The K_sp of calcium phosphate is 1 × 10−³³.What is the concentration of Ca²⁺ in equilibrium with Ca₃(PO₄)₂(s)if [PO₄³⁻] = 1 × 10−⁵ M?

Question

Quizplus · Accepted Answer

The equilibrium constant for the dissolution of calcium phosphate is:

Ca3(PO4)2(s) ⇌ 3Ca2+(aq) + 2PO43-(aq)

KS1U1B1spS1U1B0 = [Ca2+]3[PO43-]2

KS1U1B1spS1U1B0 = 1 × 10−S1U1P133S1S1P0

We are given the concentration of [PO43-] and want to find [Ca2+] in equilibrium.

Let x be the concentration of Ca2+ in equilibrium.

Then according to the equilibrium constant expression:

KS1U1B1spS1U1B0 = x3(1 × 10−S1U1P133S1S1P0)2

x3 = KS1U1B1spS1U1B0 / (1 × 10−S1U1P133S1S1P0)2

x = (KS1U1B1spS1U1B0)1/3 / (1 × 10−S1U1P133S1S1P0)2/3

x = (1 × 10−S1U1P133S1S1P0)−S1U1P13S1U1B0/3

Now we can substitute the given values:

[Ca2+] = (1 × 10−S1U1P133S1S1P0)−S1U1P13S1U1B0/3 = 2 × 10−S1U1P18S1S1P0 M

Therefore, the answer is E: 2 × 10-S1U1P18S1S1P0 M.

The Ksp of Calcium Phosphate Is 1 × 10−33