Question

\(1,2,3,4,5,6\)-Hexachlorocyclohexane shows cis,trans isomerism. At one time, a crude mixture of these isomers was sold as an insecticide. The insecticidal properties of the mixture arise from one isomer, known as lindane, which is cis-1,2,4,5-trans3,6-hexachlorocyclohexane. (a) Draw a structural formula for \(1,2,3,4,5,6\)-hexachlorocyclohexane disregarding, for the moment, the existence of cis,trans isomerism. What is the molecular formula of this compound? (b) Using a planar hexagon representation for the cyclohexane ring, draw a structural formula for lindane. (c) Draw a chair conformation for lindane and label which chlorine atoms are axial and which are equatorial. (d) Draw the alternative chair conformation of lindane and again label which chlorine atoms are axial and which are equatorial. (e) Which of the alternative chair conformations of lindane is more stable? Explain.

Short answer

Answer: The first chair conformation of lindane is more stable than the second one because in the first conformation, all four cis chlorines are positioned equatorially, resulting in lower steric hindrance. In the second conformation, the cis chlorines are positioned axially, introducing increased steric hindrance and making it energetically unfavorable and less stable.

Step-by-step solution

(a) Structural formula of 1,2,3,4,5,6-hexachlorocyclohexane and the molecular formula

To draw a structural formula for 1,2,3,4,5,6-hexachlorocyclohexane, first draw a cyclohexane ring, which is a hexagon. Then, add chlorine atoms as substituents to all six vertices of the hexagon. As we're not considering cis and trans isomers yet, place the chlorine atoms as line segments sticking out from each corner. The molecular formula, considering six carbons, twelve hydrogens, and six chlorines, is C6H6Cl6.

(b) Structural formula for lindane

For lindane (cis-1,2,4,5-trans3,6-hexachlorocyclohexane), draw a planar hexagon for the cyclohexane ring. Attach chlorine atoms on the 1, 2, 4, and 5 positions in a cis orientation, meaning they will be on the same side, either downwards or upwards. Add chlorines to positions 3 and 6 in a trans orientation, which is on the opposite side of the plane compared to the remaining four.

(c) Lindane chair conformation (first alternative) and label axial/equatorial chlorine atoms

Draw a chair conformation of the hexane ring, making one carbon atom higher than the others on one side and one carbon lower than the others on the opposite side. Draw cis chlorines in equatorial positions and the trans chlorines in axial positions. Label all chlorines with their respective locations (axial or equatorial).

(d) Lindane chair conformation (second alternative) and label axial/equatorial chlorine atoms

Draw the second chair conformation of lindane by flipping the chair, with the high and low positions for carbon moving to the opposite side. For this second benzene, invert the axial and equatorial positions of all chlorines. Label all chlorines with their respective locations (axial or equatorial).

(e) Determine the stability of the chair conformations of lindane and provide an explanation

The first chair conformation of lindane is more stable than the second one. This is because, in the first chair conformation, all four cis chlorines are positioned equatorially, resulting in lower steric hindrance. In the second chair conformation, these four cis chlorines are positioned axially, which introduces increased steric hindrance, making it energetically unfavorable and less stable.

Key concepts

Cis-trans Isomerism

Cis-trans isomerism, also known as geometric isomerism, is a type of stereoisomerism where different isomers of a compound have the same molecular formula but differ in the orientation of functional groups across a double bond or a ring structure. In cyclic compounds like cyclohexane, isomers with substituents on the same side of the ring are termed 'cis', while those with substituents on opposite sides are called 'trans'.

For students studying hexachlorocyclohexane isomers, recognizing the cis and trans positions can significantly impact understanding chemical properties and the stability of various isomers. Lindane, a particular isomer of hexachlorocyclohexane with insecticidal properties, exhibits this kind of isomerism. Correctly drawing its structure requires mindful positioning of chlorines in 'cis' (1,2,4,5) and 'trans' (3,6) configurations to represent the molecule accurately.

Chair Conformation Stability

The chair conformation is one of the most stable arrangements for six-membered cyclic molecules, such as cyclohexane and its derivatives, due to the minimized steric hindrance and torsional strain. In the context of hexachlorocyclohexane, each carbon atom can have substituents in either of two positions—axial or equatorial. Axial substituents are perpendicular to the ring plane; equatorial substituents extend from the sides.

A crucial factor affecting the stability of chair conformations is the position of bulky groups, such as the chlorine atoms in hexachlorocyclohexane isomers. When bulky groups occupy equatorial positions, the molecule is more stable due to the reduced steric hindrance as compared to when these groups are in axial positions. Thus, in lindane, having four chlorines in equatorial positions makes one chair conformation more stable than the alternative, where these chlorines would be axial.

Structural Formula Drawing

Drawing the structural formula of a compound is a fundamental skill that aids in visualizing the arrangement of atoms within a molecule. It's particularly important for understanding stereoisomerism and conformations. When it comes to drawing hexachlorocyclohexane, the planar hexagon represents the cyclohexane ring, while the attached lines or wedges represent chlorine atoms indicating their position relative to the plane of the ring.

In exercises involving cis-trans isomerism and conformations, accurately representing these atoms as either solid or dashed wedges helps denote their positions as 'up' or 'down' relative to the plane of the ring, respectively. For lindane, drawing these correctly can depict the precise stereochemistry and allow for further analysis of conformational stability. Such depictions are not merely illustrative but essential for understanding the chemical behavior and interactions of the molecule in question.