Assuming complete dissociation, what is the molality of an aqueous solution of KBr whose freezing point is -2.95 °C? The molal freezing-point-depression constant of water is given in Table 13.4.

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Identify the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the molal freezing-point-depression constant, and \( m \) is the molality.

Determine the change in freezing point, \( \Delta T_f \), by subtracting the freezing point of the solution from the normal freezing point of water (0 °C).

For KBr, which dissociates into K\(^+\) and Br\(^-\), the van't Hoff factor \( i \) is 2, because it dissociates into two ions.

Rearrange the formula to solve for molality: \( m = \frac{\Delta T_f}{i \cdot K_f} \).

Substitute the known values for \( \Delta T_f \), \( i \), and \( K_f \) into the equation to calculate the molality.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point when a solute is added. The extent of this depression is directly proportional to the molality of the solution and the freezing-point-depression constant (Kf) of the solvent. For water, Kf is typically 1.86 °C kg/mol, meaning that for each mole of solute per kilogram of solvent, the freezing point decreases by this amount.

Molality

Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it directly relates to the effect of solute on the properties of the solvent. Unlike molarity, molality is not affected by temperature changes, making it a stable measure for solutions in thermal calculations.

Dissociation of Ionic Compounds

Ionic compounds, such as KBr, dissociate into their constituent ions when dissolved in water. For KBr, it dissociates into K⁺ and Br⁻ ions. This dissociation increases the number of particles in solution, which is crucial for calculating colligative properties like freezing point depression, as the effect is based on the total concentration of solute particles rather than just the number of solute molecules.