Answers
Mass of retinol = 153.0 mg = 0.153 g
Mass of solvent ( Chloroform) = 1.000 g = 0.001 kg
We have relation, B.P of solution - B.P of solvent = K b x m
Where , K b is boiling point constant of solvent , m is molality of solution
1.939 0 C = 3.630 0 C /m x m
m = 1.939 0 C / 3.630 0 C /m = 0.5342 m
We know that, molality = No. of moles of solute/ Mass of solvent in kg = (Mass / Molar mass ) of solute / Mass of solvent in kg
Therefore, Molality of retinol solution = (Mass / Molar mass ) of retinol / Mass of chloroform in kg
0.5342 m = ( 0.153 g / Molar Mass ) / 0.001 kg
( 0.153 g / Molar Mass ) = 0.5342 mol / kg x 0.001 kg = 5.342 x 10 -04 mol
Molar Mass of retinol = 0.153 g / 5.342 x 10 -04 mol = 286.41 g / mol
ANSWER : Molar mass of retinol = 286.41 g / mol
To determine molecular formula of retinol we must know the moles of constituent elements present in retinol.
Moles of C = % of C/ Atomic mass of C = 83.84 / 12.01 = 6.981
Moles of H = % of H / Atomic mass of H = 10.58 / 1.0079 = 10.50
Moles of O = % of O / Atomic mass of O = 5.58 / 16.00 = 0.3488
Hence, the ratio of number of moles of C:H:O is
(6.981 / 0.3488 = 20 , 10.50 / 0.3488 = 30 and 0.3488 / 0.3488 = 1)
Hence, empirical formula is C20H30O
Empirical formula mass = ( 20 x 12.01) + ( 30 x 1.0079) + 16.00 = 286.24
Therefore, ( molar mass / empirical formula mass ) = 286.41 / 286.24 = 1
i e molar mass = empirical mass
Therefore, Molecular formula = empirical formula = C20H30O
ANSWER : Molecular formula of retinol = C20H30O