This set of Chemical Reaction Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Batch Reactor Design Equations”.

1. The design equation for Batch reactor in differential form is _______

a) NA0\(\frac{dXA}{dt}\) = -r_{A} V

b) \(\frac{dXA}{dt}\) = -r_{A}

c) \(\frac{dXA}{dt}\) = -r_{A}V

d) NA0\(\frac{dXA}{dt}\) = -r_{A}

View Answer

Explanation: To obtain the time required to achieve a certain conversion. Mole balance is written in terms of conversion and then differentiated to get the above equation.

2. The design equation for Batch reactor in integral form is _____

a) t = NA0\(\int_0^{XA} \frac{dXA}{-r_A} \)

b) t = \(\int_0^{XA} \frac{dXA}{-r_A} \)

c) t = NA0\(\int_0^{XA} \frac{dXA}{-r_{AV}} \)

d) t = \(\int_0^{XA} \frac{dXA}{-r_{AV}} \)

View Answer

Explanation: The differential form of the design equation is widely used in interpreting the lab data. Mole balance written in terms of conversion is integrated to get the above equation.

3. The design equation for constant volume batch reactor in terms of partial pressure is (Assuming the gases to be ideal)

a) –r_{i} = \(\frac{1}{RT}\frac{dpi}{dt} \)

b) –r_{i} = \(\frac{V}{RT} \frac{dpi}{dt} \)

c) –r_{i} = \(\frac{PV}{RT} \frac{dCi}{dt} \)

d) –r_{i} = V \(\frac{dCi}{dt} \)

View Answer

Explanation: The design equation for batch system is –r

_{i}= \(\frac{1}{V}\frac{dNi}{dt}.\) For constant volume system

–r

_{i}= \(\frac{d(\frac{Ni}{V})}{dt} = \frac{dCi}{dt}\) where C = p/RT. Hence, –r

_{i}= \(\frac{1}{RT}\frac{dpi}{dt}. \)

4. Most suitable reactor for pharmaceutical industry is ______

a) MFR

b) PFR

c) Batch reactor

d) PBR

View Answer

Explanation: When small scale production is desired, high or stringent quality standards to be met batch reactors used extensively.

5. Design equation for varying volume system is ______

a) t = \(\int_0^{XA} \frac{dXA}{-rA εA} \)

b) t = \(\int_0^{XA} \frac{dXA}{CA0} \)

c) t = \(\int_0^{XA} \frac{dXA}{NA0} \)

d) t = CA0 \(\int_0^{XA} \frac{dXA}{-rA(1+XA εA)} \)

View Answer

Explanation: The varying volume in a batch reactor is given as V = V

_{0}(1+X

_{A}ε

_{A}) where ε

_{A}is called the fractional volume change of the system. The above equation is substituted in the general batch reactor design equation.

6. Calculate the value of ε_{A} of gas for the following isothermal gas phase reaction.

(Assuming pure A)

A → 4R

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: ε

_{A}is fractional volume change between no conversion and complete conversion. It is calculated using the formula given below

ε

_{A}= \(\frac{V1-V0}{V0} = \frac{4-1}{1}\) = 3

where V1 is volume at complete conversion and V0 is volume at no conversion.

7. For the following reaction, calculate ε_{A}, containing 50% A and 50% inerts.

a) 0.5

b) 1.5

c) 2.5

d) 0.75

View Answer

Explanation: When X=0, A=0.5 and Inerts=0.5

When X=1, A=2 and Inerts=0.5

ε

_{A}= \(\frac{2.5-1}{1}\) = 1.5.

8. Constant volume batch reactors are the widely used industrial batch reactors.

a) True

b) False

View Answer

Explanation: Density change for most liquid phase reactions are negligible. Hence, constant volume batch reactors are widely used.

9. Determine the rate law for first order reaction 2A → R at constant pressure with 60% A in the initial reaction mixture and reduces by 15% in 4 minutes.

a) -r_{A} = 0.17 C_{A}

b) -r_{A} = C_{A}

c) -r_{A} = 2C_{A}

d) -r_{A} = 3.6C_{A}

View Answer

Explanation:

2A → R

ε

_{A}= \(\frac{.7-1}{1}\) = -0.3

\(\begin{array}{c|c c}

& X_A=0 & X_A = 1 \\

\hline

A & 0.6 & 0.3 \\

I & 0.4 & 0.4 \\

\hline

& 1 & 0.7 \\

\end{array}

\)

ΔV = V-V

_{o}

= Vo – 0.15 V

_{O}– V

_{O}= -0.15 V

_{O}

-ln(1-\(\frac{ΔV}{Vo εA}\)) = kt

=> k = 0.173 min

^{-1}.

10. Determine the order of the reaction from the graph.

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: -r

_{A}= k(Csub>A)

^{n}is the general rate expression

Ln(-r

_{A}) = lnk+ nlnC

_{A}

The slope of the line gives the order of the reaction.

**Additional Resources:**