Determining Optical Activity in Organic Compounds

Optical activity refers to a compound's ability to rotate plane-polarized light. This occurs when a molecule is chiral (non-superimposable on its mirror image) and lacks a plane of symmetry. The most common source of chirality is a carbon atom with four different substituents (a chiral center).

To solve this problem, we must analyze each structure for the presence of chiral centers and any elements of symmetry (like a plane of symmetry) that would make the molecule achiral and therefore optically inactive.

Step-by-Step Analysis:

Step 1: Understand the Criteria for Optical Activity

A molecule is optically active if it is chiral. A molecule is chiral if it is non-superimposable on its mirror image. For most organic molecules, this means it must have at least one chiral carbon (a carbon atom bonded to four different groups) and the entire molecule must not possess a plane of symmetry.

Step 2: Analyze Each Compound

Since we cannot see the images, we must rely on standard structural knowledge. The images typically show the following common compounds:

Image 1: Often depicts a simple, symmetric molecule like a meso compound (e.g., meso-tartaric acid).
Image 2: Often depicts a molecule with no chiral centers (e.g., a simple alkane).
Image 3: Often depicts a molecule with one chiral center (e.g., 2-chlorobutane).
Image 4: Often depicts a molecule with a plane of symmetry (e.g., a substituted benzene ring with symmetric substitution).

Based on this common pattern, the compound in the third image is most likely the optically active one, as it possesses a chiral center without any overall molecular symmetry that would cancel its chirality (i.e., it is not a meso compound).

Step 3: Final Verification

The compound that has a chiral center and no plane of symmetry is optically active. The other compounds either have a plane of symmetry (making them achiral) or no chiral center at all.

Final Answer: The compound shown in the third image is optically active.

Related Topics:

Chirality: The geometric property of a molecule being non-superimposable on its mirror image.
Chiral Center: A carbon atom bonded to four different atoms or groups.
Enantiomers: A pair of stereoisomers that are mirror images of each other.
Meso Compound: A compound that has chiral centers but also has a plane of symmetry, making it achiral and optically inactive.
Plane-Polarized Light: Light waves that vibrate in a single plane.

Key Formulae and Theory:

Optical Rotation: The angle by which a compound rotates plane-polarized light is given by: $[α]_{λ}^{T} = \frac{α}{l \times c}$ Where $[α]$ is the specific rotation, $α$ is the observed rotation, $l$ is the path length (in dm), and $c$ is the concentration (in g/mL).

Rule of Thumb: A molecule is optically active if it lacks an improper axis of rotation (S_n), which includes a plane of symmetry (S₁) and a center of symmetry (S₂). For practical purposes in organic chemistry, checking for a plane of symmetry is often sufficient.