Tooth enamel is composed of the mineral hydroxyapatite. It is essentially insoluble in water with K_sp = 2.3 *10^-⁵⁹, but it reacts with weak acids in the mouth as described by one of the reaction equations below. You can determine the equilibrium constant, K, for this reaction from K_sp and K_w (the equilibrium constant for water autoionization, K_w = 1.0 *10^-¹⁴) . What is the value of K?
Ca₅(PO₄) ₃(OH) (s) $\rightleftarrows$ Ca₅(PO₄) ₃⁺(aq) + OH^-(aq)
Ca₅(PO₄) ₃(OH) (s) + H⁺(aq) $\rightleftarrows$ Ca₅(PO₄) ₃⁺(aq) + H₂O(l)

Question

Tooth enamel is composed of the mineral hydroxyapatite. It is essentially insoluble in water with K_sp = 2.3 *10^-⁵⁹, but it reacts with weak acids in the mouth as described by one of the reaction equations below. You can determine the equilibrium constant, K, for this reaction from K_sp and K_w (the equilibrium constant for water autoionization, K_w = 1.0 *10^-¹⁴) . What is the value of K?
Ca₅(PO₄) ₃(OH) (s)

\rightleftarrows

Ca₅(PO₄) ₃⁺(aq) + OH^-(aq)
Ca₅(PO₄) ₃(OH) (s) + H⁺(aq)

\rightleftarrows

Ca₅(PO₄) ₃⁺(aq) + H₂O(l)

Quizplus · Accepted Answer

The equilibrium constant for the reaction is K = [Ca(PO4)(OH)(s)][H+] / [Ca(PO4)2-][H2O]. Since pure water has an equilibrium constant of 1, the K value can be simplified to [Ca(PO4)(OH)(s)][H+]/[Ca(PO4)2-]. Using the given solubility product constant for hydroxyapatite, K_sp = 2.3 F1F1F1S1F1F1F10 10^-^{^45}, we can write K = 2.3 F1F1F1S1F1F1F10 10^-^{^45} / [Ca(PO4)2-]. However, [Ca(PO4)2-] is equal to [Ca(PO4)(OH)(s)], which is given to be a constant, so K is also equal to 2.3 F1F1F1S1F1F1F10 10^-^{^45}, which corresponds to answer choice C.

Tooth Enamel Is Composed of the Mineral Hydroxyapatite ⇄\rightleftarrows⇄ Ca5 (PO4)3+(aq) + OH-(aq) Ca5 (PO4)3(OH)(s) + H+(aq)

Tooth Enamel Is Composed of the Mineral Hydroxyapatite $\rightleftarrows$ Ca₅(PO₄)₃⁺(aq) + OH^-(aq)
Ca₅(PO₄)₃(OH)(s) + H⁺(aq)