When HNO 2 is dissolved in water, it partially dissociates...

When HNO $_{2}$ is dissolved in water, it partially dissociates according to the equation $\mathrm{HNO}_{2} \rightleftharpoons \mathrm{H}^{+}+\mathrm{NO}_{2}^{-}$. A solution is prepared that contains $7.050 \mathrm{~g}$ of $\mathrm{HNO}_{2}$ in $1.000 \mathrm{~kg}$ of water. Its freezing point is $-0.2929^{\circ} \mathrm{C}$. Calculate the fraction of $\mathrm{HNO}_{2}$ that has dissociated.

Key Concepts

Van't Hoff Factor

This is a measure of the effect of solute particles on the colligative properties of a solution. It accounts for the number of particles into which a solute dissociates in solution, and deviations from the ideal value can indicate partial dissociation of the solute.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it is independent of temperature.

Degree of Dissociation

This term refers to the fraction of the solute molecules that dissociate into ions when dissolved. It is an important concept in understanding weak electrolytes, where only a portion of the solute contributes to the total number of particles affecting colligative properties.

Colligative Properties

These are properties of solutions that depend only on the number of solute particles present and not on their identity. They are useful in determining solute concentrations and in analyzing the effects of solute dissociation, as the overall change in properties like freezing point depression reflects the total particle count in solution.

Freezing Point Depression

This is the phenomenon where the addition of a solute lowers the freezing point of a solvent. The magnitude of the depression is proportional to the molal concentration of the solute particles, making it a key method for determining the degree of dissociation of solutes in solution.

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