Question 3:
Solution:
Subject: Chemical Reaction Engineering
Topic: Reaction Kinetics
Step 1: Identify the information given in the problem
Explanation:
The reaction A → B has rate constant k =0.1 min−1 with initial concentration of A as
C A 0=2 mol / L. The conversion of A is given as X A =0.5 .
Step 2: Find the order of the reaction
Explanation:
1−n −1
The rate constant for a nth order reaction has the units ( C A ) ×time . If we put n=1, the units
of the rate constant will be time −1 which is the true for our present case with a rate constant
having the units min−1.
So, the order of the reaction is 1st order.
Step 3: Write the rate equation for 1st order reaction and calculate the time required
Explanation:
The 1st order rate equation is given as:
ln ( 1−X1 )=kt
A
Substitute the values into the equation:
ln ( 1−0.5
1
)=0.1× t
Upon solving the equation for t, the value obtained is t=¿ 6.931 min.
Final Answer:
The time required is 6.931 minutes.
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Question 5 is not available for Chemical Engineering.
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Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 5 is not available for Chemical Engineering.
Question 4:
Solution:
Subject: Chemical Reaction Engineering
Topic: Non-isothermal reactors
Given,
The reaction A → B is a first order reaction with a rate constant k =0.1 min−1 at initial
temperature T i=300 ° C , and heat of reaction ∆ H =−50 kJ /mol. The reaction takes place in
an adiabatic batch reactor with an initial concentration of A as C A 0=2 mol /l and proceeds till
80% conversion of A. So, we can say that the conversion of A is X A =0.8 .
Step 1: Write down the first order rate equation and other relevant equations
Explanation:
The first order rate equation is given as:
−kt
C A=C A 0 e
Where C A is the concentration at time t.
Also, the rate constant term depends on temperature of the reaction mixture and since the
conditions are adiabatic and the reaction is an exothermic reaction, the temperature within the
reactor will change as the reaction proceeds.
Dependence of rate constant on temperature is given by the Arrhenius equation:
ln =
[
k 2 Ea 1
−
1
k1 R T 1 T 2 ]
Where k 2, k 1 are the rate constants at temperatures T 2, T 1. E a is the activation energy required
for the reaction and R is the gas constant.
Step 2: Calculate the rate constant at the final temperature (k 2) when the reaction has
reached 80% completion.
Explanation:
On observing the Arrhenius equation, we observe that we do have data for the final reaction
temperature T 2 and the activation energy of the reaction E a. So, it is not possible to proceed
further without knowledge of these parameters. Neither do we have the heat capacity data of
the reactants and products from which we can calculate the final temperature T 2.
Final Answer:
The calculation for reaction time requires additional data particularly the activation energy of
the reaction and the final temperature of the reaction mixture. So, there is insufficient data in
the problem.
Question 4:
Solution:
Subject: Chemical Reaction Engineering
Topic: Non-isothermal reactors
Given,
The reaction A → B is a first order reaction with a rate constant k =0.1 min−1 at initial
temperature T i=300 ° C , and heat of reaction ∆ H =−50 kJ /mol. The reaction takes place in
an adiabatic batch reactor with an initial concentration of A as C A 0=2 mol /l and proceeds till
80% conversion of A. So, we can say that the conversion of A is X A =0.8 .
Step 1: Write down the first order rate equation and other relevant equations
Explanation:
The first order rate equation is given as:
−kt
C A=C A 0 e
Where C A is the concentration at time t.
Also, the rate constant term depends on temperature of the reaction mixture and since the
conditions are adiabatic and the reaction is an exothermic reaction, the temperature within the
reactor will change as the reaction proceeds.
Dependence of rate constant on temperature is given by the Arrhenius equation:
ln =
[
k 2 Ea 1
−
1
k1 R T 1 T 2 ]
Where k 2, k 1 are the rate constants at temperatures T 2, T 1. E a is the activation energy required
for the reaction and R is the gas constant.
