calcs_key.html

Stereochemistry: Specific Rotation and Related Calculations
Exercise Solutions

a. 0.856 g in 10.0 mL of solution = 0.0856 g ml^-1.
[a]_l^T = a/lc
So: [a]_D^20.0 = +1.06^o/ (1.00 dm) (0.0856 g ml^-1) = +12.38^o

b. [a]_l^T = a/lc
c = 0.0001 M = 0.0001 moles L^-1 = (0.0001) (853.93 g mole^-1) (0.001 L) = 0.00085 g ml^-1
Assume l = 1.0 dm (standard polarimeter tube)
Solving for a: a = [a]_l^Tlc = (-49^o) (1.0 dm) (0.00085 g ml^-1) = -0.042^o.

c. Solutions of enantiomers of equal concentrations rotate plane polarized light to an equal extent but in opposite directions. If a certain compound has a specific rotation of -43.2^o (c = 5, toluene) then the enantiomer has a specific rotation of +43.2^o (c = 5, toluene). From the previous question,
a = [a]_l^Tlc = (+43.2^o) (1.00 dm) (1.00 g ml^-1) = +43.2^o. We could have anticipated this result without doing a calculation, as the rotation is observed under the "standard conditions" of 1.00 dm tube and 1.00 g ml^-1 concentration.

d. i) If the sample is levorotatory, then the concentration of the (-) enantiomer is greater than the concentration of the (+) enantiomer. We cannot calculate the exact concentration, as we do not know how much (-) enantiomer is being canceled by the (+) enantiomer. For example, the sample might contain 1.1 g ml^-1 of the (-) enantiomer and 1.0 g ml^-1 of the (+) enantiomer. This solution would have the same rotation as a 0.1 g ml^-1 solution of the (-) enantiomer alone.

ii) Enantiomers have equal but opposite rotations. An observed rotation of zero implies the enantiomers are present in equal concentrations (a racemic mixture).

Link to: