Question

2-methylpenta- 2,3 -diene is achiral as it has (a) A centre of symmetry (b) A plane of symmetry (c) A \(\mathrm{C}_{2}\) axis of symmetry (d) Both centre and a plane of symmetry

Short answer

2-methylpenta-2,3-diene is achiral because it lacks symmetry elements.

Step-by-step solution

Identify the structure

First, write down or draw the structure of 2-methylpenta-2,3-diene. The compound has a six-carbon chain where a methyl group is attached to the second carbon, and two double bonds are present between C2-C3 and C3-C4. The structure looks like this: CH3-C(CH3)=C=CH-CH2-CH3.

Check for a centre of symmetry

A molecule has a centre of symmetry if at a point in the molecule, anything on one side has an identical counterpart directly opposite at an equal distance. In the case of 2-methylpenta-2,3-diene, such a point does not exist because the substituents are not symmetrically arranged around any central atom.

Check for a plane of symmetry

A plane of symmetry divides a molecule into two mirror-image halves. Examine the structure to see if you can divide the molecule into two symmetrical pieces. In 2-methylpenta-2,3-diene, there is no plane that symmetrically divides the molecule due to the arrangement of its atoms.

Check for a C2 axis of symmetry

A molecule has a C2 axis if it can be rotated 180° to give a configuration indistinguishable from the original. For 2-methylpenta-2,3-diene, such an axis does not exist, as rotating the molecule does not result in a structure that appears identical.

Determine the symmetry elements

Since 2-methylpenta-2,3-diene has neither a plane of symmetry, a centre of symmetry, nor a C2 axis, it can be concluded that the molecule is achiral due to the absence of these symmetry elements. Therefore, it has no symmetry that would lead to chirality constraints being violated.

Key concepts

Molecular Symmetry

Molecular symmetry is an essential concept in understanding the structure and behavior of molecules. It refers to the idea that certain operations, like rotations or reflections, can transform a molecule into a configuration that is indistinguishable from the original one. Symmetry is not only an aesthetic factor but also dictates many physical and chemical properties of molecules.

Organic molecules often display various types of symmetry, which can help determine their chirality or achirality. Chirality refers to the "handedness" of molecules, which is the property of a molecule not being superimposable on its mirror image. A molecule without chiral centers is often achiral and can exhibit certain types of symmetries, such as rotational and reflectional symmetries, that helps in identification.

Understanding molecular symmetry is crucial in fields like stereochemistry, spectroscopy, and crystallography. It serves as a foundational concept to explore how molecular orientation affects chemical reactions and properties.

Centre of Symmetry

The centre of symmetry in a molecule is a point from which all parts, when extended equally in opposite directions, show identical features. Essentially, for every atom or group found at some distance and direction from this center, an identical atom or group must exist at the same distance but in the reverse direction.

Not all molecules have a center of symmetry, especially those that are chiral. In our case of 2-methylpenta-2,3-diene, a center of symmetry does not exist. This is because the substituents are not arranged in a manner that allows for an equal counterpart at the opposite end of the molecule.

The absence of a center of symmetry is a key factor contributing to a molecule's achirality. It leads to an understanding that despite lacking this symmetry element, a molecule like 2-methylpenta-2,3-diene does not exhibit chirality.

Plane of Symmetry

A plane of symmetry is an imaginary plane dividing a molecule into two equal halves that are mirror images of each other. If a molecule possesses a plane of symmetry, it inherently lacks chirality, as a chiral molecule cannot be divided into symmetrical mirror-image halves.

In 2-methylpenta-2,3-diene, despite its linear nature, no plane of symmetry exists. The specific arrangement and bonding of carbon atoms and substituents in this molecule prevent it from being bisected into two equal and reflective portions.

Identifying the absence of a plane of symmetry is integral in the classification of molecular structures, especially when assessing whether a molecule is capable of optical activity, which relates to chirality.

C2 Axis of Symmetry

The C2 axis of symmetry refers to a rotational symmetry where a molecule can be turned by 180 degrees to look the same as it did in its original position. To possess such an axis, the structure must repeat after this specific rotational transformation.

For 2-methylpenta-2,3-diene, no C2 axis of symmetry exists. Turning the molecule by 180 degrees does not return a configuration identical to the starting arrangement, due to the unique positions of the methyl groups and double bonds.

The absence of such a rotational symmetry axis in a molecule is another indicator of achirality. Aligning molecular configurations with symmetry concepts aids in identifying symmetry elements and understanding why some molecules exhibit certain spatial properties, leading to further chemical implications.