a temperature T

D
the fraction of molecules with energy greater than the activation energy of the reaction

Solution

E_a (activation energy) is the energy required to activate the reactant so that they may collide and give the final product. Below point B, the reactants will not react at all.
Question 4
4 / -1

In the upper atmosphere, form ation of H₂O₂ takes place as
H₂O+O → 2OH → H₂0₂
ΔH⁰ = 72.0 Kj mol^-1; E_a= 77.0 kJ mol^-1
E_a for the bim olecular recombination of two OH radicals to form H₂O and O is

A
149 kJ mol^-1

B
-149 kJ mol^-1

C
5 kJ mol^-1

D
-5 kJ mol^-1

Solution
Question 5
4 / -1

How much rate is affected in the presence of catalyst at 300 K?

A
20 times

B
14 times

C
28 times

D
2 times

Solution

k₁(no catalyst) = Ae ^-Ea/RT
∴
∴
Thus, rate is affected (28.03) times.
k₁ (no catalyst) = Ae^-E_a/RT
k₂ (with catalyst) = Ae^{-(E_a - 2)/RT}
Question 6
4 / -1

For a reaction,
A → Product
t₅₀ = 100 min at temprature T₁
and t₅₀= 80 min at temprature T₂
Thus,

A
T₁ > T2 and reaction is endothermic

B
T2 > T₂ and reaction exothermic

C
T₁ > T₂ and reaction is exothermic

D
T₂ > T₁ and reaction can be exothermic or endothermic

Solution

On increasing temperature, number of collisions hence kinetic energy increases.
Thus,

Thus rate of the reaction or rate constant increases with increase in temperature.
Half-life of any reaction
Thus, half-life decreases with increase in temperature, reaction may be exothermic or endothermic.
Thus,
Question 7
4 / -1

Rate constant (k) of a reaction has least value at

A
high T and high E_a

B
high T and low E_a

C
low T and low E_a

D
low T and high E_a

Solution

k varies with temperature as given by Arrhenius equation

k has least value at low 7 and high E_a.
Question 8
4 / -1

Two reactions with different activation energies have the same rate at room temperature. Which statement correctly describes the rates of these two reactions at the same higher temperature?

A
The reaction with the greater activation energy will be faster

B
The reaction with the smaller activation energy will be faster

C
The two reactions will have the same rate at higher temperature also

D
Temperature range is also required

Solution

If temperature is increased to T`,

If
Thus, reaction with smaller activation energy will be faster on increasing temperature.
Question 9
4 / -1

The activation energy of the reaction at a given temperature is found to (2.303 RT) J mol^-1. The ratio of rate constant to the Arrhenius factor is

A
0.01

B
0.1

C
0.02

D
0.001

Solution
Question 10
4 / -1

From the given figure, select the correct statement about activation energy.

Activation energy of

A
forward reaction is (E₁ + E₂) and product is less stable than the reactant

B
forward reaction is (E₁ + E₂) and product is more stable than the reactant

C
backward reaction is E₂ and that of forward reaction is E₁

D
backward reaction is E₁ and product is more stable than the reactant

Solution

Energy required to take the reactant to the activated state is (E₁ + E₂). Since, reactions is endothermic, product is less stable.
Question 11
4 / -1

The rate of a chemical reaction doubles for every 10°C rise of temperature. If the tem perature is raised by 50°C, the rate of the reaction increases by about
[AIEEE 2011]

A
10 times

B
24 times

C
32 times

D
60 times

Solution

Number of ten degrees in
Increase in rate due to 10° rise in temperature = 2
Increase in rate due to 50^° rise in temperature = 2⁵ = 32 times
Question 12
4 / -1

A reactant A forms two products B and C as given
A B, Activation energy E_a1
A C, Activation energy E_a2
if E_a2 = 2E_a1, then k₁ and K₂ are related as
[AIEEE 2011]

A

B

C

D

Solution

∴
Question 13
4 / -1

Choices for the correct combination of elements from Column I and Column II are given as options (a), (b), (c) and (d), out of which one is correct.

Rate constant {k) of a reaction is given by

Match the given property in Column I with its related value in Column II and select answer from codes given:

A
a

B
b

C
c

D
d

Solution

By Arrhenius equation,

∴
Thus, (i)→(r)

Unit of k is in min^-1.

Thus, (ii)→(p)
At 500 K,
k = 10 min^-1

∴
10 min^-1(0.2M) = 2 M min^-1
Thus (iii)→(q)

Thus, (iv)→(s)
Question 14
4 / -1

Direction (Q. Nos. 14-17)This section contains 2 paragraphs, which describing theory, experiments, data, etc. Four questions related to the paragraphs have been given. Each question has only one correct answer among the four given options (a), (b), (c) and (d).

Passage I

For the displacement reaction,

[Co(NH₃)₅Cl]²⁺ (aq) + H₂O (l) → [Co(NH₃)₅H₂O]³⁺ + Cl^- (aq)

The rate constant is given by

Q.

Rate constant at 25°C is

A
5.10 x 10^-5s^-1

B
2.60 x 10^-8s^-1

C
3.06 x 10^-3s^-1

D
2.60 x 10^-5s^-1

Solution
Question 15
4 / -1

Passage I
For the displacement reaction,
[Co(NH₃)₅Cl]²⁺ (aq) + H₂O (l) → [Co(NH₃)₅H₂O]³⁺ + Cl^- (aq)
The rate constant is given by
Q.
Energy of activation for this reaction is

A
211.90 kJ mol^-1

B
92.02 kJ mol^-1

C
-211.90 kJ mol^-1

D
-92.02 kJ mol^-1

Solution

At 298 K, log k (min^-1)
Question 16
4 / -1

Passage II
For the opposing reaction,
E_a (forward reaction) = 100 kJ mol^-1
Pre-exponential factor A = 1.0 x 10¹⁰ M^-1s^-1
Q.
The value of k₁ and k₂ at 700K respectively are

A
20M^-1s^-1 and 2.0 M^-1s^-1

B
345 M^-1s^-1 and 34.5 M^-1s^-1

C
34.5 M^-1s^-1 and 3.45 M^-1s^-1

D
200M^-1s^-1 and 20 M^-1s^-1

Solution

Also,

=345 M^-1s^-1

∴
Question 17
4 / -1

Passage II
For the opposing reaction,
E_a (forward reaction) = 100 kJ mol^-1
Pre-exponential factor A = 1.0 x 10¹⁰ M^-1s^-1
Q.
The rate constant (k₁) for the forward reaction at 1000 K is

A

B

C

D

Solution

Also,

345 m^-1s^-1

∴
Question 18
4 / -1

Direction (Q. Nos. 18-20) This section contains 3 questions. When worked out will result in one integer from 0 to 9 (both inclusive).

At room temperature (27°C) milk turns sour in about 64 h. In a refrigerator at -3°C, milk can be stored x times as long before it sours. The activation energy of the reaction that causes the souring of milk is 11.231 kcal mol-1.
What is the value of x?

A
8

B
9

C
5

D
2

Solution

Rate of souring of milk at 27°C (300 K) is times faster than at-3°C(270K).
∴
∴
11.231 kcal mol^-1 = 2.303 x 2 x10^-3 kcal mol^-1k^-1
Question 19
4 / -1

The Arrhenius equations for the rate constant of decomposition of methyi nitrite and ethyl nitrite are

Find the temperature (in °C), at which rate contants are equal.

A
6

B
7

C
9

D
3

Solution

Both are first order reactions (unit of k beings^-1)

∴
Question 20
4 / -1

For the following sequence of reactions

Thus, observed E_a is .....kJ mol^-1.

A
4

B
5

C
9

D
7

Solution

∴
Question 21
4 / -1

The half life of a first order reaction is equal to:

A
k

B
Cannot be predicted

C
0.693/k

D
1/k

Solution

The correct answer is Option C

For a first-order reaction, the half-life is given by: t_1/2 = 0.693/k
Question 22
4 / -1

The half life period of first order reaction is 15 min. Its rate constant will be equal to

A
0.0462 min^-1

B
0.462 min^-1

C
0.00462 min^-1

D
0.562 min^-1

Solution

The half life of a reaction is 15 min
So,
Here we go..
Formula to be used :

K =0.693/t = 0.693/15
__= 0.462/10 = 0.0462 min^-1

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