Consider a saturated solution of calcium fluoride in 0.086 M potassium nitrate. Complete the following tasks, and then answer the question.

a) Write the chemical equation corresponding to Ksp.
b) Write the defining expression for the thermodynamic solubility product constant, Kspo.
c) Write the defining expression for the conditional solubility product constant, Ksp'.
d) For the Ca2+ and F- ions, write the mathematical relations defining activity of each ion in terms of its concentration and activity coefficient.
e) Based on your answers above, derive a relationship for Ksp' in terms of Kspo and activity coefficients, and calculate the value of Ksp', given that Kspo = 3.9 x 10-11. (Note: Compute the activity coefficient for each ion using the Debye-Huckel equation. You can disregard the contribution of the dissolved CaF2 to the overall ionic strength. Also disregard the formation of any HF in the equilibrium solution.)
Question:
Calculate the molar solubility of the calcium fluoride.

a) The chemical equation corresponding to Ksp is:

CaF2(s) ⇌ Ca2+(aq) + 2F-(aq)
b) The defining expression for the thermodynamic solubility product constant, Kspo, is:
Kspo = [Ca2+][F-]^2
c) The defining expression for the conditional solubility product constant, Ksp', is:
Ksp' = [Ca2+][F-]^2/γ[Ca2+][γ(F-)]^2
where γ represents the activity coefficient of each ion.
d) For the Ca2+ ion, the mathematical relation defining its activity in terms of its concentration and activity coefficient is:
a(Ca2+) = γ(Ca2+)[Ca2+]
For the F- ion, the mathematical relation defining its activity in terms of its concentration and activity coefficient is:
a(F-) = γ(F-)[F-]
e) Based on the above expressions, the relation for Ksp' in terms of Kspo and activity coefficients can be derived as follows:
Ksp' = Kspo / (γ(Ca2+)[Ca2+][γ(F-)][F-]^2)
To calculate the value of Ksp', we need to calculate the activity coefficients and substitute them into the equation. The Debye-Huckel equation can be used to calculate the activity coefficients of the ions.
The molar solubility of calcium fluoride can be calculated using the relation:
[S] = x = (Ca2+)eq = (F-)eq
where [S] represents the molar solubility.
Please note that the calculation of activity coefficients and the Debye-Huckel equation involve more complex calculations and may require additional information like temperature, dielectric constant, and ionic strength of the solution.

To calculate the molar solubility of calcium fluoride, we need to use the information provided and the definition of the solubility product constant (Ksp). Let's go step by step:

a) Write the chemical equation corresponding to Ksp:
CaF2(s) ⇌ Ca2+(aq) + 2F-(aq)

b) Write the defining expression for the thermodynamic solubility product constant, Kspo:
Kspo = [Ca2+][F-]²

c) Write the defining expression for the conditional solubility product constant, Ksp':
Ksp' = a(Ca2+) * a(F-)²

d) For the Ca2+ and F- ions, write the mathematical relations defining activity of each ion in terms of its concentration and activity coefficient:
a(Ca2+) = γ(Ca2+) * [Ca2+]
a(F-) = γ(F-) * [F-]

e) Based on the answers above, derive a relationship for Ksp' in terms of Kspo and activity coefficients, and calculate the value of Ksp', given that Kspo = 3.9 x 10^-11:
Ksp' = γ(Ca2+) * [Ca2+] * γ(F-)² * [F-]²

To calculate the molar solubility of calcium fluoride (which is the concentration of Ca2+ or F- in a saturated solution), we need to find the concentrations that satisfy Ksp'. However, to find the concentrations, we need to know the values of the activity coefficients (γ).

To calculate the activity coefficients, we can use the Debye-Huckel equation. However, since the Debye-Huckel equation involves the ionic strength of the solution, we need to first calculate the ionic strength.

In this case, the contribution of dissolved CaF2 to the overall ionic strength can be disregarded. Therefore, the ionic strength is solely determined by the potassium nitrate solution, which has a concentration of 0.086 M. The ionic strength (I) is calculated as the sum of the squares of the ion concentrations:

I = (0.086 M)² = 0.007396 M²

Using the Debye-Huckel equation, we can then calculate the activity coefficients for Ca2+ and F- ions. After obtaining the values of the activity coefficients, we can use them to find the molar solubility of calcium fluoride by solving for the concentrations that satisfy Ksp'.

Note: The Debye-Huckel equation takes the form: log(γ) = -Az(sqrt(I))/(1 + B(sqrt(I))), where A and B are constants depending on the nature of the solvent, and z is the charge of the ion.