Calcium ions form slightly soluble compounds with phosphate ions such as PO4 3–, HPO4 2–, and H2PO4 — Equilibrium / Solubility Chemistry Question
Problem Context
Calcium ions form slightly soluble compounds with phosphate ions such as PO4 3–, HPO4 2–, and H2PO4 –.
Write the formula and give the Ksp expression for the compound formed by Ca2+ and each of these two ions.
i. PO4 3–
Model Answer
Ca3(PO4)2
Ksp = [Ca2+]3[PO4 3–]2
ii. H2PO4 –
Model Answer
Ca(H2PO4)2
Ksp = [Ca2+][H2PO4 –]2
Calculate the equilibrium concentration of Ca2+ in a saturated solution with each of the phosphate ions given in part a.
i. Ksp for calcium phosphate equals 1.0 × 10–25.
Model Answer
1.0 × 10–25 = [Ca2+]3[PO4 3–]2
Then, let 3x = [Ca2+] and 2x = [PO4 3–]
1.0 × 10–25 = (3x)3(2x)2
1.0 × 10–25 = 108x5 and x5 = 9.26 × 10–28 and x = 3.9 × 10–6
[Ca2+] = 3(3.9 × 10–6) = 1.2 × 10–5 M
ii. Ksp for calcium dihydrogen phosphate equals 1.0 × 10–3.
Model Answer
1.0 × 10–3 = [Ca2+][H2PO4 –]2
Then, let x = [Ca2+] and 2x = [H2PO4 –]
1.0 × 10–3 = (x)(2x)2
1.0 × 10–3 = 4x3 and x = 6.3 × 10–2
[Ca2+] = 6.3 × 10–2 M
Determine the [H+] needed to just prevent precipitation by H2PO4 – in a 0.25 M H3PO4 solution that has [Ca2+] = 0.15 M. The Ka1 of H3PO4 is 7.1 × 10–3.
Model Answer
Ca(H2PO4)2(s) æ Ca2+(aq) + 2H2PO4 –(aq)
1.0 × 10–3 = [Ca2+][H2PO4 –]2
[H2PO4 –]2 = 1.0 × 10–3 / 0.15 = 6.67 × 10–3
[H2PO4 –] = 8.2 × 10–2 M
H3PO4(aq) æ H+(aq) + H2PO4 –(aq)
Therefore, to prevent precipitation, [H+] must be greater than = 1.7 × 10–2 M