Cholesterol is poorly soluble in water,but it will dissolve in nonpolar solvents such as cyclohexane (C₆H₁₂,84.18 g/mol,K_f = 20.2 $\circ$ C/m,T_f = 6.55 $\circ$ C).When 10.0 g cholesterol was dissolved in 0.500 kg cyclohexane,the freezing point of the solution was 5.50 $\circ$ C.What is the approximate molar mass of cholesterol?

Question

Quizplus · Accepted Answer

We can use the freezing point depression formula to solve the problem:

ΔTf = Kf · m

where ΔTf is the freezing point depression, Kf is the freezing point depression constant of cyclohexane, and m is the molality of the solution.

We are given ΔTf = 5.50°C, Kf = 20.2°C/m, and m = (10.0 g / 384.18 g/mol) / (0.500 kg / 84.18 g/mol) = 0.0310 m.

We can solve for the molar mass of cholesterol:

ΔTf = Kf · m

5.50°C = 20.2°C/m · 0.0310 m

m = 385 g/mol

Therefore, the approximate molar mass of cholesterol is 385 g/mol, which corresponds to choice B.

Cholesterol Is Poorly Soluble in Water,but It Will Dissolve in Nonpolar