Physical Chemistry of Foods

Answer

The simplest solution appears to be to calculate the molar concentration, which is for
Ca (molar mass 40) 2.5 and for citrate (89) 5.6 mmol per liter. Then the ion product is

ð 2 : 5? 10 
^3 Þ^3 ?ð 5 : 6? 10 
^3 Þ^2 ¼ 4 : 9? 10 
^13

which is 210,000 times the solubility product. (If we had equal concentrations of Ca
and citrate, we could say in such a case that the supersaturation would be by a factor
of 210,000^1 =^5 ¼ 11 : 6 :ÞWe have, however, made several errors: (a) The blood serum
contains about 90%water by weight. This implies that the millimolal concentrations
become 2.8 and 6.3, respectively. (b) We should ascertain that the citric acid can fully
dissociate. Since blood has apH& 7 :2 and the pKað 3 Þof citric acid is 5.2, this is
virtually the case. (c) We should take the ion activity coefficients into account. The
ionic strength of blood serum is about 0.14 molal. By use of Eq. (2.30) we calculate
for ions of valence 1, 2, and 3 activity coefficients of 0.74, 0.30, and 0.07, respectively.
We can now calculate an ion activity product of

ð 0 : 0025? 0 : 30 Þ^3 ð 0 : 0056? 0 : 07 Þ^2 ¼ 6 : 4? 10 
^17

Since we know which still is by a factor of 28 higher than the solubility product. (d)
However, we also have to take ion association into account. The most important
association is likely to be Ca^2 þþCit^3
ÐCaCit
and taking from Table 2.3 that
KA& 105 we obtain by use of Eq. (2.29)

½CaCit
Š?g
ðz¼ 1 Þ

½Ca^2 þŠ?gþðz¼ 2 Þ 6 ½Cit^3 
Š?g
ðz¼ 3 Þ

Since we know theg’s and we also know that½CaCit
Šþ½Ca^2 þŠ¼ 0 :0028 and that
½CaCit
Šþ½Cit^3
Š¼ 0 :0063, we can solve the equations and obtain
½CaCit
Š¼ 0 :00261, implying that there are almost no Ca^2 þions left. We obtain
for the activity product

ð 0 : 0028 
 0 : 00261 Þ^3? 0 : 1436 ð 0 : 0063 
 0 : 00261 Þ^2? 0 : 072 ¼ 10 
^21

which is far below the intrinsic solubility product.

Note Because of the fairly high ionic strength, Eq. (2.30) is not accurate

anymore, and the free ion activity coefficients are likely to be somewhat

higher than calculated. On the other hand, other associations undoubtedly

occur, for instance of citrate withKþ, which is abundant in blood, thereby

further decreasing the free ion concentrations.