The solubility product constant for iron(III) hydroxide at 22 °C is 6.0 × 10^-38. What mass of this compound will dissolve in 100 mL of 0.20 M sodium hydroxide, assuming no complex formation?

Question

Quizplus · Accepted Answer

The balanced equation for the dissolution of iron(III) hydroxide in sodium hydroxide is:

Fe(OH)3(s) + 3 NaOH(aq) → Na3Fe(OH)6(aq)

The equilibrium expression for the dissolution of iron(III) hydroxide is:

Ksp = [Fe3+][OH-]^3 = 6.0 × 10^-38

Assuming that all of the iron(III) hydroxide dissolves, the concentration of Fe3+ and OH- in the solution will be equal to the initial concentration of sodium hydroxide, which is 0.20 M.

Therefore, we can use the Ksp expression to calculate the concentration of Fe3+:

Ksp = [Fe3+][OH-]^3
6.0 × 10^-38 = [Fe3+](0.20)^3
[Fe3+] = 8.574 × 10^-35 M

The molar mass of iron(III) hydroxide is:

Fe(OH)3 = 56.85 + 3(17.01) = 107.88 g/mol

The number of moles of iron(III) hydroxide that will dissolve in 100 mL of 0.20 M sodium hydroxide is:

n = [Fe3+] × V = (8.574 × 10^-35 mol/L) × 0.1 L = 8.574 × 10^-36 mol

The mass of iron(III) hydroxide that will dissolve is:

m = n × M = (8.574 × 10^-36 mol) × (107.88 g/mol) = 9.243 × 10^-34 g

Rounded to two significant figures, the answer is 8 × 10^-35 g or 8 × 10^-35 g, which corresponds to choice C.

The Solubility Product Constant for Iron(III) Hydroxide at 22 °C