Question

A few years ago there was a hazardous waste spill into the Danube River, coming from an aluminum processing plant. Some of the compounds in the sludge were iron oxide, aluminum oxide, silicon dioxide, calcium oxide, and titanium (IV) oxide.

1.Calculate the [Al³⁺] in a saturated solution of wavellite, Al₃(PO₄)₂(OH)F₂. K_sp=3.41 x 10^-95

2. Calculate the solubility of wavellite in a solution of 0.15 M AlF₃ (100% soluble).

Answer 1

Al3(PO4)2(OH)F2 ===> 3Al^3+ + 2PO4^3+ + OH- + 2F-

s                                    3s               2s          s       2s

(3s)^3* (2s)^2*s * (2s)^2 = Ksp

or, 27s^3 * 4s^2 *s *4s^2 = 3.41 x 10^-95

or, 432s^8 = 3.41 x 10^-95

or, s = 4.049*10^-12 M

[Al^3+] = 3 * 4.049*10^-12 M = 1.23 *10^-11 M

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Al3(PO4)2(OH)F2 ===> 3Al^3+ + 2PO4^3+ + OH- + 2F-

s                                    (3s + 0.15)    2s          s       (2s + 0.45)

(3s+ 0.15)^3* (2s)^2*s * (2s+ 0.45)^2 = Ksp

As s is very small, so 3s + 0.15 ~ 0.15 and 2s + 0.45 ~0.45

4s^3 * 3.075 *10^-4 = 3.41 *10^-95

or, 1.23 *10^-3 s^3 = 3.41 *10^-95

or, s = 3.03 *10^-31

solubility in 0.15 M AlF3 is 3.03 *10^-31 M