Posted by Rudy on Sunday, January 26, 2014 at 7:24pm.
Hydroxylapatite, 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) + 6PO43-(aq) + 2OH-(aq)
Solid hydroxylapatite is dissolved in water to form a saturated solution. What is the concentration of Ca2 in this solution if [OH–] is somehow fixed at 4.30 × 10-6
I understand to set this question up as such:
2.34e-59 = (10x)^10(6x)^6(4.3e-6+2x)
But I don't understand the next step, can anyone help? you don't have to give the answer just the next few steps
wouldn't the Ca ion cncentration be 5 times the OH conc?
First, I think you left a squared term off the OH^-.
Ca10(PO4)6(OH)2(s) --> 10Ca2+(aq) + 6PO43-(aq) + 2OH-(aq)
(Ca^2+) = 10x
(PO4^3-) = 6x
(OH^-) = 2x
Ksp = (Ca^2+)^10(PO4^3-)^6(OH^-)^2
Substituting the x values we have
Ksp = (10x)^10(6x)^6(4.3e-6 + 2x)^2
I would make the assumption that
4.3e-6 + 2x = 4.3e-6 so we have
Ksp = (10x)^10(6x)^6(4.3e-6)^2
2.34e-59 = 10^10*x^10 (6x)^6*(1.85e-11)
2.34e-59 = 10^10*x^10*4.66e4*x^6*(1.85e-11)
2.34e-59/[(10)^10*(4.66e4)*(1.85e-11) = x^16.
To solve this problem, we need to use the solubility product expression and the given dissociation equation. Here's how you can proceed:
1. Write the solubility product expression using the molar concentrations of the ions involved in the dissociation equation:
Ksp = [Ca2+]^10 [PO43-]^6 [OH-]^2
2. In the dissociation equation, we are given that [OH-] is fixed at 4.30 × 10-6. Substitute this value into the solubility product expression:
Ksp = [Ca2+]^10 [PO43-]^6 (4.30 × 10-6)^2
3. Rearrange the equation to solve for [Ca2+]:
[Ca2+]^10 = Ksp / ([PO43-]^6 (4.30 × 10-6)^2)
4. Take the 10th root of both sides to isolate [Ca2+]:
[Ca2+] = (Ksp / ([PO43-]^6 (4.30 × 10-6)^2))^(1/10)
5. Substitute the given values to calculate [Ca2+]. You will need the value of Ksp and the concentration of the phosphate ion ([PO43-]).
Note: In order to fully solve this problem, you will need the concentration of [PO43-]. If that value is not given, you may need to use additional information or assumptions to proceed.