Page 442 - Elements of Chemical Reaction Engineering Ebook

Chap. 7' Questions and Problems 41 3
P7-8* Consider the application of the PSSH to epidemiology. We shall treat each of
the following steps as elementary in that the rate will be proportional to the
number of people in a particular state of health. A healthy person, H, can
become ill, I, spontaneously,
H k')I (E'-8.1)
or he may become ill through contact with another ill person:

I+" ' 21 (P7'-8.2)
)
The ill person may become healthy:
I ">H (W-8.3)
or he may expire:
I k4>D (P7-8.4)
The reaction given in Equation (P7-8.4) is normally considered completely
irreversible, although the reverse reaction has been reported to occur.
(a) Derive an equation for the death rate.
(b) At what concentration of healthy people does the death rate become crit-
ical? [Ans.: When [HI = (k3 + k4)/k2.]
(c) Comment on the validity of the PSSH under the conditions of part (b).
(d) If k, = h-*, k2 = IO-' (peopleah)-', k3 = 5 X h, k4 = lo-'
h, and H, = lo9 people, plot H, I, and D versus time. Vary k, and describe
what you find. Check with your local disease control center or search the
WrW to modify the model and/or substitute appropriate values of k,.
P7-9c (Postacidijication in yogurt) Yogurt is produced by adding two strains of bac-
teria (Lactobacillus bulgaricus and Streptococcus thermophilus) to pasteur-
ized milk. At temperatures of llO"F, the bacteria grow and produce lactic
acid. The acid contributes flavor and causes the proteins to coagulate, giving
the characteristic properties of yogurt. When sufficient acid has been pro-
duced (about 0.90%), the yogurt is cooled and stored until eaten by consum-
ers. A lactic acid level of 1.10% is the limit of acceptability. One limit 0111 the
shelf life of yogurt is "postacidification," or continued production of acid by
the yogurt cultures during storage. The table that follows shows acid produc-
tion (% lactic acid) in yogurt versus time at four different temperatures.

Time (days) 35°F 40°F 45°F 50°F
1 1.02 1.02 1.02 1.02
14 1.03 1.05 1.14 1.19
28 1.05 1.06 1.15 1.24
YO@d 35 1.09 1.10 1.22 1.26
42 1.09 1.12 1.22 1.31
49 1.10 1.12 1.22 1.32
Chemical Engineering 56 1.09 1.13 1.24 1.32
in the Food Industry 63 1.10 1.14 1.25 1.32
- 70 1.10 1.16 1.26 1.34

Acid production by yogurt cultures is a complex biochemical process.
For the purpose of this problem, assume that acid production folllows
first-order kinetics with respect to the consumption of lactose in the yogurt to
produce lactic acid. At the start of acid production the lactose concentration is