Although the results may be only approximate, they are very much better
than those obtained when ignoring association, or even worse, when
ignoring activity coefficients. For ionic strengths above 0.1 molal, however,
a more refined treatment would be needed to obtain reasonable results.
At very high concentrations the activity coefficients tend to increase
again (possibly even to>1), owing to the mechanisms under 2, ‘‘High
concentration,’’ in Section 2.2.5.
Question 1
What is the value of the ionic strength of a 0.025 molar solution of calcium oxalate?
Answer
Denoting calcium oxalate as CaOx, it will dissociate into Ca^2 þand Ox^2 . Assuming
complete dissociation, this results in an ionic strength [see Eq. (2.27)] ofð 0 : 02564 þ
0 : 02564 Þ= 2 ¼ 0 :1 molar. The activity coefficients would then be [Eq. (3.30)]:
gþ¼g&expð 0 : 8? 22 ?H 0 : 1 Þ¼ 0 :36. However, association of Ca^2 þand Ox^2 will
occur. Assuming the fraction dissociated to bea, Eq. (2.21) can be written as
ða?m 6 gÞ^2
ð 1 aÞm
¼
1
KAAccording to Table 2.3,KA&700 L?mol^1. Moreover,m¼ 0 :025 mol?L^1 andg
was calculated at 0.36, which then yieldsa¼ 0 :48. This would mean that only about
half of the salt is in the dissociated form. That implies that the ionic strength is far
smaller than supposed, so that the ion activity coefficient is higher than calculated
and the calculation ofa thus was incorrect. An iterative calculation, inserting
adapted values ofgorauntil agreement is reached between both parameters, would
be needed. This yields abouta¼ 0 :37, leading toI&37 mmolar.
Question 2
Bovine blood serum contains about 10 mg Ca and 50 mg citrate per 100 g. The
solubility product of Ca 3 Cit 2 ¼ 2 : 3? 10 ^18 mol^5 ?kg^5. Does this not imply that
calcium citrate is far supersaturated in the blood?