volume required to bring solution to equivalence

Question

What volume of 8.3 x 10^-5 M yttrium (VI) hydroxide would be required to bring 55 mL of a 5.9 x 10^-3 M sulfurous acid solution to equivalence?

Answer 1

Y(OH)₆ + 3H₂SO₃ ==> 6H₂O + Y(SO₃)₃

moles H₂SO₃ present = 55 ml x 1 L / 1000 ml x 5.9x10^-3 mol / L = 0.0003245 moles

moles Y(OH)₆ needed = 0.0003245 mol H₂SO₃ x 1 mol Y(OH)₆ / 3 mol H₂SO₃ = 0.0001082 mols Y(OH)₆

volume of Y(OH)₆ needed = 0.0001082 mols x 1 L / 8.3x10^-5 mols = 0.01303 L = 1300 mls (2 sig.figs.)

Answer 2

Reaction : Y(OH)₆ + 3 H₂SO₃ --> 6 H₂O + Y⁶⁺ + 3 SO₃^2-.

Equivalence : n(Y(OH)₆) = n(H₂SO₃) / 3 so C(Y(OH)₆)xV(Y(OH)₆) = C(H₂SO₃)xV(H₂SO₃) / 3 and the volume of Y(OH)₆ is : V(Y(OH)₆) = 5.9 x 10^-3 x 55 / (8.3 x 10^-5 x 3) = 1300 mL.