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Chapter 13: Problem 80

Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of \(5.00 \mathrm{~g}\) of lauryl alcohol in \(0.100 \mathrm{~kg}\) of benzene freezes at \(4.1^{\circ} \mathrm{C}\). What is the molar mass of lauryl alcohol from this data?

Short Answer

Expert verified
The molar mass of lauryl alcohol can be determined using the freezing point depression data. The freezing point depression ΔT is calculated as 1.4°C. Using the formula ΔT = k_f × molality × i, molality is calculated as 0.2734375 mol/kg. The number of moles of lauryl alcohol is then obtained by multiplying molality by the mass of the solvent (benzene) in kg, resulting in 0.02734375 mol. The molar mass is calculated as \(\frac{5.00 g}{0.02734375 mol}\), yielding a molar mass of approximately 182.9 g/mol for lauryl alcohol.

Step by step solution

01

Find the freezing point depression

First, calculate the freezing point depression by subtracting the freezing point of the pure solvent (benzene) from the freezing point of the solution. The normal freezing point of benzene is 5.5°C. Freezing point depression = ΔT = T (solvent) - T(solution) ΔT = 5.5 - 4.1 = 1.4°C
02

Use the formula for freezing point depression

Now, use the formula: ΔT = k_f × molality × i where: ΔT is the freezing point depression k_f is the cryoscopic constant for the solvent (benzene) which is 5.12°C·kg/mol molality is the moles of solute per kilogram of solvent i is the van 't Hoff factor, which is the number of particles the solute splits into upon dissolving in the solvent (1 for nonelectrolytes like lauryl alcohol)
03

Calculate molality

In this case, i = 1, and ΔT = 1.4°C. Rearrange the formula to find molality: molality = \(\frac{ΔT}{k_f × i}\) molality = \(\frac{1.4}{5.12 \times 1}\) molality = 0.2734375 mol/kg
04

Determine the number of moles

Now that we have molality, we can find the number of moles of lauryl alcohol. Multiply the molality by the mass of the solvent (benzene) in kg. Number of moles = Molality × mass (solvent) Number of moles = 0.2734375 mol/kg × 0.100 kg Number of moles = 0.02734375 mol
05

Calculate the molar mass

Now we have the moles of lauryl alcohol and the given mass of lauryl alcohol, so we can calculate the molar mass. Molar mass = \(\frac{mass}{moles}\) Molar mass = \(\frac{5.00 g}{0.02734375 mol}\) Molar mass ≈ 182.9 g/mol Therefore, the molar mass of lauryl alcohol is approximately 182.9 g/mol.

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Most popular questions from this chapter

List the following aqueous solutions in order of decreasing freezing point: \(0.040 \mathrm{~m}\) glycerin $\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right), 0.020 \mathrm{~m} \mathrm{KBr}$,

A solution contains \(0.50 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) and an unknown number of moles of sodium chloride. The vapor pressure of the solution at \(29^{\circ} \mathrm{C}\) is \(3.85 \mathrm{kPa}\). The vapor pressure of pure water at this temperature is \(4.05 \mathrm{kPa}\). Calculate the number of grams of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

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(a) Calculate the mass percentage of \(\mathrm{NaNO}_{3}\) in a solution containing \(13.6 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) in \(834 \mathrm{~g}\) of water. (b) An alloy contains \(2.86 \mathrm{~g}\) of chromium per $100 \mathrm{~kg}$ of alloy. What is the concentration of chromium in ppm?

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