When HNO₂ is dissolved in water, it partially dissociates according to the equation HNO₂ ⇌ H⁺ + NO₂^-. A solution is prepared that contains 7.050 g of HNO₂ in 1.000 kg of water. Its freezing point is -0.2929 °C. Calculate the fraction of HNO₂ that has dissociated.

Dissociation refers to the process by which an acid separates into its constituent ions in solution. For weak acids like HNO2, this process is not complete, meaning only a fraction of the acid molecules dissociate into hydrogen ions (H+) and nitrite ions (NO2-). Understanding the degree of dissociation is crucial for calculating properties such as freezing point depression.

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of this depression depends on the number of solute particles in solution, which can be calculated using the formula ΔTf = i * Kf * m, where 'i' is the van 't Hoff factor, 'Kf' is the freezing point depression constant, and 'm' is the molality of the solution.

Molality is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is expressed in moles per kilogram (mol/kg) and is particularly useful in colligative property calculations because it remains unaffected by temperature changes. In this problem, calculating the molality of the HNO2 solution is essential for determining the extent of freezing point depression and, subsequently, the fraction of dissociated HNO2.