Physical Chemistry of Foods

small differences are found for most inorganic ions, except for the hydrogen
ion, which has a higher activity coefficient than predicted by Eq. (2.28).

2.3.3 Not Very Dilute Solutions

The situation becomes far more complicated for higher concentrations, say
I> 0 :03 molar, which still is fairly dilute, i.e., a few times 0.1%for many
salts. The most important aspect may be that theassociation of ionsintoion
pairs, i.e., undissociated salt molecules (or ions, e.g., CaClþ), becomes
significant. It is often assumed that salts completely dissociate into ions,
unless the concentration is very high. This assumption is generally not true,
and it would lead to considerable error in many foods. To be sure, most ion
pairs are very short lived, but at any time a certain proportion of the ions is
in the associated form.
Consider the association of a cation C and an anion A according to
CzþþAz
ÐCA where the ion pair CA may be neutral or not, according to
the values ofzþandz
. We may write for the association constant

KA¼

aðCAÞ

aðCzþÞ?aðAz
Þ

¼

½CAŠ

½CzþŠ?½Az
Š

6

gðCAÞ

gðCÞ?gðAÞ

ð 2 : 29 Þ

where allgdenote free ion activity coefficients, except possibly (CA), which
&1 if CA is neutral. AlthoughKAvaries among ions, in first approximation
it is governed by the valence of the ions, as given in Table 2.3. Taking the
values given there, we obtain for the proportion dissociated of a salt of
valence

1:1 0.01 molar dissociation¼0.99

0.1 molar dissociation¼0.95

2:2 0.01 molar dissociation¼0.33

0.1 molar dissociation¼0.22

TABLE2.3 Order of Magnitude of

Intrinsic Association Constants in

(L?mol
^1 ) for Ions of Various ValencesðzÞ

zc

jzAj 12 3

1 1 10 50

2 10 700 105

See Eq. (2.29).