Sulfuric acid in water dissociates completely into H+ and HSO4− ions. The HSO4− ion dissociates to a limited extent into H+ and SO42−. The freezing point of a 0.1778 m solution of sulfuric acid in water is 272.47 K. For water, Kf=1.86∘C/m. Required:
Calculate the molality of SO4(2-) in the solution, assuming ideal solution behavior.

0.0010m SO₄²⁻

Explanation:

The freezing point depression due the addition of a solute into a pure solvent follows the equation:

ΔT = Kf×m×i (1)

Where ΔT are °C that freezing point decreases (273.15K - 272.47K = 0.68K = 0.68°C). Kf is the constant of freezing point depression (1.86°C/m), m is molality of the solution (0.1778m) and i is Van't Hoff factor.

Van't Hoff factor could be understood as  in how many one mole of the solute (sulfuric acid, H₂SO₄), is dissociated.

H₂SO₄ dissociates as follows:

H₂SO₄ → HSO₄⁻ + H⁺

HSO₄⁻ ⇄ SO₄²⁻ + H⁺

Not all HSO₄⁻ dissociates.

1 Mole of H₂SO₄ dissociates in 1 mole of H⁺+ 1 mole of HSO₄⁻ + X moles of   SO₄²⁻= 2 + X

Replacing in (1):

0.68°C = 1.86°C/m×0.1778m×i

2.056 = i

Moles of SO₄²⁻ are 2.056 - 2 = 0.056moles SO₄²⁻.

If 1 mole has a concentration of 0.1778m, 0.056moles are:

0.056moles ₓ (0.1778m / 1mole) =