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Arrhenius Equation MCQ - Practice Questions with Answers

Arrhenius Equation MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

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Quick Facts

Exception(Arrhenius Theory), Effective Activation Energy is considered one of the most asked concept.
130 Questions around this concept.

Solve by difficulty

Two reactions R₁ and R₂ have identical pre-exponential factors. The activation energy of R₁exceeds that of R₂ by 10 kJ mol⁻¹. If k₁ and k₂ are rate constants for reactions R₁ and R₂ respectively at 300 K, then ln(k2/k1) is equal to :

(R=8.314 J mol⁻¹K⁻¹)

A

6

Correct Answer

Wrong Answer

B

4

Correct Answer

Wrong Answer

C

8

Correct Answer

Wrong Answer

D

12

Correct Answer

Wrong Answer

How does an increase in temperature affect the rate of a reaction, according to transition state theory?

A

It has no effect on the rate of reaction

Correct Answer

Wrong Answer

B

If decreases the rate of reaction

Correct Answer

Wrong Answer

C

It increases the rate of reaction

Correct Answer

Wrong Answer

D

It stabilizes the activated complex.

Correct Answer

Wrong Answer

In collision theory of chemical reaction, $Z_{AB}$ represents

A

the collision frequency of reactants, A and B

Correct Answer

Wrong Answer

B

steric factor

Correct Answer

Wrong Answer

C

the fraction of molecules with energies equal to $E_{a}$

Correct Answer

Wrong Answer

D

the fraction of molecules with energies greater than $E_{a}$

Correct Answer

Wrong Answer

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NEET PYQ's & Solutions: Physics | Chemistry | Biology

Rate of a reaction can be expressed by Arrhenius equation as : $k=Ae^{-E/RT}$ . In this equation, $E$ represents

A

the energy above which all the colliding molecules will react

Correct Answer

Wrong Answer

B

the energy below which colliding molecules will not react

Correct Answer

Wrong Answer

C

the total energy of the reacting molecules at a temperature , $T$

Correct Answer

Wrong Answer

D

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

Correct Answer

Wrong Answer

The rate of the reaction $2NO+Cl_{2}\rightarrow 2NOCl$ is given by the rate equation rate=k [NO]²[Cl₂]

The value of the rate constant can be increased by:

A

Increasing the concentration of NO

Correct Answer

Wrong Answer

B

Increasing the temperature

Correct Answer

Wrong Answer

C

Increasing the concentration of the Cl₂

Correct Answer

Wrong Answer

D

Doing all of these

Correct Answer

Wrong Answer

Consider the reaction $\mathrm{A \rightarrow B}$ having rate constant (k). If $\mathrm{k_{28^{\circ}}: k_{30^{\circ}}<1}$ , then

A

Rate increase with the rise in temperature

Correct Answer

Wrong Answer

B

Rate decrease withe rise in temperature

Correct Answer

Wrong Answer

C

Rate does not change with rise in temperature.

Correct Answer

Wrong Answer

D

None of these.

Correct Answer

Wrong Answer

Activation energy (E_a) and rate constants (k₁ and k₂) of a chemical reaction at two different temperatures (T₁ and T₂ ) related by :

A

$\ln \frac{{\text{k}_2 }} {{\text{k}_1 }} = - \frac{{\text{E}_\text{a} }} {\text{2R}}\left( {\frac{1} {{\text{T}_2 }} - \frac{1} {{\text{T}_1 }}} \right)$

Correct Answer

Wrong Answer

B

$\ln \frac{{\text{k}_2 }} {{\text{k}_1 }} = - \frac{{\text{E}_\text{a} }} {\text{R}}\left( {\frac{1} {{\text{T}_2 }} + \frac{1} {{\text{T}_1 }}} \right)$

Correct Answer

Wrong Answer

C

$\ln \frac{{\text{k}_2 }} {{\text{k}_1 }} = \frac{{\text{E}_\text{a} }} {\text{R}}\left( {\frac{1} {{\text{T}_1 }} - \frac{1} {{\text{T}_2 }}} \right)$

Correct Answer

Wrong Answer

D

$\ln \frac{{\text{k}_2 }} {{\text{k}_1 }} = - \frac{{\text{E}_\text{a} }} {\text{R}}\left( {\frac{1} {{\text{T}_1 }} - \frac{1} {{\text{T}_2 }}} \right)$

Correct Answer

Wrong Answer

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For a gaseous reaction, the rate constant (k) is $\mathrm{25 \times 10^{-3} \mathrm{Lmot}^{-1} \mathrm{5}^{-1} at 300 \mathrm{~K}}$ . If the rate constant increases by a factor of 3 as the temperature is raised to $\mathrm{400 \mathrm{~K}.}$ What is the activation energy (Ea) for the reaction?

A

$2.5 \mathrm{~kJ} / \mathrm{mwl}$

Correct Answer

Wrong Answer

B

$1.5 \mathrm{~kJ} / no ll$

Correct Answer

Wrong Answer

C

$2.2 \mathrm{~kJ} / \mathrm{mer}$

Correct Answer

Wrong Answer

D

$1.1 \mathrm{~kJ} / \mathrm{meol}$

Correct Answer

Wrong Answer

Two recreations $\mathrm{R_1}$ and $\mathrm{R_2}$ have identical pro -exponential factors. Activation energy of $\mathrm{R_1}$ rate constants for reactions $\mathrm{R_1}$ and $\mathrm{R_2}$ respectively at $\mathrm{ 250 \, k}$ , the $\mathrm{ \ln \left(k_2 / k_1\right)}$ in equal to.

A

4.48

Correct Answer

Wrong Answer

B

15.67

Correct Answer

Wrong Answer

C

9.62

Correct Answer

Wrong Answer

D

20.64

Correct Answer

Wrong Answer

Most Scoring concepts for NEET

This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.

In the respect of the equation $k=Ae^{-E_{a}/RT}$ in chemical kinetics, which one of the following statements is correct?

A

$k$ is equilibrium constant

Correct Answer

Wrong Answer

B

$A$ is adsorption factor

Correct Answer

Wrong Answer

C

$E_a$ is energy of activation

Correct Answer

Wrong Answer

D

$R$ is Rydberg constant.

Correct Answer

Wrong Answer

Concepts Covered - 9

Effect of Temperature on Rate of Reaction: Approximate Dependency of K on T

We know that on increasing the temperature, the rate of the reaction or rate constant increases.
The rate equation is given as follows:

$\mathrm{Rate\: =\: k[conc]^{n}}$

Here k is the rate constant

Now, we will see the relation between k and T or also known as 'approximate dependency of k on T'.

Generally on 10^oC rise in temperature, rate constant nearly doubles.

Temperature Coefficient: It is the ratio of two rate constants. Thus, mathematically it is given as:

$\mathrm{T_{coeff}\: =\: \frac{k_{(t\: +\: 10)^{o}C}}{k_{t^{o}C}}}$

Thus, the temperature coefficient is showing the dependency of the rate constant(k) on temperature(T).

NOTE: The standard value of the temperature coefficient is given at t = 25^oC and (t+10) = 35^oC.

Effect of Temperature on Rate of Reaction: Accurate Dependency of K on T

The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation. It was first proposed by Dutch chemist, J.H. van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation.

$\mathrm{k=A e^{-E a / R T}}$

where A is the Arrhenius factor or the frequency factor. It is also called pre-exponential factor. It is a constant specific to a particular reaction. R is gas constant and E_a is activation energy measured in joules/mole(J mol^–1).

Ratio of Two Rate Constants at Two Different Temperatures

We have the rate constant K₁ at temperature T₁ and rate constant K₂ at temperature T₂.

We know that the Arrhenius equation is given as follows:

$\mathrm{log_{10}K_{1}\: =\: log_{10}A\: -\: \frac{E_{a}}{2.303RT_{1}}\quad\quad\quad\quad\quad............(i)}$

$\mathrm{log_{10}K_{2}\: =\: log_{10}A\: -\: \frac{E_{a}}{2.303RT_{2}}\quad\quad\quad\quad\quad............(ii)}$

On subtracting equation (i) from (ii), we get:

$\mathrm{log_{10}K_{2}\: -\: log_{10}K_{1}\: =\: \frac{E_{a}}{2.303RT_{1}}\: -\: \frac{E_{a}}{2.303RT_{2}}}$

$\mathrm{\mathbf{Thus,}\: log\frac{K_{2}}{K_{1}}\: =\: \frac{Ea}{2.303R}\left [ \frac{1}{T_{1}}\: -\: \frac{1}{T_{2}} \right ]}$

Exception(Arrhenius Theory)

Although the Arrhenius equation explains the exact relationship between the rate of reaction and the temperature but there are still some exceptions in this theory. Actually, on increasing the temperature rate may decrease sometimes and may not follow Arrhenius equation. Following examples will illustrate these exceptions.

Bacterial decomposition

From the graph, it is clear that first on increasing the temperature the rate also increases but at T_i (also known as inversion temperature) rate starts to decrease on further increasing the temperature.

Complex Reaction - Mechanism of Reaction

On the basis of mechanism, we have two types of reactions:

Simple or elementary reaction
Complex or multi-step reaction

Simple or Elementary reaction

The reactions, which occur in single step, are called simple or elementary reactions. For example:

$\mathrm{NO(g)\: +\: O_{3}(g)\: \rightarrow \: NO_{2}(g)\: +\: O_{2}(g)}$
An elementary reaction is an individual molecular event that involves breaking or making of chemical bonds. The overall reaction describes the stoichiometry of the overall process but provides no information how the reaction occurs.

Complex Reaction

A complex reaction takes place in a sequence of a number of elementary steps.
Molecularity of complex reaction is not defined. Molecularity of each step can be defined but not for overall.
Overall rate of reaction is given by slowest step of the complex reaction.
For example, combination of NO₂ and CO occurs in a sequence of elementary steps.

$\\\mathrm{NO_{2}(g)\: +\: NO_{2}(g)\: \rightarrow \: NO_{3}(g)\: +\: NO(g)\quad\quad\quad\quad(elementary\: step\: I)}\\\\\mathrm{NO_{3}(g)\: +\: CO(g)\: \rightarrow \: NO_{2}(g)\: +\: CO_{2}(g)\quad\quad\quad\quad(elementary\: step\: II)}$

Important Facts:

The numbeer of reactant molecules taking part in an elementary step or in an elementary reaction is expressed as molecularity of that step of molecularity of that reaction respectively.
For elementary reactions usually order of reaction and molecularity are same. Thus, it can be said that if order of a reaction for a change is fractional it cannot be an elementary reaction.

Complex Reaction (When Intermediate is Incorporated)

This example will illustrate how to determine the rate law when the intermediate is involved in rate-determining step.

$\mathrm{2O_{3}\: \rightarrow \: 3O_{2}}$

Mechanism

$\\\mathrm{O_{3}\: \rightleftharpoons \: O_{2}\: +\: O\quad\quad\quad\quad\quad K_{1}\: and \: K_{2}\: are\: the \:forward\: and\: backward\: reaction\: constants\: respectively}\\\\\mathrm{O\: +\: O_{3}\: \rightarrow \: 2O_{2}\quad\quad\quad\quad\quad K_{3}\: is\: the\: rate\: constant}$

In this case, step 1 is fast and step 2 is slow.

The rate law is given as follows:

$\mathrm{rate\: =\: K_{3}[O]^{1}[O_{3}]^{1}}$

We know from equilibrium theory that:

$\\\mathrm{K_{eq}\: =\: \frac{K_{1}}{K_{2}}\: =\: \frac{[O_{2}][O]}{[O_{3}]}}\\\\\mathrm{[O]\: =\: \frac{K_{1}[O_{3}]}{K_{2}[O_{2}]}}\\\\\mathrm{Thus, rate\: =\: \frac{K_{3}.K_{1}}{K_{2}}\frac{[O_{3}][O_{3}]}{[O_{2}]}\: =\: \frac{K_{3}.K_{1}}{K_{2}}\frac{[O_{3}]^{2}}{[O_{2}]}}$

$\\\mathrm{Thus,\: Order\: =\: 2-1=1}\\\\\mathrm{rate\: constant\: =\: \frac{K_{3}.K_{1}}{K_{2}}}$

Parallel First Order Kinetics

In this situation, B and C both are forming. These types of reactions are known as parallel reactions. Both these reactions are first order reactions with rate constants K₁ and K₂ respectively and half-lives as t₍_1/2)1 and t_(1/2)2.

For these parallel reactions, we need to find:

Effective order
Effective rate constant
Effective t_1/2
Effective Activation energy
[A], [B], [C] with time (t) variation
% of [B] and % of [C]

We know that the rate equations are given as follows:

$\\\mathrm{r_{1}\:=\: \frac{-dA}{dt}\:=\: K_{1}[A] }\\\\\mathrm{r_{2}\: =\: \frac{-dA}{dt}\: =\: K_{2}[A]}$

$\\\mathrm{Thus,\: overall\: rate\: of\: reaction\: is:}\\\\\mathrm{\frac{-dA}{dt}\: =\: K_{1}[A]\: +\: K_{2}[A]\: =\: (K_{1}\: +\: K_{2})[A]}$

$\mathrm{Thus,\: rate\: =\: (K_{1}\: +\: K_{2})[A]^{1}}$

$\mathrm{\mathbf{Effective\: Rate\: Constant(K_{eff})}\: =\: (K_{1}\: +\: K_{2})}$

$\mathrm{\mathbf{Effective\: order\: of\: reaction}\: =\: 1}$

$\mathrm{Now, effective\: half-life(t_{1/2})\:=\: \frac{0.693}{K_{eff}}\: =\: \frac{0.693}{K_{1}\: +\: K_{2}}}$

$\mathrm{\Rightarrow\: \frac{0.693}{\frac{0.693}{(t_{1/2)_{1}}}+\frac{0.693}{(t_{1/2})_{2}}}}$

$\\\mathrm{Thus,\: effective\: half\: life\: is\: given\: as:}\\\\\mathrm{\frac{1}{(t_{1/2})_{eff}}\: =\: \frac{1}{(t_{1/2})_{1}}\: +\:\frac{1}{(t_{1/2})_{2}} }$

NOTE: Effective activation energy, [A], [B], [C] with time (t) variation and % of [B] and % of [C] will be discussed in later concepts.

Effective Activation Energy

We know that Arrhenius equation is given as:

$\mathrm{K\: =\: A.e^{-Ea/RT}}$

$\mathrm{K_{eff}\: =\: K_{1}\: +\: K_{2}}$

$\mathrm{Thus, A_{eff}.e^{-Ea_{eff}/RT}\: =\: A_{1}.e^{-Ea_{1}/RT}\: +\: A_{2}.e^{-Ea_{2}/RT}}$

$\mathrm{Differentiate\: this\: equation\: with\: respect\: to\: temperature\: 'T'}$

$\mathrm{Thus,\: we\: have:}$

$\mathrm{A_{eff}.e^{-Ea_{eff}/RT}\left ( \frac{+Ea_{eff}}{RT^{2}} \right )\: =\:A_{1}.e^{-Ea_{1}/RT}\left ( \frac{+Ea_{1}}{RT^{2}} \right ) \: +\: A_{2}.e^{-Ea_{2}/RT}\left ( \frac{+Ea_{2}}{RT^{2}} \right )}$

$\mathrm{K_{eff}\, E_{eff}\: =\: K_{1}Ea_{1}\: +\: K_{2}Ea_{2}}$

$\mathrm{E_{eff}\: =\: (K_{1}Ea_{1}\: +\: K_{2}Ea_{2})/K_{eff}}$

[A], [B], [C] Vs time(t)

We know that the rate equations are given as follows:

$\\\mathrm{r_{1}\:=\: \frac{-dA}{dt}\:=\: K_{1}[A] }\\\\\mathrm{r_{2}\: =\: \frac{-dA}{dt}\: =\: K_{2}[A]}$

The overall rate of the reaction is:

$\mathrm{\frac{-dA}{dt}\: =\: K_{1}[A]\: +\: K_{2}[A]\: =\: (K_{1}\: +\: K_{2})[A]}$

$\mathrm{\Rightarrow\: \frac{dA}{dt}\: =\: (K_{1}\: +\: K_{2})[A]^{1}}$

$\mathrm{\Rightarrow\: \frac{dA}{A}\: =\: -(K_{1}\: +\: K_{2})dt}$

On integrating both sides of the above equation, we get:

$\mathrm{\int_{A_{o}}^{A}\frac{dA}{A}\: =\: -\int_{0}^{t}(K_{1}\: +\: K_{2})dt}$

$\Rightarrow \mathrm{\left [ logA \right ]^{A}_{A_{o}}\: =\, -(K_{1}\: +\: K_{2})\left [ t \right ]^{t}_{0}}$

$\mathrm{\Rightarrow log\, A\: -\: log\, A_{o}\: =\: -k_{eff}t}$

$\mathrm{\Rightarrow log\, \frac{A}{A_{o}}\: =\: -k_{eff}t}$

$\mathrm{\Rightarrow \frac{A}{A_{o}}\: =\: e^{-k_{eff}t}}$

$\mathrm{Thus,[A]\: =\: [A_{o}] e^{-k_{eff}t}\quad\quad\quad\quad\quad\quad...........(i)}$

Now, the rate equation for B can be given as follows:

$\mathrm{\frac{dB}{dt}\: =\: k_{1}[A]\: =\: k_{1}[A_{o}]e^{-(k_{1}\: +\: k_{2})t}\quad\quad\quad\quad\quad(From\: equation\: (i))}$

$\mathrm{\Rightarrow\int_{0}^{B}{dB}\: =\: \int_{0}^{t}k_{1}[A_{o}]e^{-(k_{1}\: +\: k_{2})t}dt}$

$\mathrm{Thus, [B]\: =\: \frac{k_{1}A_{o}}{k_{1}+k_{2}}\left [ 1\: -\: e^{-(k_{1}\: +\: k_{2})t} \right ]}$

Similarly, [C] is given as follows:

$\mathrm{[C]\: =\: \frac{k_{2}A_{o}}{k_{1}+k_{2}}\left [ 1\: -\: e^{-(k_{1}\: +\: k_{2})t} \right ]}$

Study it with Videos

Effect of Temperature on Rate of Reaction: Approximate Dependency of K on T

Effect of Temperature on Rate of Reaction: Accurate Dependency of K on T

Ratio of Two Rate Constants at Two Different Temperatures

Exception(Arrhenius Theory)

Complex Reaction - Mechanism of Reaction

Complex Reaction (When Intermediate is Incorporated)

Parallel First Order Kinetics

Effective Activation Energy

[A], [B], [C] Vs time(t)

Study other Related Concepts

Arrhenius Equation Current Topic

Rate of Reaction

Order of Reaction

Zero Order Reaction

First Order Reaction

Second Order Reaction

nth Order Reaction

Methods of Determining Reaction Order

Molecularity of reaction

Pseudo First Order Reaction

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