# Optical Rotation¶

## All Chiral Molecules are Optically Active¶

• Optically active here meaning that they rotate polarised light
• This can be measured using a polarimeter as shown in the diagram

• While all chiral compounds are optically active, each possible configuration of the compound will rotate the light in a different direction, a different amount. This can be used to isolate and identify the compound but also to calculate the “optical purity”, or how much of each enantiomer there is.

## (d)/(l) (+)/(-)¶

• If one molecule will rotate the light counter clockwise 40$$^\circ$$, it is designated the (-) or the (l) enantiomer, and it’s (-) or (d) counterpart will rotate the light 40^∘ clockwise.

## Optical Purity¶

Since the optical activity is stoichiometrically identical, a racemic mixture (equal parts of (+) and (-) enantiomers) will have 0$$^\circ$$ of rotation. Using this fact we can measure the observed roataion with a polarimiter and use it to calculate the specific rotation using the following formula,

Where:

• $$[\alpha]_D=$$ the specific roation at the sodium D line
• $$\alpha=$$ the observed rotation
• $$l=$$ the path length in decimetres (10cm)
• $$c=$$ the concentration in g/ml
$[\alpha]_D=\frac{\alpha}{l×c}$

We can then use the specific rotation to identify the enantiomeric purity (enantiomeric excess) of the solution:

$\text{optical purity}=\frac{\alpha}{[\alpha]_D}\times100$
• It is important to note though that this will tell us how much of the mixture is pure with the remaining amount being racemic.
• We need to calculate further to determine how much of each compound is in the solution