Question

A 0.170 M solution of an enantiomerically pure chiral compound D has an observed rotation of 0.22° in a 1-dm sample container. The molar mass of the compound is 112.0 g/mol.

(a) What is the specific rotation of D?

(b) What is the observed rotation if this solution is mixed with an equal volume of a solution that is 0.170 M in L, the enantiomer of D?

(c) What is the observed rotation if the solution of D is diluted with an equal volume of solvent?

(d) What is the specific rotation of D after the dilution described in part (c)?

(e) What is the specific rotation of L, the enantiomer of D, after the dilution described in part (c)?

(f) What is the observed rotation of 100 mL of a solution that contains 0.01 mole of D and 0.005 mole of L? (Assume a 1-dm path length.)

Answer 1

Optical Rotation: The ability to rotate the plane of a polarized monochromatic light by a solution of a chiral compound in a polarimeter is called the optical activity and the rotation in degrees is called optical rotation. The factors which affect the optical rotations are the concentration including the solvent, path length, temperature and the wavelength of light.

Specific Rotation: It is measured using the following specification-

            Path length, l = 1 decimeter (dm)

            Concentration, c = 1 g/ml

Temperature, wavelength of monochromatic light and the solvent are mentioned with specific rotation.

The relationship between specific rotation [α] and observed rotation α is given below.

[α] = α/c.l

(a) Here the observed rotation, α = + 0.22°, l = 1dm, c = 0.170M. We need to convert this in to g/ml. molar mass of the sample = 112.0 g/mol.

1 ml of this solution will contain 0.170 mmol

1 mmol = 112 mg, therefore, 0.17 mmol =112*0.17 mg =19.04 mg = 19.04e-3 g

Now, c = 19.04e-3 g/ml

Substituting all the values, we get-

[α] = α/c.l =0.22/19.04e-3/1 = +11.55^o is the specific rotation of D-enantiomer.

(b) The observed rotation will be zero because it will become a racemic mixture.

(c) The concentration will become 19.04e-3/2 g/ml, [α]=+11.55^o

So, the observed rotation, α = [α]*c*l = 11.55*(19.04e-3/2)*1 = + 0.11^o

(d) Under the same condition, the specific rotation will be the same.