Answer: The concentration of [tex]Ca^{2+}[/tex] ions in the solution is [tex]7.81\times 10^{-4}M[/tex]
Explanation:
We are given:
Concentration of hydroxide ion = [tex]3.90\times 10^{-6}M[/tex]
Solubility product is defined as the product of concentration of ions present in a solution each raised to the power its stoichiometric ratio.
The equation for the ionization of the hydroxyapatite is given as:
[tex]Ca_{10}(PO_4)_6(OH)_2(s)\leftrightharpoons 10Ca^{2+}(aq.)+6PO_4^{3-}(aq.)+2OH^-(aq.)[/tex]
10s 6s [tex](3.90\times 10^{-6}+2s)[/tex]
The expression for the solubility product of hydroxyapatite will be:
[tex]K_{sp}=[Ca^{2+}]^10[PO_4^{3-}]^6[OH^-]^2\\\\K_{sp}=(10s)^{10}\times (6s)^6\times (3.90\times 10^{-6}+2s)^2=4.6656\times 10^{14}\times s^{16}\times (3.90\times 10^{-6}+2s)^2[/tex]
We are given:
[tex]K_{sp}=2.34\times 10^{-59}[/tex]
Putting values in above equation, we get:
[tex]2.34\times 10^{-59}=4.6656\times 10^{14}\times s^{16}\times (3.90\times 10^{-6}+2s)^2\\\\s=7.81\times 10^{-5},-7.86\times 10^{-5}[/tex]
Neglecting the negative value of 'x' because concentration cannot be negative.
So, the concentration of calcium ions in the solution = 10s = [tex][10\times (7.81\times 10^{-5})]=7.81\times 10^{-4}M[/tex]
Hence, the concentration of [tex]Ca^{2+}[/tex] ions in the solution is [tex]7.81\times 10^{-4}M[/tex]
Answer:
Hydroxyapatite, Ca10(PO4)6(OH)2 , has a solubility constant of Ksp = 2.34×10−59 , and dissociates according to Ca10(PO4)6(OH)2(s)↽−−⇀10Ca2+(aq)+6PO3−4(aq)+2OH−(aq) Solid hydroxyapatite is dissolved in water to form a saturated solution.
Explanation:
