The relationship between the mean ionic activity coefficient γ of Ca
3(PO
4)
2 and its ions can be expressed as:
where γ± is the mean ionic activity coefficient of Ca
3(PO
4)
2 and γ
+ and γ
− are the ionic activity coefficients of its constituent cations (Ca
2+) and anions (PO
43-), respectively.
This relationship is based on the Debye-Hückel theory, which provides a mathematical framework for describing the behavior of electrolyte solutions at low concentrations.
According to this theory, the mean ionic activity coefficient of a salt is related to the ionic activity coefficients of its constituent ions by a product of powers of their concentrations, which depend on their charges and sizes.
In the case of Ca
3(PO
4)
2, which is a highly insoluble salt, its mean ionic activity coefficient is very small and its constituent ions are highly dissociated, so their ionic activity coefficients are close to 1. Therefore, the relationship between them simplifies to:
γ ± approx 1.
This means that Ca
3(PO
4)
2 behaves as a weak electrolyte and its constituent ions are in equilibrium with their undissociated form.
The correct answer is option 3.