ChE-370 Homework

Assignment No. 1

Due: 01-14, Wed

Problem 1-17

Assignment No. 2

Due: 01-16, Fri

Problem 1-15

Assignment No. 3

Due: 01-21, Wed

A tank contains 50 liters of salt solution. The initial concentration of the salt is 10 g/L. At time = 0, pure water is fed into the tank at the rate of 1 L/minute. At the same time the liquid in the tank is withdrawn through a pipe connected at the bottom of the tank.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 = (0.01)V, L/minute, where V is the volume of liquid in the tank. The liquid is well agitated. The density of liquid stays constant. There is no chemical reaction.

(a) Using Polymath, determine the amount of the salt, the concentration of the salt, and volume of liquid in the tank when time = 100 minutes. Consider mole balance on salt and overall mass balance in terms of liquid volume (V).

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

Assignment No. 4

Due: 01-23, Fri

Problem 2-7

Assignment No. 5

Due: 01-26, Mon

Problem 3-7

Assignment No. 6

Due: 01-28, Wed

Problem 3-10 (a) & (b).

Assignment No. 7

Due: 01-30, Fri

Problem 3-11, (a), (b), (c). Assume elementary reaction.

Assume CSTR in (a). space time volume ® space time.

(c) Stoichiometric mixture means that the feed composition is proportional to the stoichiometric coefficients.

Problem 3-15

Take H₂ as component A.

Assume a steady-state flow reactor in part (a).

Assignment No. 8

Due: 02-02, Mon

Problem 3-17

Assignment No. 9

Due: 02-04, Wed

1. Revisit 3-17 and calculate the reaction time required to achieve 50% of conversion (Use Polymath).

2. Problem 3-16

Assignment No. 10

Due: 02-06, Fri

Problem 4-7 (a), (b), (e)

Note: Ignore cost in part (e), also change Table 4-1 to Table 4-3.

Assignment No. 11

Due: 02-09, Mon

1. Derive Eq. 4-17, p. 170.

2. Problem 4-7 (f) with a correction: (a) through (c) ----- (a), (b), & (e). Use Polymath where necessary.

Assignment No. 12

Due: 02-16, Mon

Problem 4-11

Problem 4-13

Assignment No. 13

Due: 02-18, Wed

Problem 4-17 (a)

Notes: This is a trial and error problem with two unknown parameters (α and kC_A02/F_A0).

Assignment No. 14

Due: 02-20, Fri

1. Problem 4-18 (b) and (c)

Additional question: (e) The reactor position is now reversed (PBR first), everything else remaining the same. Calculate the conversion after PBR and CSTR.

2.

Assignment No. 15

Due: 02-23, Mon

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

2. CD-Problem 4-33_B (Modified) – Unsteady-state Polymath Problem.

(CSTR train) The elementary liquid-phase reaction

A + B C

is to be carried out in a CSTR with three impellers. The mixing patterns in the CSTR are such that it is modeled as three equal-sized CSTRs in series. Species A and B are fed in separate lines to the CSTR, which is initially filled with inert material. each CSTR is 200 dm³ and the volumetric flow to the first reactor is 10 dm³/min of A and 10 dm³/min of B.

A. Plot the concentration of A exiting each tank as a function of time.

B. Determine the time necessary to reach steady state (i.e., when C_A exiting the third reactor is 99% of the steady-state value).

C. What is the steady-state conversion of A?

D. Suppose that the feed for species B is split so that half is fed to the first tank and half to the second tank. Repeat part A.

Additional Information

C_A0 = C_B0 = 2.0 mol/dm³
k = 0.025 dm³/mol/min

Assignment No. 16

Due: 02-25, Wed

Problem 4-23 (a) and (c).

Notes: Take ethylene chlorohydrin as component A. Conversion should be based on component A.

Assignment No. 17

Due: 02-28, Fri

Problem 4-25 (a) and (b).

Correction: first-order → elementary

Assignment No. 18

Due: 03-04, Wed

Problem 5-6 (a) with revision: Use differential, integral, and non-linear methods.

Assignment No. 19

Due: 03-06, Fri

Problem 5-5 (a) & (b). Use two different methods for (a).

Problem 5-8 (a) & (b). Apply all possible methods for (b).

Assignment No. 20

Due: 03-09, Mon

Homework Problem in CD: P5-G_B

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.

Assignment No. 21

Due: 03-11, Wed

Problem 5-10

Assignment No. 22

Due: 03/13, Fri

An elementary reaction of A® B® C occurs in a CSTR. Determine the yield of B, Y_B.

Assignment No. 23

Due: 03/27, Fri

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.

Assignment No. 24

Due: 03/30, Mon

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

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

2. Problem 6-5.

Assignment No. 25

Due: 04/01, Wed

1. Problem 6-14 (a) & (b).

2. For an elementary reaction of A® B® C, show that

C_Bmax = C_A0 (k₂/k₁)^k2/(k1-k2)

Assignment No. 26

Due: 04/06, Mon

Problem 8-5

Assignment No. 27

Due: 04/10, Fri

Problem 8-6, (a)-(d)

Assignment No. 28

Due: 04/13, Mon

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

Remarks: Ignore the case where a= 0.019 in (d).

Assignment No. 28

Due: 04/15, Wed

(20 points for this problem)

Problem 8-9 (a), (b), (d) with the following revision.

Ua/ρ_b = 2.0 J/(s.Kg.^oK)

Assume constant pressure throughout.

Additional question in part (d): Find the value of Ua/ρ_b that will maximize the conversion for co-current operation.

Assignment No. 29

Due: 04/17, Fri

Problem 8-12, (a) – (d)

Assignment No. 30

Due: 04/20, Mon

1. Problem 8-9 (c) with the following revisions:

The CSTR is cooled by a heat exchanger coil. Note that the temperature of coolant is not uniform.

UA = 50 J/s.K

m_C = 0.2 kg/s

2. Problem 8-18

Ignore all the questions, (a)-(j).

Calculate the reactor temperature and conversion. Note that there may be more than one solution.

Assignment No. 31

Due: 04/22, Wed

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

Assignment No. 32

Due: 04/24, Fri

1. The following liquid parallel reaction takes place in a CSTR.

A → B, k₁ = 3.2x10^-4 mol/L.min. at 300^oK

A → C, k₂ = 1.2x10^-5 mol/L.min. at 300^oK

E₁ = 18,000 cal/mol

E₂ = 24,000 cal/mol

v₀ = 2.0 L/min

V = 10 L

C_A0 = 1.0 mol/L

Determine optimum reactor temperature that will maximize production of B.

2. The same reaction is now carried out by a PFR equipped with a co-current heat exchanger. All of above information apply here.

Additional information:

C_pA = C_pB = C_pC =18.0 cal/mol

C_pcoolant = 1.0 Kcal/Kg

H_A = 5,500 cal/mol

H_B = 1,600 cal/mol

H_C = 4,000 cal/mol

Ua = 3.0 cal/min.^oK.L

T₀ = 350^oK

Ta₀ = Temperature of inlet coolant temperature =310^oK

Determine the flow rate of coolant (m_C, Kg/minute) that will maximize production of B. Calculate the yield of B and Selectivity (B/C) under this condition.

Assignment No. 33

Due: 04/27, Mon

Problem 9-11 (a) with the following revision.

UA = 250 (not 2500)