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Answer:
The concentration of [Ca²⁺] is 8.47 x 10⁻³ M
Explanation:
We consider the solubility of hydroxyapatite,
Ca₁₀(PO₄)₆(OH)₂ ⇔ 10Ca²⁺ + 6PO₄³⁻ + 2 OH⁻
Assumed that there is <em>a</em> mol of hydoxyapatite disolved in water, yielding <em>10a</em> mol Ca²⁺ of and <em>6a</em> mol of PO₄³⁻
We also have Ksp equation,
Ksp = [Ca²⁺]¹⁰ x [PO₄³⁻]⁶ x [OH⁻]² = 2.34 x 10⁻⁵⁹
⇔ 10a¹⁰ x 6a⁶ x (5.30 x 10⁻⁶)² = 2.24 x 10⁻⁵⁹
⇔ 60a¹⁶ = 2.24 x 10⁻⁵⁹ / 5.30 x 10⁻¹²
⇔ a¹⁶ = 0.007 x 10⁻⁴⁷ = 7 x 10⁻⁵⁰
⇔ a = = 8.47 x 10⁻⁴
Hence,
[Ca²⁺] = 10<em>a</em> = 8.47 x 10⁻³ M