# Chemical Reaction Engineering Questions and Answers – Tanks in Series Model

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

1. If τ is the average residence time and σ2 is the standard deviation, then the number of tanks necessary to model a real reactor as N ideal tanks in series is ____
a) N = $$\frac{\tau^2}{σ^2}$$
b) N = $$\frac{σ^2}{τ^2}$$
c) N = σ2
d) N = $$\frac{1}{τ^2}$$

Explanation: τ2 = 1 and σ2 = $$\frac{1}{N}.$$ The standard deviation is obtained as, σ2 = $$\int_0^∞$$(t-τ)2E(t)dt.

2. State true or false.
The tank in series model is a single parameter model.
a) False
b) True

Explanation: The tank in series model is used to represent non – ideal flow in PFR. It is a one parameter model and the parameter is the number of tanks.

3. State true or false.
The tank in series model depicts a non – ideal tubular reactor as a series of equal sized CSTRs.
a) True
b) False

Explanation: A number of tanks in series represent a PFR. Any CSTR behaves like a PFR if its volume is reduced. Infinite CSTRs are connected in series to approach PFR behaviour.

4. For a first order reaction, where k is the first order rate constant, the conversion for N tanks in series is obtained as ____
a) XA = 1-$$\frac{1}{(1+\frac{τk}{N})^N}$$
b) XA = 1+$$\frac{1}{(1+\frac{τk}{N})^N}$$
c) XA = $$\frac{1}{(1+\frac{τk}{N})^N}$$
d) XA = $$\frac{1}{(1+\frac{τk}{N})^N}$$– 1

Explanation: For N tanks in series, the combination approaches non – ideal PFR behaviour. The concentration in the Nth CSTR is given as CN = $$\frac{C_0}{(1+ τk)^N}.\frac{C_N}{C_0} = \frac{1}{(1+ τk)^N}.$$ XA = 1 – $$\frac{C_N}{C_0}.$$ For N – tanks, XA = 1-$$\frac{1}{(1+\frac{τk}{N})^N}.$$

5. Which of the following correctly represents the Damkohler number for a first order reaction? (Where, τ is the space time)
a) k
b) τ
c) $$\frac{1}{kτ}$$
d) k τ

Explanation: Damkohler number is the product of first order rate constant and space time. It is the measure of the degree of completion of reaction.
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6. According to tanks in series model, the spread of the tracer curve is proportional to ____
a) Square of distance from the tracer origin
b) Square root of distance from the tracer origin
c) Cube of distance from the tracer origin
d) Inverse square of distance from the tracer origin

Explanation: $$σ_{tracer \, curve}^2$$ α Distance from point of origin
Spread of the curve α $$\sqrt{Distance \, from \, origin}.$$

7. If τ2 = 100 and σ2 = 10, the number of tanks necessary to model a real reactor as N ideal tanks in series is ____
a) 1
b) 10
c) 5
d) 100

Explanation: N = $$\frac{τ^2}{σ^2}$$
N = $$\frac{100}{10}$$ = 10.

8. If τ = 5 s, first order rate constant, k = 0.25 sec-1 and the number of tanks, N is 5, then the conversion is ____
a) 67.2%
b) 75%
c) 33%
d) 87.45%

Explanation: XA = 1-$$\frac{1}{(1+\frac{τk}{N})^N}$$
1-$$\frac{1}{(1+\frac{5×0.25}{5})^5}$$ = 67.2%.

9. The exit age distribution as a function of time is ____
a) E = $$\frac{t^{N-1}}{τ^N}\frac{N^N}{(N-1)!}e^\frac{-tN}{τ}$$
b) E = $$\frac{t^{N-1}}{τ^N}\frac{N}{(N-1)!}e^\frac{-tN}{τ}$$
c) E = $$\frac{t^N}{τ^N}\frac{N^N}{(N-1)!}e^\frac{-tN}{τ}$$
d) E = $$\frac{t^{N-1}}{τ^2}\frac{N^N}{(N-1)!}e^\frac{-tN}{τ}$$

Explanation: For N tanks in series, the exit age distribution is, E = $$\frac{t^{N-1}}{τ^N}\frac{N^N}{(N-1)!}e^\frac{-tN}{τ}.$$ The number of tanks in series, N = $$\frac{τ^2}{σ^2}.$$

10. There are 5 tanks connected in series. If the average residence time is 5 sec, first order rate constant is 0.5 sec-1, the initial concentration is 5$$\frac{mol}{m^3},$$ then the conversion at the exit of 5th reactor in ($$\frac{mol}{m^3}$$) is ____
a) 0.34
b) 0.51
c) 0.65
d) 0.81

Explanation: CN = C0 $$\frac{1}{(1+\frac{τk}{N})^N}$$
CN = 5×$$\frac{1}{(1+\frac{5×0.5}{5})^5}$$
CN = 0.65$$\frac{mol}{m^3}.$$

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