Assignment #3, Due September 19. 2022
The following problems are for both BPE 421 and BPE 621 classes
4.1 Our winery has discovered that all of last year's crop now being stored for aging contained
200 ppm of a chemical which gives it a garlic flavor. However, we find that the concentration
of this chemical is 50 ppm one year after it was put in storage. Taste tests in which this
chemical was added to good wine shows that it can be detected only if its concentration is
greater than 10 ppm. How long will we have to age this wine before we can sell it?
4.2 Our winery chemist has just found that the reaction by which the garlic flavored compound
of the previous problem disappears is by a reaction that produces a tasteless dimer of the
chemical.
a) With this mechanism, how long must we age our wine before we can sell it?
b) Since we don't entirely trust his judgment (why would a competent chemist work for a
winery?), we decide to test his results by analyzing the wine after the second year of
aging. What percentages should we find if the reaction is first or second order?
4.7 An aqueous ester hydrolysis reaction A  B + C has k = 0.02 min-l and an equilibrium
constant of 10 with all concentrations in moles/liter.
a) Starting with CA0 = 1 mole/liter, and CB0 = CC0 = 0, what is the equilibrium composition?
b) What is the reverse rate constant in the above reaction?
c) Find CA (t), CB(t), and CC(t) in a batch reactor for these initial conditions.
4.12 One hundred moles of A per hour are available in concentration of 0.1 mole/ liter by a
previous process. This stream is to be reacted with B to produce C and D. The reaction
proceeds by the aqueous-phase reaction,
A + B  C + D, k = 5 liters/mole h
The amount of C required is 95 moles/h. In extracting C from the reacted mixture A and B
are destroyed; hence recycling of unused reactants is not possible. Calculate the optimum
reactor size as well as feed composition for this process if the shifting time between batches
is 10 hours.
Data: B costs $1.25/mole in crystalline form. It is highly soluble in the aqueous solution and
even when present in large amounts does not change the concentration of A in solution.
Capital and operating costs are $0.015/(h  liter).
4.16. A pulp mill utilizing the saw dust from nearby lumber mills to produce a market pulp for
paper production. A recent development had the company thinking of increasing the pulp
production by 50% for entering the nonwoven market. A close examination at the pulp mill
has the engineers to conclude that the digesters were the bottleneck. Currently, the
woodchips were steamed, mixed with a pulping liquor and underwent delignification at
150C for 3 hours. For each load of woodchips, a minimum of 2 hours is needed for
loading, heating the digester up, explosive decompression unloading, and cleaning up the
digester for the next load. Your task is to find a way to ease the bottleneck quickly at a low
cost. State your assumptions clearly and your solution to the problem as stated.
The following problems are for BPE 621 class
4.8 A gaseous reaction
A  B + C
r  kCA2 , with k = 0.1 mol·L-1·s-1
is occurring in an isothermal constant pressure batch reactor. The reactor is at 373 K charged
initially with 1 bar of A and 0.2 bar of N2 (not A, B or C), that is not reacting. Determine the
time required for the reaction volume to expand by 50%, i.e. V/V0 = 1.5.
4.9. Sterilization is a batch process by which bacteria and molds in food are killed by heat
treatment. A can of vegetables that originally contained 10,000 viable spores has 100 spores
remaining after heating for 10 min at 250°F. Assuming first-order kinetics, how long must
this can be heated at this temperature to reduce the probability of having a single spore to an
average of 1 in 1 million cans?