Question

A 1.0L aqueous solution contains 0.25M PO₄^3-. Solid indium nitrate In(NO₃)₃, is slowly added to the solution. The K_sp for InPO₄=2.3x10^-22 and K_sp for In(OH)₃=1.3x10^-37.

Assuming that the volume remains constant, calculate the following:

The [In³⁺] when InPO₄ first starts to precipitate.

The [In³⁺] when In(OH)₃ first starts to precipitate.

The [PO₄^3-] when In(OH)₃ first starts to precipitate.

I understand the neccessity to make ICE tables and calculate the concentrations, however my study group cant seem to figure out why solving the quadratics lead to extraneous solutions, and initial concentrations in steps following part 1 are also a tad confusing.

showing all steps would be highly appreciated.

Answer 1

The K_sp for InPO₄=2.3x10^-22

K_sp for In(OH)₃=1.3x10^-37

here Ksp In(OH)₃ < K_sp for InPO₄

so In(OH)₃ first precipitate

1)

InPO4   ----------------> In+3   +   PO43-

Ksp = [In+3][PO43-]

2.3x10^-22 = [In+3 ] x 0.25

[In+3] = 9.2 x 10^-22 M

2)

In(OH)3   ---------------> In+3   + 3 OH-

Ksp = [In+3][OH-]^3

1.3x10^-37 = 27 S^4

S = 2.63 x 10^-10

[In+3] = 2.63 x 10^-10 M

3)

InPO4   ----------------> In+3   +   PO43-

Ksp = [In+3][PO43-]

2.3x10^-22 = 2.63 x 10^-10 x [PO43-]

[PO43-] = 8.73 x 10^-13 M