(Postacidification in yogurt) Yogurt is produced by adding two strains of
bacteria (Lactobacillus bulgaricus and Streptococcus thermophilus) to
pasteurized milk. At temperatures of \(110^{\circ} \mathrm{F}\), 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 produced (about \(0.90 \%\) ), the yogurt is cooled and
stored until eaten by consumers. A lactic acid level of \(1.10 \%\) is the limit
of acceptability. One limit on the shelf life of yogurt is
"postacidification," or continued production of acid by the yogurt cultures
during storage. The table that follows shows acid production (\% lactic acid)
in yogurt versus time at four different temperatures.
Acid production by yogurt cultures is a complex biochemical process. For the
purpose of this problem, assume that acid production follows 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
about \(1.5 \%,\) the bacteria concentration is \(10^{11}\) cells/dm \(^{3}\), and
the acid concentration at which all metabolic activity ceases is \(1.4 \%\)
lactic acid.
(a) Determine the activation energy for the reaction.
(b) How long would it take to reach \(1.10 \%\) acid at \(38^{\circ} \mathrm{F}\)
?
(c) If you left yogurt out at room temperature, \(77^{\circ} \mathrm{F}\), how
long would it take to reach 1.10\% lactic acid?
(d) Assuming that the lactic acid is produced in the stationary state, do the
data fit any of the modules developed in this chapter? [Problem developed by
General Mills, Minneapolis, Minnesota]
(e) List ways you can work this problem incorrectly.
(f) How could you make this problem more difficult?