We’re being asked to find the molality of SO_{4}^{2-} solution assuming ideal behavior.

When calculating the freezing point of a solution, we’re going to use the equation for Freezing Point Depression.

$\overline{){\mathbf{\u2206}}{{\mathbf{T}}}_{{\mathbf{f}}}{\mathbf{=}}{\mathbf{i}}{\mathbf{\xb7}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{\xb7}}{\mathbf{m}}}$

∆T_{f} = change in freezing point = T_{f pure solvent} –T_{f solution}

K_{f} = freezing point depression constant

i = van' t Hoff factor of the solute = no. of ions

m = molality

Recall that the formula for **molality **is:

$\overline{){\mathbf{Molality}}{\mathbf{,}}{\mathbf{}}{\mathbf{m}}{\mathbf{=}}\frac{\mathbf{moles}\mathbf{}\mathbf{solute}\mathbf{}\mathbf{\left(}\mathbf{mol}\mathbf{\right)}}{\mathbf{kilogram}\mathbf{}\mathbf{solvent}\mathbf{}\mathbf{\left(}\mathbf{kg}\mathbf{\right)}}}$

Determine the required values for the Freezing Point Depression equation:

Sulfuric acid in water dissociates completely into H^{+} and HSO_{4}^{-} ions. The HSO_{4}^{-} ion dissociates to a limited extent into H^{+} and SO_{4}^{2-}. The freezing point of a 0.1000 m solution of sulfuric acid in water is 272.72 K.

Calculate the molality of SO_{4}^{2-} in the solution, assuming ideal solution behavior.

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