Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of 5.00 g of lauryl alcohol in 0.100 kg of benzene freezes at 4.1 °C. What is the molar mass of lauryl alcohol from this data?

Verified step by step guidance

1. Identify the freezing point depression formula: \( \Delta T_f = K_f \cdot m \), where \( \Delta T_f \) is the freezing point depression, \( K_f \) is the cryoscopic constant of the solvent, and \( m \) is the molality of the solution.
2. Calculate the freezing point depression \( \Delta T_f \) by subtracting the observed freezing point of the solution (4.1 °C) from the normal freezing point of benzene (5.5 °C).
3. Determine the molality \( m \) of the solution using the formula \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \).
4. Rearrange the freezing point depression formula to solve for the moles of solute: \( \text{moles of solute} = \frac{\Delta T_f}{K_f} \cdot \text{kg of solvent} \). Use the known \( K_f \) value for benzene.
5. Calculate the molar mass of lauryl alcohol by dividing the mass of lauryl alcohol (5.00 g) by the moles of solute obtained in the previous step.

Key Concepts

Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of this depression depends on the number of solute particles in the solution, not their identity. The formula used to calculate the change in freezing point is ΔTf = Kf * m, where Kf is the freezing point depression constant of the solvent 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 because it directly relates to the number of solute particles in a given mass of solvent. In this case, knowing the mass of lauryl alcohol and the mass of benzene allows for the calculation of molality, which is essential for determining the molar mass of lauryl alcohol.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of lauryl alcohol in this scenario, one can rearrange the freezing point depression equation to solve for the molar mass using the known mass of the solute, the change in freezing point, and the mass of the solvent. This calculation is crucial for identifying the molecular weight of lauryl alcohol based on the experimental data provided.