Question

If 0.025 g of Fe(OH)3 is added to 3.28 L of water, what mass (g) will dissolve? Ksp is 2.8E-39.

Answer 1

Write down the dissociation of Fe(OH)₃ in water as below.

Fe(OH)₃ (s) <=======> Fe³⁺ (aq) + 3 OH^- (aq)

If x mol/L Fe(OH)₃ is dissolved in water, then, [Fe³⁺] = x mol/L and [OH^-] = 3x mol/L.

The solubility product constant is given as

K_sp = [Fe³⁺][OH^-]³ = (x).(3x)³

======> 2.8*10^-39 = 27x⁴

======> x⁴ = 1.0370*10^-40

======> 4*log x = -39.9842

======> log x = -9.99605

======> x = antilog (-9.99605) = 1.009*10^-10

The concentration of Fe(OH)₃ dissolved in water is 1.009*10^-10 mol/L; the mole(s) of Fe(OH)₃dissolved in 3.28 L water = (1.009*10^-10 mol/L)*(3.28 L) = 3.30952*10^-10 mole.

Molar mass of Fe(OH)₃ = (1*55.845 + 3*1.008 + 3*15.9994) g/mol = 106.8672 g/mol.

Mass of Fe(OH)₃ dissolved = (3.30952*10^-10 mole)*(106.8672 g/mol) = 3.53679*10^-8 g ≈ 3.537*10^-8 g (ans).