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 these data? See Table 13.3 for the normal freezing point and 𝐾_f of benzene.

Verified step by step guidance

1. Determine the normal freezing point and the cryoscopic constant (Kf) of benzene from Table 13.3. The normal freezing point is the temperature at which pure benzene freezes, and Kf is a constant used in calculating the freezing point depression.
2. Calculate the freezing point depression (ΔTf) by subtracting the freezing point of the solution from the normal freezing point of benzene. ΔTf = (normal freezing point of benzene) - (freezing point of the solution).
3. Use the freezing point depression equation ΔTf = Kf * m, where m is the molality of the solution (moles of solute per kilogram of solvent), to solve for the molality of the solution. Rearrange the equation to find m: m = ΔTf / Kf.
4. Convert the mass of lauryl alcohol to moles using its molar mass (M), which is unknown. The relationship is moles = mass / molar mass (moles = 5.00 g / M).
5. Finally, use the definition of molality (moles of solute per kilogram of solvent) and the molality calculated in step 3 to find the molar mass of lauryl alcohol. Rearrange m = moles / mass of solvent (in kg) to solve for M: M = mass of lauryl alcohol / (molality * mass of solvent).

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 is directly proportional to the molality of the solution and the freezing point depression constant (Kf) of the solvent. This principle is crucial for determining the molar mass of a solute by measuring the change in freezing point.

Molality

Molality 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 an important concept in colligative properties because it provides a direct relationship between the amount of solute and the effect on the physical properties of the solvent, such as freezing point and boiling point.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of a solute using freezing point depression, one can rearrange the formula that relates freezing point change to molality and Kf, allowing for the determination of the molar mass based on the mass of the solute and the observed freezing point change.