Hydroxyapatite, Ca10(PO4)6(OH)2Ca10(PO4)6(OH)2 , has a solubility constant of Ksp = 2.34×10−592.34×10−59 , and dissociates according to
Ca10(PO4)6(OH)2(s) --> 10Ca2+(aq) + 6PO4^3-(aq) + 2OH-(aq)
Solid hydroxyapatite is dissolved in water to form a saturated solution. What is the concentration of Ca2+ in this solution if [OH−] is fixed at 2.80×10−6 M?
I tried the question and got 3.99, but my answer was wrong...pleasee tell me where i went wrong.
I can't tell where you went wrong because you didn't show your work. Show your work and I'll find th error.
((2.34x10^-59)/ (2.80x10^-6)^2 (3/5)^6)^1/16= 3.99
To find the concentration of Ca2+ in the solution, we need to use the solubility product expression and apply stoichiometry.
First, let's write the solubility product expression for hydroxyapatite:
Ksp = [Ca2+]^10 [PO4^3-]^6 [OH^-]^2
Since the concentration of [OH^-] has been fixed at 2.80×10^-6 M in the question, we can substitute this value into the expression:
Ksp = [Ca2+]^10 [PO4^3-]^6 [2.80×10^-6]^2
Next, we need to consider the stoichiometry of the dissociation reaction:
Ca10(PO4)6(OH)2(s) → 10Ca2+(aq) + 6PO4^3-(aq) + 2OH-(aq)
From the reaction, we can see that for every 1 mol of Ca10(PO4)6(OH)2 that dissolves, it forms 10 mol of Ca2+. Therefore, the concentration of [Ca2+] in the solution will be 10 times higher than the concentration of [OH^-].
Now, let's rewrite the solubility product expression with the concentration of [Ca2+]:
Ksp = (10[Ca2+])^10 [PO4^3-]^6 [2.80×10^-6]^2
Now, we can solve for [Ca2+]. Rearranging the equation:
[Ca2+]^10 = Ksp / [(10[OH^-])^2 [PO4^3-]^6]
Taking the 10th root of both sides:
[Ca2+] = (Ksp / [(10[OH^-])^2 [PO4^3-]^6])^(1/10)
Substitute the given values:
[Ca2+] = (2.34×10^-59) / [(10(2.80×10^-6))^2 (PO4^3-)^6]^(1/10)
Since the concentration of [PO4^3-] is not given, we cannot solve the problem without that information. Please check if you missed any given information or let me know if there was any other relevant data provided.