Tooth enamel is composed of the mineral hydroxyapatite. It is essentially insolu

Question

Tooth enamel is composed of the mineral hydroxyapatite. It is essentially insoluble in water with Ksp = 2.3 x 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 Ksp and Kw (the equilibrium constant for water autoionization, Kw = 1.0 x 10–14). What is the value of K?

Ca5 (PO4)3(OH)(s) « Ca5 (PO4)3+(aq) + OH–(aq)

Ca5 (PO4)3(OH)(s) + H+(aq) « Ca5 (PO4)3+(aq) + H2O(l)

a.         9.9 x 10–15

b.         4.3 x 1045

c.         2.3 x 10–45

d.         1.1 x 10–14

e.         2.3 x 10–73

Explanation / Answer

Equilibrium constant(K) = K1 ×K2

K1=Ksp=2.3×10^-59 = Equilibrium constant for first step

K2=Kw= 1.0×10^-14 = Equilibrium constant for second step

Equilibrium constant for overall reaction=K

K= 2.3×10^-59 × 1.0×10^-14 = 2.3×10^-73

So answer is option "e".

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