Lauryl alcohol is a nonelectrolyte obtained from coconut oil and is used to make detergents. A solution of 8.80 g of lauryl alcohol in 0.100 kg of benzene freezes at 3.0 ∘C. You may want to reference (Page) Section 13.5 while completing this problem. What is the approximate molar mass of lauryl alcohol?

The molar mass of lauryl alcohol is approximately 180 g/mol

Explanation:

Step 1: Data given

Mass of lauryl alcohol = 8.80 grams

Mass of benzene = 0.100 kg = 100 grams

Freezing point of Benzene is 5.5 °C

Kf value for benzene = 5.12 °C/molal

Step 2: Calculate the freezing point depression

ΔTf = 5.5 - 3.0 °C = 2.5 °C

Step 3: Calculate molality

⇒ with ΔTf = the freezing point depression = 2.5 °C

⇒ with i = the van't Hoff factor = 1

⇒ with kf = the free point depression constat pf benzene = 5.12°C/m

⇒ with m =the molality = TO BE DETERMINED

molality = ΔTf / kf

molality = 2.5 °C / 5.12 °C /m

molality =  0.488 molal

Step 4: Calculate moles lauryl alcohol

Molality = moles lauryl alcohol / mass benzene

Moles lauryl alcohol = molality * mass benzene

Moles lauryl alcohol = 0.488 m * 0.100 kg

Moles lauryl alcohol = 0.0488 moles

Step 5: Calculate molar mass of lauryl alcohol

Molar mass lauryl alcohol = mass lauryl alcohol/ moles lauryl alcohol

Molar mass lauryl alcohol = 8.80 grams / 0.0488 moles

Molar mass lauryl alcohol = 180 g/mol

The molar mass of lauryl alcohol is approximately 180 g/mol