Physical Chemistry of Foods

turn on the type and concentration of biopolymers present. For beef and
bread, the curves become horizontal above
308 C, which implies thatTg^0 is
reached.
Theconcentration of solutes increasesupon freezing. As long as only
water crystallizes, the molality of a solute after a mass fractionciof the
water has frozen is given by the original molality divided by ð 1
ciÞ.
Moreover, the activity coefficients (g) may change (Chapter 2): for most
neutral solutes, gincreases with concentrating, for ionic solutes, it will
initially decrease.
The concentrating effect implies thatreactions can increase in rate. For
a simple second-order reaction of the type AþB?reactant (s), the rate of
change of A will be given by

d½AŠ

dt

¼
kðTÞ

mðTÞ

m 0

½AŠ 0 ½BŠ 0 ð 16 : 3 Þ

(if the activity coefficients equal unity). Herekis the second-order rate
constant,mis the molar concentration, and subscript 0 refers to conditions
before freezing. Provided thatkdecreases relatively less with decreasingT
thanmincreases, the reaction rate will increase. This is often observed, at
least for moderate freeze-concentration. The relation is comparable to that
shown in Figure 8.10a.
A first-order reaction may increase in rate if it is catalyzed by a
substance that is concentrated. An example is the mutarotation of reducing
sugars. The reaction is virtually first order (as long asaWdoes not alter
greatly) and is catalyzed by protons, for example. Figure 16.11a gives an
example for glucose (the reactant) and HCl (providing the catalyst). It is
seen that the rate constant decreases with decreasing temperature until the
freezing point of the solution is reached. The freeze concentration upon
further cooling then causes an increase in rate.
Concentrating the solutes implies that all colligative propertieswill
increase in magnitude, including freezing point depression, osmotic
pressure, and
lnaW. We will discuss this forwater activity. Equation
(8.6) states thataW¼pv,solution/pv,water, wherepvis water vapor pressure. At
equilibrium, moreover,pv,ice¼pv,solution, which then leads to

aW¼

pv;ice

pv;water

ð 16 : 4 Þ

Since the vapor pressure of pure water and of ice are only dependent on
temperature (at constant pressure), water activity of a partly frozen system
at equilibrium will only depend on temperature. The relations are illustrated
in Figure 16.12a; Figure 16.12b gives the dependence ofaWonT. Notice