Physical Chemistry of Foods

and it is seen that especially for valences higher than 1 the effect is great. In
calculating the above figures, one has to knowg+, which means that one has
to know the dissociation to obtain the ionic strength, which is needed to
calculate the ion activity coefficients. This can be done by first taking an
assumed activity coefficient and then reiterating the calculation until the
coefficient is in agreement with the dissociation.
This reveals an important problem. Mostion activity coefficientsgiven
in the literature, including those of Figure 2.11, are total ion activity
coefficients, i.e., they relate to the total salt concentration; moreover, the
ionic strength is calculatedas ifthe dissociation of the salt were complete.
This is a suitable method if there is only one salt in solution, or if there are
only monovalent ions and the concentration is very small. But in all other
cases, which implies in almost all foods, where we have several ions, some of
which have valences larger than unity, the method does not work. One
should rather take the ions only, thus taking the association into account,
for calculating the ionic strength as well as the activity coefficients. The
latter then are calledfree ion activity coefficients. Another complication is
that for concentrated solutions, where this may also mean that there are
other solutes than ionizable ones (say, sugars), the concentration unit of
moles per liter is not suitable any longer. It is much better to usemolality,
i.e., moles per kg water.
Taking the above considerations into account, it turns out that
reasonable agreement between theory and results is obtained if we express
the free ion activity coefficient of an ion of valencejzjas

gþ;
¼expð
 0 : 8 z^2

ffiffiffi

I

p

Þð 2 : 30 Þ

whereIis in moles per kg water. Some results are given in Table 2.4.

TABLE2.4 Approximate Free

Ion Activity Coefficientsa

I

jzj 0.003 0.01 0.03 0.1

1 0.96 0.92 0.87 (0.78)

2 0.84 0.73 0.57 (0.36)

3 0.67 0.49 0.29 (0.10)

Ionic strength is in moles per kg water

aCalculated according to Eq. (2.30).