If the concentration of Pb^2+ is known to be roughly 2.1 x 10 to the power of -9 mol/L within a saturated solution of Pb(PO4)2, calculate the Ksp of Pb3(PO4)2?

Show me what you know and tell me what you don't understand. Start by writing the solubility equation.

Pb3(PO4)2 = 3 Pb + 2 PO4 = (2.3 x 10-9 )^3 (2.3 x 10-9 )^2 = 6.43 X 10^-44

If (Pb^+2) = 2.1 x 10^-9, then (PO4^-3) = 2/3 x (2.1 x 10^-9), and

Ksp = (2.1 x 10^-9)^3*[(2/3)* 2.1 x 10^-9]^2??

To calculate the Ksp (solubility product constant) of Pb3(PO4)2, we need to use the given concentration of Pb^2+ and make use of the stoichiometry of the balanced equation for the dissolution of Pb3(PO4)2.

The balanced equation for the dissolution of Pb3(PO4)2 is:

Pb3(PO4)2(s) <--> 3Pb^2+(aq) + 2PO4^3-(aq)

The Ksp expression for this reaction is:

Ksp = [Pb^2+]^3 * [PO4^3-]^2

We are given the approximate concentration of Pb^2+ as 2.1 x 10^-9 mol/L. Since we are assuming that Pb3(PO4)2 is at its saturation point, all the Pb^2+ ions from the compound must have dissolved. Therefore, the concentration of Pb^2+ after Pb3(PO4)2 has dissolved completely will be three times the given concentration:

[Pb^2+] = 3 * (2.1 x 10^-9 mol/L) = 6.3 x 10^-9 mol/L

Substituting this concentration into the Ksp expression:

Ksp = (6.3 x 10^-9 mol/L)^3 * [PO4^3-]^2

Now, we need to find the concentration of PO4^3-. Since Pb3(PO4)2 is a salt, it dissociates completely in water, so the concentration of PO4^3- will be twice the concentration of Pb3(PO4)2:

[PO4^3-] = 2 * (2.1 x 10^-9 mol/L) = 4.2 x 10^-9 mol/L

Substituting this concentration into the Ksp expression:

Ksp = (6.3 x 10^-9 mol/L)^3 * (4.2 x 10^-9 mol/L)^2

Calculating the value:

Ksp = (6.3 x 10^-9)^3 * (4.2 x 10^-9)^2 = 6.912 x 10^-54

Therefore, the Ksp of Pb3(PO4)2 is approximately 6.912 x 10^-54.