A sample of carvone was found to be 39% optically pure in favor of the dextrorotatory
enantiomer. The specific rotation for enantiomerically pure carvone is 61o. The polarimetry
experiment that led to this result was performed utilizing a 2.5 dm polarimeter tube and a
solution that was prepared by dissolving 3.49 g of carvone in 55 mL of ethanol. What was the
observed rotation for this experiment?
23.78
To find the observed rotation for this experiment, we need to calculate the specific rotation for the mixture using the formula:
Observed Rotation = Specific Rotation × Concentration × Length
1. Calculate the concentration of the carvone solution:
Concentration = mass of carvone / volume of solution
Concentration = 3.49 g / 55 mL
Note: The units need to be consistent, so convert mL to dm^3 by dividing by 1000.
Concentration = 3.49 g / (55 mL / 1000) = 63.45 g/dm^3
2. Calculate the observed rotation:
The specific rotation for enantiomerically pure carvone is given as 61°.
The length of the polarimeter tube is given as 2.5 dm.
Since 39% of the mixture is in favor of the dextrorotatory enantiomer, we only need to consider 39% of the specific rotation.
Observed Rotation = 61° × 0.39 × 63.45 g/dm^3 × 2.5 dm
Observed Rotation ≈ 608.65625°
Therefore, the observed rotation for this experiment is approximately 608.65625°.