91Ó°ÊÓ

The molality of a solution is a measure of the concentration of a solute in a solvent and is represented in terms of moles of solute per kilogram of solvent. Unlike molarity, which depends on volume, molality is based on the mass of the solvent and thus, remains constant with temperature changes. This makes it particularly useful in situations involving temperature changes, such as boiling point elevation. To compute molality, you need to know:

• The moles of the solute
• The mass of the solvent in kilograms

In the given exercise, the problem requires calculating the molality without directly knowing the moles of citric acid. Instead, the boiling point elevation and the boiling-point-elevation constant are used to calculate it. Knowing that the formula for boiling point elevation is \[ \Delta T = i K_{b} m \]where \( \Delta T \) is the boiling point elevation, \( K_{b} \) is the constant, and \( m \) is the molality, we can rearrange to solve for \( m \): \[ m = \frac{\Delta T}{K_{b}} \]This calculation provides a practical way to find molality when temperature changes are involved.

The molal boiling-point-elevation constant, denoted as \( K_{b} \), is specific to each solvent and represents how much the boiling point of the solvent increases per molal concentration (mol/kg) of a non-volatile solute. This constant reflects the unique properties of the solvent and its interactions with solutes. It is essential to note that:

• \( K_{b} \) is dependent on the solvent, not the solute.
• It has the units of \( ^{\circ}C \cdot \text{kg/mol} \), aligning with the requirements of the boiling point elevation equation.

For example, in our exercise, it is given that acetic acid has a \( K_{b} \) value of \(3.07 \; ^{\circ}C \cdot \text{kg/mol}\). This indicates that for every mol/kg of solute added, the boiling point of acetic acid will rise by \(3.07^{\circ}C\). Utilizing \( K_{b} \) in boiling point calculations simplifies the determination of changes in boiling points due to solute additions.

The van't Hoff factor, \( i \), is a dimensionless quantity used in calculating colligative properties, like boiling point elevation or freezing point depression. It reflects the number of particles the solute splits into when dissolved.Understanding the van’t Hoff factor:

• For non-electrolytes that do not dissociate in solution, \( i = 1 \).
• For electrolytes, \( i \) is the number of ions a solute dissociates into.
• It directly multiplies the effect a solute has on boiling point elevation or other colligative properties.

In the given case of citric acid (a molecular, non-dissociating solute), the van't Hoff factor \( i \) is 1, indicating no change in particle number in solution. Thus, its impact on the boiling point is based solely on its molality, simplifying calculations since \[ \Delta T = i K_{b} m \rightarrow \Delta T = K_{b} m \]