Chapter 5 Octave Solutions Manual

CHAPTER 5 Solution’s for CHEMICAL REACTION ENGINEERING BY-OCTAVE LVENSPIL CHAPTER 5

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Problem 5.1 (p. 113) reaction 2 A →R + 2 S with kinetic unknown. If required a space velocity of 1 min-1 to achieve 90% conversion of A in a plug flow reactor, find the Consider the gas phase Space and time corresponding mean residence time of the fluid in the plug flow reactor soln

If the system is of constant density and residence time time space are equal, but in this case the system is of variable density because the flow rate varies during the reaction, since it is a gaseous and varies the total number of moles. Conclusion No one can calculate the mean residence time of the fluid with the data available

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Problem 5.2 (p. 113) In a batch reactor operated isothermally reached 70% conversion of liquid reagent in 13 min. What is space weather required to perform this operation in a plug flow reactor and one complete mix?

because the system is constant density so you (is liquid)

Can not be calculated τ, or s for mixed reactor because kinetics known.

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Problem 5.3 (p. 113) An aqueous stream of monomer A (1 mol / L, 4 L / min) enters a complete mixing reactor 2 where L is the radiated and polymerizes follows A→R→ S → T ........ In the output current CA = 0.01 mol / L and for a particular product W must be CW = 0.0002 mol / L. Find reaction rate of A and W Solution A→R R + A→S S + A→T T + A→U U + A→V V + A→W Assuming that the reactions are elementary -RA = k1CA + k2 + k3 CA CA CR CS CT + CA + k4 k5 + k6 CA CA CU CV rW = CV + k6 k7 CA CA CW There are 7 kinetic constants involved, so I require at least 8 points experimental to calculate the numerical value of the constants.

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Problem 5.4 (p. 113) It is planning to replace a mixed reactor with one that has twice the volume. For the same feed rate and the same aqueous feed (10 mol of A / L), find the new conversion. The The reaction kinetics are represented by CA1-rA = k, 5

A→R

The actual conversion is 70%. Solution

6

Calculated

4

Correct

M

2 0 0.74

0.76

0.78

0.8

0.82

Conversion

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Problem 5.5 (p. 113) An aqueous feed A and B (400 L / min, 100 mmol / L of A, 200 mmol / L of B) will be converted to product in a flow reactor piston. The kinetics of the reaction is represented by: CA-CB rA = 200 mol / L min

A + B→R

Find reactor volume required to achieve 99.9% A product conversion in Solution

Constant density liquid system

-

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Problem 5.6 (p. 113) A plug flow reactor (2 m3) processes an aqueous feed (100 L / min) containing a reagent A (CA0 = 100 mmol / L). This reaction is reversible and is represented by: A

R

-RA = 0.04 min-1CA - 0.01 min-1 CR

Find first equilibrium constant and after the reactor the conversion Solution System fluid density is constant because

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Problem 5.7 (p. 114) The gas coming out of a nuclear reactor containing a full range of radioactive traces, the conflict being the Xe-133 (mean life = 5.2 days) This gas flows continuously through a tank with a high retention, with residence time of 30 days, which may be assume that the contents are well mixed. Find activity fraction that is removed in the tank Solution Assuming that the reaction is of constant density and that is first order can be calculated from the kinetic constant through time life

For mixed reactor

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Problem 5.8 (p. 114) A mixed reactor (2 m3) processes an aqueous feed (100 L / min) containing a reagent A (CA0 = 100 mmol / L). This reaction is reversible and is represented by: A

R

-RA = 0.04 min-1CA - 0.01 min-1 CR

What is the equilibrium conversion and the actual conversion of the reactor? Solution System fluid density is constant because

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Problem 5.9 (p. 114) A specific enzyme catalyzes the fermentation of A. Find the volume of the plug flow reactor required for 95% of conversion of reactant A (CA0 = 2 mol / L) at a given concentration of enzyme. Fermentation kinetics of this enzyme concentration is given by: enzyme

A


→ R

CA-rA = 0.1 / (1 + 0.5 CA)

Solution System constant density because 1 mol of A yields 1 mol of R

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Problem 5.10 (p.114) In a plug flow reactor a gaseous feed of pure (2 mol / L, 100 mol / min) decomposes to give a variety of products. The kinetics of the reaction is represented by A→2.5 products

-RA = 10 min-1 CA

Find expected conversion reactor 22 L Solution System variable density varies because Ftotal, which causes the flow volume varies

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Problem 5.11 (p. 114) The enzyme catalyzes the fermentation E substrate A (reactive), obtaining R. Find size required mixed reactor for 95% conversion of a feed stream (25 L / min) reagent (2 mol / L) and enzyme. Fermentation kinetics at this enzyme concentration is given by enzyme

A


→ R

CA-rA = 0.1 / (1 + 0.5 CA)

Solution Constant density System

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Problem 5.12 (p.114) An aqueous solution (400 L / min, to 100 mmol / L, 200 mol of B / L) will be converted to product in a mixed reactor. The kinetics of the reaction is represented by A + B→R

CA-CB rA = 200 mol / L min

Find reactor volume required to achieve 90% conversion Solution System fluid density is constant because

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Problem 5.13 (p. 115) At 650 ° C the vapor decomposes as follows PH3 4 PH3 →P4 (g) +6 H2

-RPH3 = 10 h-1 CPH3

What size of plug flow reactor operating at 649 ° C and 11.4 atm required to achieve 75% conversion of 10 mol / H PH3 having 2/3 of PH3 y1 / 3 inert? Solution System variable density varies because it is gaseous and Ftotal, which causes the volumetric flow varies

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Problem 5.14 (p. 115) A gas stream of pure reagent A (CA0 = 660 mmol / L) enters a plug flow reactor at a rate FA0 = 540 mmol / min and polymerized as follows 3A→R

-RA = 54 mmol / L min

How big should the reactor to CAF = 330 mmol / L? Solution System variable density because it varies Ftotal gas and as the flow volume also vary

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Problem 5.15 (p. 115) A gaseous feed of pure A (1 mol / L) enters reactor complete mixture (2 L) and reacts as follows: 2A→R

CA2-rA = 0.05 mol / L s

Find feed rate (L / min) to give a concentration of CAf output = 0.5 mol / L Solution System variable density as it is gaseous and Ftotal varies during During the reaction, the volumetric flow varies

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Problem 5.16 (p. 115) The gaseous reagent is decomposed as follows A→3R

-RA = 0.6 min-1 CA

Find A conversion is obtained in a complete mixing reactor of 1 m3 which is fed with a stream containing 50% A and 50% of inert (v0 = 180 L / min, CA0 = 300 mmol / L) Solution System variable density as it is gaseous and Ftotal varies during During the reaction, the volumetric flow varies

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Problem 5.17 (p. 115) A mixture of ozone 20% - 80% air at 1.5 atm and 95 ° C passes at a rate of 1 L / s through a plug flow reactor. Under these conditions decomposes ozone by reaction homogeneous -RA = k Coz2 k = 0.05 L / mol s

2 O3 →3 O2

What size decomposition?

reactor

is

requires

for

achieve

50

%

of

Solution The rate of reaction is second order and the system of density Yavariable design equation and varies because Ftotal is gaseous. integrated in the text for this case.

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Problem 5.18 (p. 116) An aqueous feed containing A (1 mol / L) is processed in a plug flow reactor 2 L (2 A →R, CA2-rA = 0.05 mol / L s). Find the The outlet concentration for a feed rate of 0.5 L / min Solution The system is liquid, so it is of constant density and
εA =0

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Problem 5.19 (p. 116) Is fed to a complete mixing reactor 1 a gas stream L A pure approximately 3 atm and 30 ° C (120 mmol / L). There are decomposed and the concentration of A in the output is measured for each flow rate. From the data the following equation Find represents the decomposition rate of A. Suppose that only A concentration affects the rate of reaction v0 (L / min) CA (mmol / L)

0.06 30

0.48 60

1.5 80

8.1 105

Solution The system is of variable density varies because it is gaseous and F total

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A→3R

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Problem 5.20 (p. 116) You are using a mixed reactor to determine the reaction kinetics whose stoichiometry is A →R. For this different flow of an aqueous solution containing 100 mmol / L of A are fed to a reactor of 1 L and for each run the concentration of A output is recorded. Find the equation representing the speed following. Assume that only the reagent A affects the speed of reaction v (L / min) CA (mmol / L)

4

6 20

24 50

Solution The system is fluid density is constant because

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Problem 5.21 (p.116) It is planning to operate a batch reactor to convert A into R by reaction in liquid phase with the stoichiometry A →R, whose reaction rate is shown in the following table CA (Mol / L) -RA (Mol / Lmin)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1.0

1.3

2.0

0.1

0.3

0.5

0.6

0.5

0.25

0.1

0.06

005

0.045

0.042

How long must react each tuned to the concentration falls from CA0 = 1.3 mol / L to CAF = 0.3 mol / L? Solution System fluid density is constant because

-RA is plotted vs CA to complete the data between CA = CA = 0.8 to 1.3 mol / L. Axis is used to facilitate the representation semilog

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Problem 5.22 (p. 116) For the reaction of 5.21 problem, what size flow reactor the piston is required for 80% conversion of a stream of 1000 A mol / h with CA0 = 1.5 mol / L Solution The density is constant and CA0 CAF = (1 - XA) = 1.5 (1 -0.8) = 0.3 mol / L

Chart values are taken from problem 5.21. Reproduced extended the necessary part of the graph

0.1 0

0.5

1

1.5

2

Reaction rate

Concentration A

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2.5

Problem 5.23 (p. 117) a) For the reaction of 5.21 problem, what size CSTR Full required to obtain 75% conversion of stream A 1000 mol / h with CA0 = 1.2 mol / L b) Repeat part a) with the modification that the power is double, or A 2000 mol / h with CA0 = 1.2 mol / L c) Repeat part a) with the modification that CA0 = 2.4 mol / L, 1000 mol treating A / h and CAF = 0.3 mol / L Solution

b) Assuming that the volume is still 1500 L and that what varies is XA

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correct calculated

XAF /-RAF never going to be 0.75, said physically with τ not occur as small reaction

Assuming XA = 0.75 and the volume required varies

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Problem 5.24 (p. 117) A gaseous hydrocarbon of high molecular weight is fed a continuously mixed reactor which is heated to high temperatures to cause thermal cracking (homogeneous reaction gaseous) materials of lower molecular weight, collectively called R using approximate stoichiometry A →5 R. Changing feed rate is obtained different extensions cracking as shown

FA0 (mmol / h) CAs (mmol / L)

300 16

1000 30

3000 50

The vacuum inside the reactor volume is 0.1 L and temperature A feed concentration is CA0 = 100 mmol / L. Find the equation which represents the cracking reaction Solution System variable density varies because it is gaseous and Ftotal

Draw a graph of rate of reaction vs concentration of A

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5000 60

Problem 5.25 (p. 117) The aqueous phase decomposition of A is studied in a reactor thorough mixing. The results in the table were obtained P.5.25 steady state runs. What residence time required for obtain 75% conversion of reagent feeding with CA0 = 0.8 mol / L CAe CAs

2.00 0.65

2.00 0.92

2.00 1.00

1.00 0.56

1.00 0.37

0.48 0.42

0.48 0.28

0.48 0.20


t (S)

300

240

250

110

360

24

200

560

Solution The system density is constant, so

These values are plotted for values-rA vs CA necessary

Reaction rate

Concentration A

.

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Problem 5.26 Repeat the previous problem, but for a completely mixed reactor Solution

=

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Problem 5.28 (p. 118) In a batch reactor operating at constant volume and 100 ° C. The following data were obtained from the decomposition of gaseous reactant A t (s) pA (atm)

0 1.00

20 0.80

40 0.68

60 0.56

80 0.45

100 0.37

140 0.25

200 0.14

260 0.08

The stoichiometry of the reaction is 2 to →R + S What size of plug flow reactor (in L) can operate at 1 atm A treat 100 mol / h in a stream containing 20% inerts in to obtain 95% conversion of A Solution The system is of constant density, both in the batch reactor as in the plug flow because Ftotal = Ntotal = constant

-rA =KC

n

If first-order

kt = - ln (1-X A )

PA/pA0 is plotted vs. t gives a straight line and if it means 1st order

1

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330 0.04

420 0.02

Then the reaction is first order

For plug flow reactor using equation 5.23 (p. 103)

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Problem 5.29 (p. 119) Repeat the previous problem, but for a completely mixed reactor Solution

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