Page 235 - Elements of Chemical Reaction Engineering 3rd Edition

Chap. 4 Questions and Problems 207

P4-4* Nutrition is an important part of ready-to-eat cereal. To make cereal healthier,
many nutrients are added. Unfortunately, nutrients degrade over time, making
it necessary to add more than the declared amount to assure enough for the life
of the cereal. Vitamin X is declared at a level of 20% of the Recommended
Daily Allowance per sewing size (serving size = 30 g). The Recommended
Daily Allowance is 6500 IU (1.7 X 106 IU I= 1 g). It has been found that the
degradation of this nutrient is first-order in the amount of nutrients. Accelerated

Temperature ("C) 45 55 65
k (week-') 0.0061 0.0097 0.0185

(a) Given the information above and that the cereal needs to have a vitamin
level above the declared value of 6500 Ttr for 1 year at 25°C what IU
should be present in the cereal at the time it is manufactured? Your
answer may also be reported in percent overuse: (Ans. 12%)
C (t = 0) - C (t = 1 yr)
%OU = x 100
c (t= 1 yr)
(b) 14t what percent of declared value of 6500 1U must you apply the vita-
min? If 10,000,000 lb/yr of the cereal is made and the nutrient cost is $5
per pound, how much will this overuse cost?
(c) If this were your factory, what percent overuse would you actually apply
and why?
(d) How would your answers change if you stored the material in a I3angkok
warehouse for 6 months, where the daily temperature is 40°C, before
moving it to the supermarket? (Table of results of accelerated storage
tests on cereal; and Problem of vitamin level of cereal after storage cour-
tesy of General Mills, Minneapolis, MM.)
The liquid-phase reaction
AS-B --+ C

follows an elementary rate law and is carried out isothermally in a flow sys-
tem. The concentrations of the A and B feed streams are 2 M before mixing.
The volumetric flow rate of each stream is 5 dm3/min and the entering tem-
perature is 300 K. The streams are mixed immediately before entering. Two
reactors are available. One is a gray 200.0-dm3 CSTR that can be heated to
77°C or cooled to O"C, and the other is a white 800.0-dm3 PFR operated at
300 K that cannot be heated cr cooled but can be painted red or black. Note
k = 0.07 dm3/mol.min at 300 K and E = 20 kcal/mol)
(a) Which reactor and what conditions do you recommend? Explain the rea-
son for your choice (e.g., color, cost, space available, weather condi-
tions). Back up your reasoning with the appropriate calculations.
(b) How long would it take to achieve 90% conversion in a 2Wdm3 batch
reactor with C,, = C,, = 1 M after mixing at a temperature of 77"C?
(c) How would your answer to part (b) change if the reactor were cooled to
WC? (Ans. 2.5 hays)
(d) What concerns would you have to carry out the reaction at higher tem-
peratures?
(e) Keeping Table 4-1 in mind, what batch reactor volume would be: neces-
sary to process the same amount of species A per day as the flow reactors