Physical Chemistry of Foods

Note Up till now, we have used concentrations in the rate

equations, whereas we have learned in Chapter 2 that activities

should be used. In many cases the difference is unimportant, not

because it is small, but because we generally have no way of

predicting the rate constant from first principles. Whether a

reaction is slow because of a low activity coefficient or because of

a low rate constant then would be a mere academic question.

Nevertheless, there may be situations where it is important to know

about activity coefficients, for instance when comparing the same

reaction in different media or when the activity coefficient of one of

the reactants varies in a different manner with conditions than that

of another reactant.

Question

A food company pasteurizes a beverage for 15 s at 70 8 C in a heat exchanger, and it is
then aseptically packaged in 1 liter cartons. The product occasionally spoils, and it is
established that a bacterium is responsible. It may be present in concentrations up to
2 per mL. Its first-order rate constant for thermal death at 70 8 C is determined at
0 :7s
^1. How long should the pasteurization time be to ensure absence of spoilage?

Answer

A guarantee for absence of spoilage can never be given, since there always will be a
probability that one bacterium is present in a package, and since it can grow out to
high numbers, this would eventually mean spoilage. Presume that a risk of 1 in 10^5 is
taken. That means that the average bacterial count after pasteurization should be
10
^5 per liter or 10
^8 per ml. The original count was 2. Applying Eq. (4.2b), we thus
have lnð 10
^8 = 2 Þ¼
0 : 7 t, which directly givest¼ 27 :3 s, clearly longer than the 15 s
previously applied.

Notes

1. Most microbiologists would use a decimal reduction time rather than a
   rate constant. HereD¼ 2 : 3 = 0 : 7 ¼ 3 :3 s, and reduction by a factor of
   2? 108 means logð 2? 108 Þ¼ 8 :3 decimal reductions; hence a heating
   time of 8: 363 : 3 ¼ 27 :3s.


2. In practice, there are many uncertainties: (a) The rate constant for
   thermal destruction of bacteria always varies, even within one
   population, and those bacteria being most heat resistant have of
   course the greatest chance of survival; in other words, a curve as given
   in Figure 4.1b need not be linear and will often curve upwards at longt.
   (b) The effective heating conditions in a laboratory test may be