Question

A solution of 0.613 g erucic acid in 8.115 g stearic acid is measured to have a freezing point of 68.60 ºc. what is the molar mass of erucic acid? hint: mw stearic acid is 284.48 g/mol. tf (stearic acid) = 69.60 ºc. kf (stearic acid) = 4.50 ºc/m. density (stearic acid) = 847 kg/m3. select one:
a. none of these answers is correct.
b. 96.8 g/mol
c. 0.340 g/mol
d. 339 g/mol
e. 315 g/mol

Answer 1

Mass of erucic acid = 0.613 g 
Mass of stearic acid = 8.115 g
Tf solution = 68.6°C
Tf solvent = 69.6°C
Kf = 4.5 °C / m
Δ Tf = Kf * m
where: ΔTf : freezing point depression
Kf : freezing point depression constant
m : molality of solution
ΔTf = Tf solvent - Tf soln = 69.6 - 68.6 =1°C
m = ΔTf / Kf = 1 / 4.5 = 0.22 molal
molality = number of moles of solute (n) / Mass of solvent (in kg)
 number of moles = molality * mass of solvent (kg) = 0.22 * (8.115 * 10⁻³) = 1.8 x 10⁻³ mol
number of moles of solute = weight of solute (g) / Molar mass
Molar mass = weight (g) / n (moles) = 0.613 g / (1.8 x 10⁻³)
                    = 339 g / mol
so the correct answer is d)