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) . How do you do this?
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) . How do you do this?
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, K, for the reaction is equal to the product of the concentrations of the products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients. For the given reaction, the equilibrium constant expression is: K = [Ca5(PO4)3OH][H+][OH-] / [Ca5(PO4)3OH]. The concentration of water is not included in the expression since it is in excess and its concentration remains constant. The equilibrium constant for water autoionization, Kw, is given by the equation: Kw = [H+][OH-]. Dividing the reaction equilibrium constant by the water ionization constant: K / Kw = [Ca5(PO4)3OH] / [H+][OH-] or K = [Ca5(PO4)3OH] / [H+][OH-] * Kw. Thus, K = K_sp/K_w.

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)