This set of Chemical Reaction Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Design of CSTRS in Series”.

1. State true or false.

It is preferable to use a number of CSTRs in series to achieve a specific conversion than a single CSTR.

a) True

b) False

View Answer

Explanation: Total volume required to achieve a given conversion is less than the volume of a single CSTR. A number of CSTRs in series approaches Plug Flow behavior.

2. What is the mole balance of a component in a CSTR? (Where F_{0} is the molar flowrate of reactant entering and F is the exit molar flowrate)

a) F_{0} = FX + F

b) F_{0} = FX + F_{0}

c) F_{0} = F_{0}X + F

d) F_{0} = X + F

View Answer

Explanation: The mole balance of a component in a CSTR is given as F

_{0}= F

_{0}X + F. Molar flowrate of a component A fed to the reactor is the sum of molar flowrate at which A is consumed and molar flowrate at which A leaves the reactor.

3. For ‘i’ CSTRs of variable volume in series, the residence time in the i^{th} reactor is ____

a) τ_{i} = \(\frac{- C_i}{-r_i} \)

b) τ_{i} = \(\frac{C_{i-1}- C_i}{-r_i} \)

c) τ_{i} = \(\frac{C_i}{-r_i} \)

d) τ_{i} = \(\frac{C_{i-1}}{-r_i} \)

View Answer

Explanation: For 2

^{nd}reactor in series, the mole balance in 2

^{nd}reactor is vC

_{1}= vC

_{2}+ (-r

_{2})V

_{2}.

v is the volumetric flowrate and V

_{2}is the volume of the 2

^{nd}reactor. Rearranging, \(\frac{V_2}{v} = \frac{C_1- C_2}{-r_2}\) , τ2 = \(\frac{C_1- C_2}{-r_2}.\) For i

^{th}reactor in series, τ

_{i}= \(\frac{C_{i-1}- C_i}{-r_i}. \)

4. What is the concentration C_{4} at the end of 4^{th} reactor, for n unequal sized CSTRs in series, where X_{4} is the conversion in 4^{th} reactor?

a) C_{4} = (1 – X_{4})

b) C_{4} = C_{0}X_{4}

c) C_{0} = C_{4} (1 – X_{4})

d) C_{4} = C_{0}(1 – X_{4})

View Answer

Explanation: Conversion in the 4

^{th}reactor is the ratio of reactant converted in the 4

^{th}reactor to the initial concentration. X

_{4}= \(\frac{C_0 – C_4}{C_0}.\) Hence, C

_{4}= C

_{0}(1 – X

_{4}).

5. The plot of rate of the reaction and the reactant concentration for unequal sized CSTRs in series is ____

a)

b)

c)

d)

View Answer

Explanation:For i

^{th}reactor, \(\frac{-1}{-τ_i} = \frac{-r_i}{C_i-C_{i-1}}.\) For the 1

^{st}reactor in series, the rate is high and decreases for every consecutive reactor. Hence, the plot shows a high rate for the initial concentration.

6. For equal sized CSTRs in series carrying out 1^{st} order reactions of constant density, which of the following is true? (k_{i} is the rate constant in a reactor ‘i’ in series)

a) k_{1} ≠ k_{2} ≠ … ≠ k_{n}, τ_{1} = τ_{2} = … = τ_{n}

b) k_{1} = k_{2} = … = k_{n}, τ_{1} = τ_{2} = … = τ_{n}

c) k_{1} = k_{2} = … = k_{n}, τ_{1} ≠ τ_{2} ≠ … ≠ τ_{n}

d) k_{1}< k_{2}< …<k_{n}, τ_{1} = τ_{2} = … = τ_{n}

View Answer

Explanation: All the CSTRs are operated at the same temperature. Hence, k

_{1}= k

_{2}= … = k

_{n}. The volume of all the CSTRs is the same, V

_{1}= V

_{2}= … = V

_{n}. τ = \(\frac{V}{v_0},\) hence τ

_{1}= τ

_{2}= … = τ

_{n}.

7. For very low conversion, the value of Damkohler number is ____

a) ≤0.1

b) >10

c) ≥0.1

d) = 10

View Answer

Explanation: Damkohler number estimates the conversion that can be achieved in a flow reactor. At low conversions nearly 10%, Da≤0.1

8. State true or false.

For different sized CSTRs in series, the best system is the one having a minimum volume for a specific conversion.

a) True

b) False

View Answer

Explanation: The optimum size ratio of CSTRs in series depends on the reaction kinetics. For a first order reaction, equal sized CSTRs are operated. For positive order reactions, smaller CSTR is followed by larger ones.

9. For equal sized CSTRs in series carrying out 1^{st} order reaction, the concentration at the outlet of n^{th} reactor is ____

a) C_{N} = \(\frac{1}{(1 + τk)^N} \)

b) C_{N} = \(\frac{C_0}{(1 + τ)^N} \)

c) C_{N} = \(\frac{C_0}{(1 + k)^N} \)

d) C_{N} = \(\frac{C_0}{(1 + τk)^N} \)

View Answer

Explanation: τ

_{1}= \(\frac{C_0- C_1}{-r_1} = \frac{C_0- C_1}{kC_1}.\) Rearranging, C

_{1}= \(\frac{C_0}{(1+ τk)}.\) In 2

^{nd}reactor, τ

_{2}= \(\frac{C_1- C_2}{kC_2}.\) Similarly, for n

^{th}reactor, C

_{N}= \(\frac{C_0}{(1 + τk)^N}.\)

10. If Da is the Damkohler number, for equal sized CSTRs in series carrying out first order reaction, the plot representing conversion and number of CSTRs is ____

a)

b)

c)

d)

View Answer

Explanation: At kτ ≥ 1, nearly 90% conversion is achieved. Such a high conversion is achieved in 2 or three consecutive reactors.At kτ<1, conversion increases significantly with the addition of every reactor.

**Sanfoundry Global Education & Learning Series – Chemical Reaction Engineering.**

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