Assignment 2 Solution

CHME 314 Chemical Reaction Engineering

Assignment #2

Due date: April 4th, beginning of the class

Dr. Anand Kumar

Homework and exams should meet the following guidelines:  Submit the assignment on time. 10% marks/day will be deduced for delay in submission.  State all the assumptions clearly.  Draw and label all the necessary sketches.  Work should be neat and readable.  Show all the steps to help TA understand what you are doing.  Use computer generated plots.  Staple all of the pages

Question 1: For a gas reaction at 400 oK the reaction rate is reported as:



[10 pts]

dp A  10.0 p A2 , atm / hr dt

a) What are the units of the rate constant? b) What is the value of the rate constant for this reaction if the rate equation is expressed as:

 rA  k C A2 ,

Solution:

mol liter hr

Question 2: For the gas-phase oxidation of ethylene oxide,

[10 pts]

C2H4 + ½ O2 → C2H4O Construct a stoichiometric table in terms of moles on the basis that only the reactants are present initially, and ethylene in the limiting reactant. Solution:

Question 3: [30 pts] Biodiesel company is working to convert the waste cooking oils from local dining halls and restaurants into diesel fuel to run the local shuttle buses. Waste cooking oils can be converted to biodiesel in several ways. One way is by gasphase pyrolysis: (RC(O)OCH2)3 → (RCH2)3 + 3 CO2

-3

-1

This can be modeled as first-order irreversible reaction with a measured k=5x10 min at 150 ⁰C and a measured Ea=85 kJ/mole. Pure cooking oil is injected into a hot (T=227 ⁰C) reactor at a rate of 2.5 mole/min. At this temperature all the species are in the vapor phase. The steady-state pressure in the reactor is 10 atm. (a) If the reactor is a CSTR, what reactor volume is required to achieve 90% conversion? (b) If the reactor is a PFR and the pressure drop is negligible, what reactor volume is required to achieve 90% conversion? (c) If you had a PFR half the volume you computed in part (b), and then fed its output into a CSTR half the volume you computed in part (a), what would the conversion be? What if you hooked them up the other way round: the half-size CSTR first and the halfsize PFR afterwards? (d) Suppose the reaction is carried out in a batch reactor, by filling it with enough cooking oil and heating rapidly to 227 ⁰C, so that when the oil vaporizes, but before any significant reaction has occurred, the initial pressure in the reactor will be 2.7 atm. What will the pressure be in the isothermal batch reactor when the reaction has run to 90% conversion? (e) What would the batch reactor volume have to be if we were to process 3600 moles/day (= 2.5 moles/minute) of cooking oil this way? Assume that the batch reactor can be emptied and refilled very rapidly, and that it is not necessary to clean the reactor between batches. (f) Which reactor (CSTR, PFR, batch) would you recommend be used for this process? Explain briefly. Solution:

f)

Question 4: Calculate the total reactor volumes to process 4 liters/min to 90% conversion for the reaction: [30 pts]

for CAO = 2 moles/liter with k = 0.5 liter/mole min for: (a) Two equal volume CSTRs in series (b) A CSTR followed by a PFR, with equal volumes

Solution:

Question 5: Consider the first reversible liquid reaction: [15 pts] k1 A

R k2

Where for this system, -rA = rR = k1 CA - k2 CR

and k1 = 1.0 min -1, k2 = 0.25 min -1, vo = 5 liter/min initially CAo = 5.0 mol/liter and CRo,= 0, (a) Find the residence time for 60% conversion in a CSTR and the required volume. (b) Find the residence time for 60% conversion in a PFR and the required volume. (c) Find the maximum conversion (equilibrium conversion) for this system. Is it the same for both systems?

Question 6: [20 pts] An aqueous reactant stream at the concentration given below (CAo) passes through a PFR unit followed by a CSTR. The reaction is given by 2A

R,

-rA = k CA

Find the concentration at the exit of the CSTR if in the PFR CA1 = 5 mol/liter and the volume of the PFR unit is of the same volume of the CSTR unit. The value of the constant “k” is not given. CA1= 5 mol/liter CAo= 10 mol/liter

VPFR CA2 = ? VPFR = VCSTR

Solution: