# Chemical Reaction Engineering Questions and Answers – Batch Reactor Design Equations

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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$$\frac{dXA}{dt}$$ = -rA V
b) $$\frac{dXA}{dt}$$ = -rA
c) $$\frac{dXA}{dt}$$ = -rAV
d) NA0$$\frac{dXA}{dt}$$ = -rA

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 = $$\int_0^{XA} \frac{dXA}{-r_{AV}}$$

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) –ri = $$\frac{1}{RT}\frac{dpi}{dt}$$
b) –ri = $$\frac{V}{RT} \frac{dpi}{dt}$$
c) –ri = $$\frac{PV}{RT} \frac{dCi}{dt}$$
d) –ri = V $$\frac{dCi}{dt}$$

Explanation: The design equation for batch system is –ri = $$\frac{1}{V}\frac{dNi}{dt}.$$ For constant volume system
–ri = $$\frac{d(\frac{Ni}{V})}{dt} = \frac{dCi}{dt}$$ where C = p/RT. Hence, –ri = $$\frac{1}{RT}\frac{dpi}{dt}.$$

4. Most suitable reactor for pharmaceutical industry is ______
a) MFR
b) PFR
c) Batch reactor
d) PBR

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 $$\int_0^{XA} \frac{dXA}{-rA(1+XA εA)}$$

Explanation: The varying volume in a batch reactor is given as V = V0 (1+XA εA) where εA 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 εA of gas for the following isothermal gas phase reaction.
(Assuming pure A)
A → 4R
a) 1
b) 2
c) 3
d) 4

Explanation: εA is fractional volume change between no conversion and complete conversion. It is calculated using the formula given below
εA = $$\frac{V1-V0}{V0} = \frac{4-1}{1}$$ = 3
where V1 is volume at complete conversion and V0 is volume at no conversion.

7. For the following reaction, calculate εA, containing 50% A and 50% inerts.
a) 0.5
b) 1.5
c) 2.5
d) 0.75

Explanation: When X=0, A=0.5 and Inerts=0.5
When X=1, A=2 and Inerts=0.5
εA = $$\frac{2.5-1}{1}$$ = 1.5.

8. Constant volume batch reactors are the widely used industrial batch reactors.
a) True
b) False

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) -rA = 0.17 CA
b) -rA = CA
c) -rA = 2CA
d) -rA = 3.6CA

Explanation:
2A → R
εA = $$\frac{.7-1}{1}$$ = -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-Vo
= Vo – 0.15 VO – VO = -0.15 VO
-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