A solution of citric acid, C6H8O7, in 50.0 g of acetic acid has a boiling point elevation of ΔT = 1.76 °C. What is the molality of the solution if the molal boilin# g-point-elevation constant for acetic acid is Kb = 3.07 1°C kg2>mol.

Verified step by step guidance

1. Identify the formula for boiling point elevation: \( \Delta T = K_b \times m \), where \( \Delta T \) is the boiling point elevation, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality.
2. Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T}{K_b} \).
3. Substitute the given values into the formula: \( \Delta T = 1.76 \, ^\circ\text{C} \) and \( K_b = 3.07 \, ^\circ\text{C} \, \text{kg/mol} \).
4. Calculate the molality \( m \) using the rearranged formula.
5. Remember that molality \( m \) is defined as moles of solute per kilogram of solvent, so the result will be in units of mol/kg.

Key Concepts

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is dissolved in it. This phenomenon occurs because the presence of solute particles disrupts the solvent's ability to evaporate, requiring a higher temperature to reach the boiling point. The relationship is quantified by the formula ΔT = Kb * m, where ΔT is the boiling point elevation, Kb is the boiling point elevation constant, and m is the molality of the solution.

Molality

Molality (m) is a measure of the concentration of a solute in a solution, 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 number of solute particles in a given mass of solvent, making it independent of temperature and volume changes. The formula for calculating molality is m = moles of solute / mass of solvent (in kg).

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding colligative properties is essential for predicting how the addition of solute affects the physical properties of a solvent, which is crucial in various chemical applications.