Topic: Kinetics of Homogeneous Reactions | Reaction Engineering - Video Lectures

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- Select activity Course Summary
  Course Summary:
  Quick Review of Theory and Solving Representative Problems on Chemical Reaction Engineering covering the undergraduate chemical engineering syllabus, and latest GATE-exam syllabus: Kinetics of Homogeneous Reactions from Batch Reactor, Performance Equations of Ideal Reactors, Combination of Reactors for Single and Multiple Reactions, Temperature Effects, Non-idealities, Heterogenous Reactions, LHHW Models, Pore Diffusion Effects.
  
  Objective Type Questions and Problems with Detailed Solutions (100 nos.) - Video Lectures with Handwritten-Transcripts
  
  Topic-wise Interactive Self-Assessment Quizzes
  
  Questions from Past GATE Exams CH, BT streams, and Standard Textbooks - Levenspiel, etc..
  
  Videos: 15 hours of recorded lectures - 3 hours of Theory; 12 hours of Problem Solving.
  
  This course is part of Chemical Engineering Video Lectures Bundle.
  
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- Select activity Levenspiel 3rd Edition - Problems
  
  Levenspiel 3rd Edition - Problems Checklist
  
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Kinetics of Homogeneous Reactions

Select activity Arrhenius Model of Rate Constant
Arrhenius Model of Rate Constant Page
Which is the correct statement from the following statements on the Arrhenius model of the rate constant $k = Ae^{-E/RT}$?

$A$ is always dimensionless

For two reactions 1 and 2, if $A_1 = A_2$ and $E_1 > E_2$, then $k_1(T) > k_2(T)$

For a given reaction, the % change of $k$ with respect to temperature is higher at lower temperatures

The % change of $k$ with respect to temperature is higher for higher $A$
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Select activity Molecularity of Reaction
Molecularity of Reaction Page
Molecularity of an elementary reaction $P +Q \rightarrow R + S$ is

1

2

3

4
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Select activity Order of Reaction and Units of Rate Constant
Order of Reaction and Units of Rate Constant Page
Overall order of reaction for which the rate constant has units of (mol/litre)$^{-3/2}$.s$^{-1}$ is

$-3/2$

1/2

3/2

5/2
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Select activity Constant Volume Reactions in Batch Reactor
Constant Volume Reactions in Batch Reactor Page
Liquid $A$ decomposes in a batch reactor, and 50% of $A$ is converted in a 5-minute run. How much additional time would it take to reach 75% conversion, with:

first order reaction _______ min

second order reaction _______ min

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Select activity Order of Reaction from Conversion Data
Order of Reaction from Conversion Data Page
In a homogeneous isothermal liquid polymerization, 20% of the monomer disappears in 34 minutes for initial monomer concentration of 0.04 mol/liter and also for 0.8 mol/liter.

What is the order ($n$) of reaction? (Choose from: 0, 0.5, 1, 2)

What is the value of $k$ in mol, liter, min units? _________ $\times 10^{-3} \text{ (mol/liter)$^{1-n}$.min$^{-1}$}$ where $n$ is the order of reaction.

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Select activity Conversion of Half-Order Reaction

Conversion of Half-Order Reaction Page

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A 10-minute experimental run in a batch reactor shows that 75% of liquid reactant is converted to product by a $1/2$-order rate. What would be the fraction converted in a half-hour run? ___________
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Select activity Rate Expression from Conversion Data
Rate Expression from Conversion Data Page
After 8 minutes in a batch reactor, reactant ($C_{A0} = 1$ mol/liter) is 80% converted; after 18 minutes, conversion is 90%.

What is the order ($n$) of reaction? (Choose from: 0, 0.5, 1, 2)

What is the value of $k$ in mol, liter, min units. _______ $\text{ (mol/liter)$^{1-n}$.min$^{-1}$}$ where $n$ is the order of reaction.

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Select activity Upper Limit of Reaction Rate

Upper Limit of Reaction Rate Page

For a non-catalytic homogeneous reaction $A \rightarrow B$, the rate expression at 300 K is \[ -r_A \quad (\text {mol.m$^{-3}$.s$^{-1}$})=\frac {10C_A}{1+5C_A} \] where $C_A$ is the concentration of $A$ (in mol/m³). Theoretically, the upper limit for the magnitude of the reaction rate ($-r_A$ in mol.m$^{-3}$.s^-1, rounded off to the first decimal place) at 300 K is ____________

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Select activity First Order Reversible Reaction
First Order Reversible Reaction Page
The first-order reversible liquid reaction \[ A \rightleftharpoons R, \qquad \qquad C_{A0} = 0.5 \text{ mol/liter}, \qquad \qquad C_{R0} = 0\] takes place in a batch reactor. After 8 minutes, conversion of $A$ is 33.3% while equilibrium conversion is 66.7%. Find the constants ($k_1 \&\ k_2$ round off to 4 decimal places) of this rate equation given as $-r_A = k_1C_A - k_2C_R$.

$k_1 = $__________ min^-1

$k_2 = $__________ min^-1

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Select activity Time Constant of First Order Reversible Reaction
Time Constant of First Order Reversible Reaction Page
A first order reversible reaction $A\xrightleftharpoons [k_2]{k_1} B$ occurs in a batch reactor. The exponential decay of the concentration of $A$ has the time constant

$\dfrac {1}{k_1}$

$\dfrac {1}{k_2}$

$\dfrac {1}{k_1-k_2}$

$\dfrac {1}{k_1+k_2}$

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Select activity Maximum Conversion of Reversible Reaction
Maximum Conversion of Reversible Reaction Page
The rate of the liquid phase reversible reaction $A \rightleftharpoons 2B$ in (kmol.m^-3.min^-1) at 298 K, is \[ -r_A = 0.02 C_A - 0.01 C_B \] where the concentrations $C_A$ and $C_B$ are expressed in (kmol.m^-3). What is the maximum limiting conversion of $A$ achievable in an isothermal CSTR at 298 K, assuming pure $A$ is fed at the inlet?

1

2/3

1/2

1/3
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Select activity Enzymatic Reaction

Enzymatic Reaction Page

Enzyme $E$ catalyzes the transformation of reactant $A$ to product $R$ as follows: \[ A \stackrel{\text{enzyme}}{\longrightarrow} R, \qquad -r_A = \frac{200C_AC_{E0}}{2+C_A}\frac{\text{mol}}{\text{liter}\cdot\text{min}} \] If we introduce enzyme ($C_{E0} = 0.001$ mol/liter) and reactant ($C_{A0}=10$ mol/liter) into a batch reactor and let the reaction proceed, find the time needed for the concentration of the reactant to drop to 0.025 mol/liter. Note that the concentration of enzyme remains unchanged during the reaction.
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Select activity First Order Variable Volume Reaction

First Order Variable Volume Reaction Page

Find the first-order rate constant for the disappearance of $A$ in the gas phase reaction $2A \rightarrow R$ if, on holding the pressure constant, the volume of the reaction mixture, starting with 80% $A$, decreases by 20% in 3 min.
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Select activity Rate of Formation or Consumption of Each Components
Rate of Formation or Consumption of Each Components Page
For the reaction $2R + S \rightarrow T$, the rates of formation, $r_R$, $r_S$ and $r_T$ of the substances $R$, $S$ and $T$ respectively, are related by

$2  r_R = r_S = r_T$

$2  r_R = r_S = -r_T$

$ r_R = 2  r_S = 2  r_T$

$ r_R = 2  r_S = -2 r_T$

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Select activity Rate of Formation / Consumption of Components of Reaction
Rate of Formation / Consumption of Components of Reaction Page
For the reaction $A + B \rightarrow 2B + C$,

$r_{A} = r_{B}$

$r_{A} = -r_{B}$

$r_{A} = 2r_{B}$

$r_{A} = r_{B}/2$
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Select activity Order of Reaction from Rate vs Concentration

Order of Reaction from Rate vs Concentration Page

Consider a reaction $aG + bH \rightarrow \text{ Products}$. When concentration of both the reactants $G$ and $H$ is doubled, the rate increases by eight times. However, when concentration of $G$ is doubled keeping the concentration of $H$ fixed, the rate is doubled. The overall order of the reaction is ________ (Choose from: 0, 1, 2, 3)
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Order of Reaction from Half-life Data Page

The following half-life data are available for the irreversible liquid phase reaction, \[ A \rightarrow \text { Products} \]

Initial concentration (kmol/m³)	Half-life (min)
2	2
8	1

The overall order of the reaction is _____ (choose from: 0.5, 1, 1.5, 2)

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Select activity Reaction Order with Half-life Time Equaling Fifty Percent of Full-life Time
Reaction Order with Half-life Time Equaling Fifty Percent of Full-life Time Page
For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100% conversion) of the reactant?

Zero order

Half order

First order

Second order
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Select activity Half-life vs Initial Concentration - Straight Line Plot
Half-life vs Initial Concentration - Straight Line Plot Page
Consider the n$^{th}$ order irreversible liquid phase reaction $A \rightarrow B$. Which one of the following plots involving half-life of the reaction $(t_{1/2})$ and the initial reactant concentration $(C_{A0})$ gives a straight line plot?

$C_{A0}$ vs. $t_{1/2}$

$\ln C_{A0}$ vs. $t_{1/2}$

$C_{A0}$ vs. $\ln t_{1/2}$

$\ln C_{A0}$ vs. $\ln t_{1/2}$
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Select activity Inert Content for a Variable Volume Reaction

Inert Content for a Variable Volume Reaction Page

An irreversible gas phase reaction $A \rightarrow 5B$ is conducted in an isothermal batch reactor at constant pressure in the presence of an inert. The feed contains no $B$. If the volume of the gas at complete conversion must not exceed three times the initial volume, the minimum mole percent of the inert in the feed must be _______ (choose from: 0, 20, 33, 50)
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Select activity Decomposition of N2O5 - Non-elementary Reaction

Decomposition of N2O5 - Non-elementary Reaction Page

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Select activity Decomposition of Azomethane - Steps Involved

Decomposition of Azomethane - Steps Involved Page

The gas phase decomposition of azomethane to give ethane and nitrogen takes place according to the following sequence of elementary reactions.

\[ \begin {align*} (\text {CH}_3)_2\text {N}_2 + (\text {CH}_3)_2\text {N}_2 &\stackrel {k_1}{\longrightarrow } (\text {CH}_3)_2\text {N}_2 + [(\text {CH}_3)_2\text {N}_2]^* \\ [(\text {CH}_3)_2\text {N}_2]^* + (\text {CH}_3)_2\text {N}_2 &\stackrel {k_2}{\longrightarrow } (\text {CH}_3)_2\text {N}_2 + (\text {CH}_3)_2\text {N}_2 \\ [(\text {CH}_3)_2\text {N}_2]^* &\stackrel {k_3}{\longrightarrow } \text {C}_2\text {H}_6 + \text {N}_2 \end {align*} \]

Using the pseudo-steady-state-approximation for $[(\text {CH}_3)_2\text {N}_2]^*$, the order with respect to azo-methane in the rate expression for the formation of ethane, in the limit of high concentrations of azomethane, is ____________

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Select activity Mechanism of Non-elementary Reaction
Mechanism of Non-elementary Reaction Page
Find a mechanism that is consistent with the rate equation and the reaction given below: \[ 2A + B \rightarrow A_2B \quad \quad \quad -r_A = kC_AC_B \]

$A + B \rightleftharpoons AB; \quad \quad AB + A \rightarrow A_2B$

$A + B \rightarrow AB; \quad \quad AB + A \rightarrow A_2B$

$A + A \rightarrow AA; \quad \quad AA + B \rightarrow A_2B$

$A + A \rightleftharpoons AA; \quad \quad AA + B \rightarrow A_2B$
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Topic outline

General

Kinetics of Homogeneous Reactions