Question

A racemic mixture has (a) zero optical rotation (b) positive optical rotation (c) negative optical rotation (d) infinite optical rotation.

Short answer

The correct answer is (a) zero optical rotation.

Step-by-step solution

Understanding Racemic Mixture

A racemic mixture is a 50:50 mix of two enantiomers. It's essential to understand that the two enantiomers in a racemic mixture rotate plane-polarized light in equal magnitudes but opposite directions.

Analyzing Optical Rotation

The rotation of plane-polarized light caused by the left-rotating enantiomer (-) is canceled out by the rotation caused by the right-rotating enantiomer (+). This is because the two rotations are of the same magnitude but in opposite directions.

Finalizing The Answer

Since the rotation caused by the two enantiomers cancels each other out, this implies that there is no apparent rotation of the plane of polarized light. So, a racemic mixture shows zero optical rotation.

Key concepts

Enantiomers

Enantiomers are mirror-image forms of the same compound, which cannot be superimposed on one another, similar to how our left and right hands are mirror images but not identical. In chemistry, this occurs when a molecule has a chiral center, typically a carbon atom with four different groups attached to it. Enantiomers are significant in the study of chemical reactions and in developing pharmaceuticals because they can exhibit drastically different biological activities despite their similar structures.

For example, one enantiomer of a drug may be therapeutically beneficial, while the other might cause adverse effects. Understanding the properties of enantiomers is crucial for students entering fields such as chemistry, pharmacy, and medicine. To differentiate between enantiomers, scientists use their interaction with plane-polarized light, a property known as optical activity.

Plane-Polarized Light

Natural light vibrates in many directions, but when it passes through certain filters, like a polarizer, it is transformed into plane-polarized light, meaning it vibrates in only one plane. Picture this as a rope lying on the floor that only moves up and down without twisting left or right. This specialized form of light is an invaluable tool in chemistry because it interacts differently with various molecular structures.

When used in conjunction with a device called a polarimeter, plane-polarized light can help determine the optical activity of a substance. By observing how a chemical sample affects this one-directional light, scientists can infer valuable information about the sample’s molecular composition. This interaction is especially important for identifying the presence of chiral molecules, which can rotate the plane-polarized light to varying degrees.

Optical Activity

Optical activity is a measure of how much a chiral substance can rotate plane-polarized light. If the light’s plane is rotated clockwise when looking towards the light source, the substance is said to be dextrorotatory, and is indicated by a positive sign (+). Conversely, if the light’s plane rotates counterclockwise, the substance is levorotatory, marked by a negative sign (-).

The degree to which the plane-polarized light is rotated is determined by the length of the sample cell and the concentration of the chiral substance within it, and this rotation is expressed in degrees. In a racemic mixture, which contains equal amounts of enantiomers, they rotate the light to an equal degree but in opposite directions, resulting in no net rotation of the light. This phenomenon is critical for the concept at hand because it explains the answer to the question in the original exercise, which is that a racemic mixture has zero optical rotation.