Calculate the molar mass of an unknown molecular (nonelectrolyte) compound in an aqueous solution containing 35.9 g of the compound in 150.0 g of water with a freezing point of -1.3 °C.

Verified step by step guidance

1. Identify the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (1 for nonelectrolytes), \( K_f \) is the freezing point depression constant for water (1.86 °C kg/mol), and \( m \) is the molality.
2. Calculate the freezing point depression \( \Delta T_f \) by subtracting the observed freezing point from the normal freezing point of water (0 °C): \( \Delta T_f = 0 - (-1.3) = 1.3 \) °C.
3. Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T_f}{i \cdot K_f} \). Substitute \( \Delta T_f = 1.3 \) °C, \( i = 1 \), and \( K_f = 1.86 \) °C kg/mol.
4. Calculate the molality \( m \) using the values from the previous step.
5. Use the definition of molality \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \) to find the moles of solute, then use the mass of the solute to calculate the molar mass: \( \text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{moles of solute}} \).

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule. Understanding molar mass is essential for converting between grams and moles, which is crucial for stoichiometric calculations in chemistry.

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 freezing point depression is directly proportional to the number of solute particles in the solution, which can be calculated using the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.

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, such as freezing point depression, because it accounts for the mass of the solvent rather than the total volume of the solution, providing a more accurate representation of the solution's properties.