CHEN-7250 Homework

Assignment No. 1

Due: 08/24, Mon

1. Problem 1-17

2. A tank contains 50 liters of water solution of A. The initial concentration of A in the tank is 10 g/L. At time = 0, additional A is fed into the tank at the rate of 1 L/minute. The concentration of A in the input stream is 20 g/L. At the same time the liquid in the tank is withdrawn through a pipe connected at the bottom of the tank. The flow rate through this pipe is v = (0.005)V, L/minute, where V is the volume of liquid in the tank. The liquid is well agitated. The density of liquid stays constant.

A chemical reaction of A→B takes place in the tank: r_A = -(0.08)C_A g/L.min.

(a) Using Polymath, determine the amount of A, the concentration of A, and volume of liquid in the tank when time = 50 minutes.

(b) Repeat part (a) by hand calculation. Hint: Take N_A (not C_A ) as the dependent variable.

Assignment No. 2

Due: 08/28, Fri

Problem 3-17 

Repeat 3-17 (b) using Polymath. Additional Question: (c) Calculate the reaction time to achieve 50% conversion.

Assignment No. 3

Due: 08/31, Mon

1. Starting from Mole Balance Equation of PFR, derive Eq. 4-17, p.170, for a second order isothermal gas reaction. Show the derivation process. Picking up the formula from Appendix is not acceptable.

2. Problem 4-7 (a), (b), (e). Ignore cost in (e). Consult Eq. 3-21.

Assignment No. 4

Due: 9/02, Wed

4-7 (f). with a revision: redo (a), (b), (e). Use Polymath where necessary.

4-12 (a)

Assignment No. 5

Due: 9/04, Fri

Problem 4-13.

Assignment No. 6

Due: 9/09, Wed

1. Problem 4-16 (a), (b), (c).

2. An elementary gas reaction, A ® 2B, is taking place in an unsteady-state CSTR. The reactor is initially filled with an inert gas. At time zero feed containing A only is fed into the reactor. Determine C_A, C_B, C_I as a function of time during the startup period of this reactor. How long would it take for C_B to reach 50% of C_A0? Calculate the steady-state conversion.

Additional information: -r_A = 0.1 C_A mols A/(min,)(L), Pure A is fed into the reactor, P_A0 = 1 atm, T = 300^oK, v₀ = 1 L/min., V = 10 L

Hint: Apply total mole balance.

Remarks: Use Polymath where necessary.

Assignment No. 7

Due: 09/14, Mon

Problem 4-17 (a) & (b).

Remarks: Use conversion method (not F_j method). Trial and error (repeated Polymath calculation) is necessary assuming certain input parameters. Pay attention to Eq. 4-29 & 4-25 for part (b).

Assignment No. 8

Due: 9/16, Wed

Problem 4-23 (a), (b)

Notes:

Conversion in part (a) is based on ethylene glycol.

Note that unit of k is in hour, not minute. Assume down-time for batch cycle = 4.5 hours in part (b).

Problem 4-25 (a), (b)

Assignment No. 9

Due: 9/23, Wed

Problem 5-6

Remarks: Use 4 different methods (Differential/Integral, Linear/Nonlinear methods)

Note: Polymath does not give the slope at the last data point (t=60), a glitch in the program. To avoid this problem, type in t=59.99, instead of 60, when you do the slope estimation.

Assignment No. 10

Due: 9/25, Fri

1. Problem 5-5

2. Problem in CD: P5-G_B. Pay attention to Eq.5-28.

The oxidation of propene (P) to acrolein (A) was carried out over a Mo-Pr-Bi catalyst [Ind. Eng. Chem. Res., 26, 1419 (1987)].

CH₃CH=CH₂+O₂CH₂=CHCHO+H₂O

It has been proposed to correlate the data using the power law model for the rate law [cf. Equation (5-2)].

r_acrolein

The reaction was carried out in a differential reactor with 0.5 g of catalyst at 623 K. From the data below, determine the reaction orders with respect to propeneand oxygenand the specific reaction rate, k.

where

F_A=exiting molar flow rate of acrolein, mmol/h
P_P= entering partial pressure of propene, atm
P_O2= entering partial pressure of oxygen, atm

Remarks: Solve by linear and nonlinear method for both problems.

Assignment No. 11

Due: 9/28, Mon

1. For an elememtary reaction of A® B® C,

(a) Prove E6-4-7 & E6-4-9 for batch reaction (replace τ with t).

(b) Determine Y_B and S_BC in a CSTR as function of τ and k_j.

2. Problem 6-5 (a) (b) (c)

Assignment No. 12

Due: 9/30, Wed

Problem 6-6, Revised as follows.

Ignore all of the questions (a) – (g), instead, answer the following. Calculate the reactor volume(s) and the selectivity, S_B/XY = r_B/(r_X + r_Y), for the following three cases. Desired conversion is 90%.

(a) A CSTR is used.

(b) A PFR is used.

(c) A CSTR and a PFR is used in series in proper order and manner so as to maximize the selectivity (S_B/XY).

Problem 6-21 (a) (b) (c).

Assignment No. 13

Due: 10/02, Fri

1. The following elementary liquid reactions are carried out by two different methods as described below. Determine Yield (Y_D/A) and Selectivity (S_D/U) for each case.

A + B → D, k₁ = 0.25 (mol/L)^-1(minute)^-1

A + 2B → U, k_2A = 0.66 (mol/L)^-2(minute)^-1

(Method 1)

Reactants A and B are kept in two separate vessels (Tank A and Tank B). The volume of each reactant is 50 liters. The concentration of reactant A is 0.8 mol/L and that of reactant B is 1.2 mol/L. The reactant B is poured abruptly into Tank A, mixed well, and the reaction is carried out in batch mode for 60 minutes.

(Method 2)

Reactant B is gradually added into Tank A at a constant flow rate of v₀ until Tank B is emptied. Assume the reaction stops at this point. The flow rate, v₀, is adjusted such that the final conversion of A is equal to that of Method 1.

2. Problem 6-11

Assignment No. 14

Due: 10/07, Wed

Problem 8-5

Assignment No. 15

Due: 10/09, Fri

Problem 8-6

Problem 8-12 (a) – (d). 20-points.

Notes: 1 M = 1 mol/L. In question (d): part (b) ® part (c).

Assignment No. 16

Due: 10/12, Mon

Problem 8-8 (a), (b), (d).

Problem 8-9 (a-1), (b), (c), (d). Change Ua/ρ_b from 0.08 to 2.0.

Remarks: Ignore the case where a= 0.019 in 8-8. Problem 8-9 carries 20-points maximum.

Assignment No. 17

Due: 10/16, Fri

Problem 8-18 (a)-(d), (f), (g)

Assignment No. 18

Due: 10/19, Mon

Problem 9-7. With the following revisions.

E1 = 10 kJ/mol

E2 = 15 kJ/mol

DH = -5 kJ/mol A

Problem 9-11 with a correction: UA=250.

Remarks: Consult Eq. 8-49 (p.523).

Assignment No. 19

Due: 10/28, Wed

(1) Show that

h = tanh (f₁)/ f₁, for a catalyst with a shape of flat-plate.

where f₁ = L[k₁/De]^1/2, L = half of the slab thickness.

(2) Problem 12-6 (a), (b)

Assignment No. 20

Due: 10/30, Fri

(1) For a catalyst of slab geometry, calculate the effectiveness factor for a second-order reaction when ф₂ = 1.5 (Use Polymath).

(2) A catalytic reaction experiment was carried out using a differential reactor packed with spherical catalyst particles. The catalysts were then taken out of the reactor, cut into two pieces (hemi-sphere form), reloaded, and the same experiment was repeated. The data indicate the reaction rate increased by 20% in the second experiment. Calculate the effectiveness factor and the Thiele modulus for the spherical catalyst. Assume first-order reaction.

Assignment No. 21

Due: 11/2, Mon

          Following the Bischoff analysis (class notes: pay attention to equations 1 and 2 on the board),

Show that

η = tanh (f₁)/ f₁, for first order reaction.  

Hint:

Assignment No. 22

Due: 11/4, Wed

1. Problem 12-16 (a)-(c).

Spinning basket reactor is a catalytic CSTR.

Assignment No. 23

Due: 11/6, Wed

Prove that

Ω = η / (1+ ηk₁L/k_C)

Note that it is same as Eq. 12-55 with k₁=k”₁ρ_CS_a, and a_C=1/(ρ_CL).

Assignment No. 24

Due: 11/16, Mon

For a CSTR, prove that:

(a) , Eq. (3-20)

(b) , Eq. (13-41)

Note:

Assignment No. 25

Due: 11/18, Wed

1. Derive the RTD function for two CSTRs connected in series (τ₁ and τ₂ represent the space times for each CSTR). Make a plot of RTD where τ₁ = 1, τ₂ = 2.

2. Using Polymath show RTD function on graph and calculate σ²_θ for above case where τ₁ = 1, τ₂ = 2.

Assignment No. 26

Due: 11/20, Fri

1. Problem 13-6. Exclude d-2. Ignore Reactor B.

2. Problem 13-19. (a) - (i), (m), (o) (20 points for this problem).

Assignment No. 27

Due: Mon, 11/30

1. Prove that s_q² = 1/n, for TIS model.

2. Problem 14-13. (c), (f), & (g).

For the sake of uniform answer, take s² = 75.4 and τ = 9.93 from the previous HW (13-19).

In (g), use RTD method and straight mole balance method to compute the conversion. Repeat it for a first-order reaction with k = 0.1 min^.-1

3. A bonus question (5-point max.):

Gathering up your chemical engineering knowledge (heat transfer, transport, etc.), make your best estimate of the following question:

It takes 5 hours to cook 10-lb turkey. How long would it take to cook a 20-lb turkey?

Remarks: Consider a convection oven, not a microwave oven.