This set of Chemical Reaction Engineering Quiz focuses on “Applications of Design Equations for Continuous – Flow Reactors”.

1. Find the volume of reactor needed for 70% conversion of A to product. Aqueous feed of A and B (200lit/min, 20mmolA/lit, 50mmolB/lit) is fed to MFR. Reaction kinetics is as follows

A+B → P

-r_{A} = 200C_{A}C_{B} mol/lit-min

a) 12.5

b) 3.6

c) 6.4

d) 1.5

View Answer

Explanation:

C

_{A0}*X

_{A}= C

_{B0}*X

_{B}

X

_{B}= \(\frac{20*0.7}{50}\) = 0.28

\(\frac{τ}{CA0} = \frac{XA}{-rA}\)

τ = \(\frac{0.7*20*10^{-3}}{200*10^{-6}[20(1-0.7)*50(1-0.28)])}\) = 0.032 = \(\frac{V}{v0} \)

V = 0.032*200 = 6.4 lit.

2. An existing MFR is to be replaced by the one 4 times larger than it. Find the new conversion if a homogeneous liquid phase reaction with reaction kinetics as follows.

A → R

-r_{A} = kC_{A}^{2} with 30% conversion.

a) 0.67

b) 0.45

c) 0.53

d) 0.92

View Answer

Explanation:

\(\frac{τ}{CA0} = \frac{XA}{-rA} \)

\(\frac{V}{CA0 V0} = \frac{0.3}{k[ CA0(1-0.3)]^2} \)

\(\frac{V}{CA0 V0}\) = kτC

_{A0}= 0.6122

When replaced by new reactor

\(\frac{4τ}{CA0} = \frac{XA}{-rA} \)

\(\frac{4Vk}{CA0 V0} = \frac{XA}{(1-XA)^2} \)

X

_{A}= 0.53.

3. Replace the existing MFR with a PFR and calculate the new conversion if a homogeneous liquid phase reaction with reaction kinetics as follows.

A → R

-r_{A} = kC_{A}^{2} with 30% conversion

a) 0.65

b) 0.43

c) 0.38

d) 0.92

View Answer

Explanation:

\(\frac{τ}{CA0} = \frac{XA}{-rA} \)

\(\frac{V}{CA0 V0} = \frac{0.3}{k[ CA0(1-0.3)]^2} \)

\(\frac{Vk}{CA0 V0} \) = kτC

_{A0}= 0.6122

When replaced with a new PFR

\(\frac{τ}{CA0} = \int_0^{XA} \frac{dXA}{-rA} \)

For 2

^{nd}order on Integration we get,

kτC

_{A0}= \(\frac{XA}{1-XA}\) = 0.6122

X

_{A}= 0.38.

4. Find the conversion of a 25 litre PFR if a gaseous feed of pure A (2 mol/lit, 150 mol/min)

Is decomposed, kinetics are as follows.

A → 2.5R

-r_{A} = (15min^{-1}) C_{A}

a) 0.89

b) 0.92

c) 0.45

d) 0.68

View Answer

Explanation:

\(\frac{τ}{CA0} = \frac{V}{FA0}\)

τ = (25*2)/150 = 0.33 min

For a 1

^{st}order reaction with variable volume on integration we get

kτ = (1+εA)ln\((\frac{1}{1-XA})\) – ε

_{A}X

_{A}

15*0.33 = (1+1.5) ln\((\frac{1}{1-XA})\) – 1.5X

_{A}

X

_{A}= 0.92.

5. For a constant volume system, the size of batch reactor is _______________ PFR.

a) smaller than

b) larger than

c) same as

d) cannot be compared

View Answer

Explanation:

For PFR, \(\frac{τ}{CA0} = \int_0^{XA}\frac{dXA}{-rA} \)

For Batch reactor, \(\frac{t}{CA0} = \int_0^{XA}\frac{dXA}{-rA} \)

From the above equations it is clear that theoretically the element of fluid reacts for same length of time in PFR and Batch reactor. But shutdown time as to be considered for actual design.

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