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 its value? 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( )

Question

Quizplus · Accepted Answer

The equilibrium constant can be found using the equation:
K = [Ca2+][HPO42-]/[CaHPO4]

Using the given reaction equations, we can determine the concentrations of the products and reactants at equilibrium. At equilibrium, the concentration of Ca2+ and OH- is equal to the solubility of hydroxyapatite in water, which is essentially equal to zero. Therefore, we can assume that the concentration of Ca2+ and OH- at equilibrium is negligible compared to the concentration of HPO42- and H+.

So, we can simplify the equation to:
K = [HPO42-]/[CaHPO4]

We can also use the equilibrium constant for water autoionization, Kw, to find the concentration of H+ at equilibrium. At room temperature, Kw = 1.0 x 10^-14. Therefore, [H+][OH-] = 1.0 x 10^-14. Since the concentration of OH- at equilibrium is negligible, we can assume that [H+] = 1.0 x 10^-14.

Therefore, we can use the equation for the dissociation of H3PO4 to find the concentration of HPO42-:
H3PO4 + H2O ↔ HPO42- + H3O+
Ka = [HPO42-][H3O+]/[H3PO4]
Ka = 7.5 x 10^-3

At equilibrium, [HPO42-]/[H3PO4] = Ka/[H+]
[HPO42-]/[H3PO4] = 7.5 x 10^-3/1.0 x 10^-14 = 7.5 x 10^11

Substituting this value into the equation for K, we get:
K = [HPO42-]/[CaHPO4]
K = (7.5 x 10^11)/1 = 7.5 x 10^11

Therefore, the answer is 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)