Map Organic Chemistry Loudon Roberts & Company Publishers presented by Sapling L
ID: 554745 • Letter: M
Question
Map Organic Chemistry Loudon Roberts & Company Publishers presented by Sapling Learning A 0.130 M solution of an enantiomerically pure chiral compound D has an observed rotation of +0.28° in a 1-dm sample container. The molar mass of the compound is 160.0 g/mol (a) What is the specific rotation of D? What is the observed rotation if this solution is mixed with an equal volume of a solution that is 0.130 M in L, the enantiomer of D? Number deg mL Number dm deg (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)? Number Number deg mL g- dm deg (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.) Number Number deg mL g' dmExplanation / Answer
Molarity of solution = 0.130M
molar mass = 160g/mole
Thus mass of enantiomer D in 1 L of solution = molarity x molar mass
= 0.130 mol/L x 160g/mol
= 20.8g
Thus the concentration in g/mL = 20.8g /1000mL
= 0.0208g/mL
a) specific rotation = observed rotation / concentration(g/mL) x length(dm)
=+0.28 deg / 0.0208g/mL x 1 dm
= +13.46 deg.mL /g.dm
b)If this solution is mixed with equal volume of that is 0.130M in L, the other enantiomer , the mixture becomes racemic mixture with no optical rotation.
Thus the specific rotation of mixture = 0
c)If the solution is diluted with equal volume of solvent, then the concentration is halved.
thus the optical rotation also is halved, as specific rotation does not changewith concentration.That is the observed rotation = 13.46/2 = 6.73deg
d) The specific rotation is independent of concentration. therefore it remains constant that is +13.46 deg.mL / g.dm
e) The specific rotation of L , is also independent of concentration and is equal to specific rotation of D but opposite in sign.
Thus the specific rotation of L = -13.46 deg.mL / g.dm
f) The observed rotation of a mixture of both enantiomers =
= [moles of excess enantiomer -moles of other enantiomer ] xsp. rotation of excess isomer /total of moles of both isomers
thus
observed rotation = [0.01 -0.005]x(+13.46)/[0.01+0.005]
= 4.487 deg