Why is racemic mixture optically inactive?

A racemic mixture is optically inactive because the rotations of plane-polarised light by each enantiomer cancel each other out.

A racemic mixture is a 50:50 mixture of two enantiomers. Enantiomers are non-superimposable mirror images of each other, much like your left and right hands. They have the same physical and chemical properties, except for one: their interaction with plane-polarised light. When plane-polarised light passes through a solution of a single enantiomer, it is rotated either to the left (levorotatory) or to the right (dextrorotatory). The degree of rotation depends on the concentration of the solution and the length of the path the light travels through it.

However, in a racemic mixture, the two enantiomers are present in equal amounts. This means that the amount of light rotated to the left by one enantiomer is exactly cancelled out by the amount of light rotated to the right by the other enantiomer. As a result, the overall rotation of the plane-polarised light is zero, making the racemic mixture optically inactive.

This property of racemic mixtures is important in many areas of chemistry and biochemistry. For example, many drugs are chiral, meaning they have two enantiomers. Often, only one enantiomer has the desired therapeutic effect, while the other may be inactive or even harmful. Therefore, the ability to separate enantiomers and produce drugs that are not racemic mixtures is a key goal in pharmaceutical chemistry.

In summary, a racemic mixture is optically inactive because it contains equal amounts of two enantiomers that rotate plane-polarised light in opposite directions, cancelling each other out. This is a fundamental concept in stereochemistry, the study of the three-dimensional structure of molecules, and has important implications in many areas of chemistry and biochemistry.