Question

The compound 1,2 -dichloroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\right)\) is nonpolar, while \(c i s\) -dichloroethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\right)\) has a dipole moment: The reason for the difference is that groups connected by a single bond can rotate with respect to each other, but no rotation occurs when a double bond connects the groups. On the basis of bonding considerations, explain why rotation occurs in 1,2 -dichloroethane but not in cis- dichloroethylene.

Short answer

Free rotation in 1,2-dichloroethane due to single bonds makes it nonpolar, unlike cis-dichloroethylene which has restricted rotation and a dipole moment due to its double bond.

Step-by-step solution

Understand Molecular Structures

1,2-Dichloroethane ( C_{2}H_{4}Cl_{2} ) has two carbon atoms connected by a single bond with each carbon atom also bonded to two hydrogen atoms and one chlorine atom. On the other hand, cis-dichloroethylene ( C_{2}H_{2}Cl_{2} ) also consists of two carbon atoms but they are connected by a double bond. Each carbon atom is bonded additionally to one hydrogen and one chlorine atom.

Analyze the Bond Types

A single bond, such as the one in 1,2-dichloroethane between the carbon atoms, consists of one sigma bond. Sigma bonds allow for free rotation around the bond axis. In contrast, a double bond such as the one in cis-dichloroethylene, includes one sigma and one pi bond. Pi bonds restrict rotation due to the overlap of p orbitals above and below the plane of the atoms involved.

Consider Molecular Geometry

The free rotation in 1,2-dichloroethane allows the entire molecule to adopt various conformations but, generally, it averages out to a nonpolar geometric arrangement over time due to symmetry in the molecule (or lack of definitive sides). Cis-dichloroethylene, however, cannot rotate; its cis configuration (both chlorine atoms on the same side of the double bond) leads to a fixed dipole moment, as there are distinct polar and non-polar ends to the molecule.

Conclusion on Polarity

The ability or inability of a molecule to rotate affects its overall symmetry in space. As 1,2-dichloroethane can rotate, it can adopt positions that make it appear symmetrical and nonpolar over time. Cis-dichloroethylene is not able to rotate and thus maintains a permanent asymmetry, resulting in a measurable dipole moment.

Key concepts

Molecular Structure

When understanding molecular structure, it's vital to consider how atoms are bonded within a molecule. For example, in 1,2-dichloroethane ( C_{2}H_{4}Cl_{2} ), two carbon atoms form a single bond, each linked to two hydrogen atoms and one chlorine atom. In molecular terms, these bonds create a relatively dynamic environment because single bonds are free to rotate.
On the other hand, cis-dichloroethylene ( C_{2}H_{2}Cl_{2} ) features two carbon atoms whose connection is a double bond. Each carbon atom here is also connected to one hydrogen and one chlorine atom. The double bond creates a more rigid structure, making the molecule less able to alter its shape because there's no rotation around a double bond.
This structural difference is crucial for understanding how molecules behave chemically and physically.

Sigma and Pi Bonds

Sigma and pi bonds dictate a molecule's flexibility. In 1,2-dichloroethane, the bond between the carbon atoms is a sigma bond. A sigma bond resembles a sausage-like cloud of electron density shared directly between two atoms. It's the simplest type of covalent bond and allows atoms to rotate freely about the bond axis.
In contrast, cis-dichloroethylene's double bond comprises one sigma and one pi bond. Pi bonds are formed from the side-by-side overlap of orbitals, creating an electron cloud above and below the bond axis. This overlap restricts rotation, locking the atoms in place. The presence of pi bonds adds rigidity to the molecular structure.

Dipole Moment

A molecule's dipole moment is influenced by its geometry and the distribution of charge within it. For 1,2-dichloroethane, free rotation due to sigma bonds results in an overall nonpolar molecule. The symmetrical rotation causes the dipoles associated with individual bonds to cancel each other out over time, resulting in no net dipole moment.
In cis-dichloroethylene, the presence of the double bond restricts rotation, locking the molecule into a particular geometry where the chlorine atoms are on the same side. This fixed arrangement creates a distinct separation of charge, leading to a permanent dipole moment. Dipole moments are vector quantities pointing from positive to negative charge, and in this case, result from the electronegativity difference between the hydrogen and chlorine atoms.

Molecular Geometry

The geometry of a molecule determines much about its chemical behavior and dipole moment. In 1,2-dichloroethane, because of its single bonds, the molecule can bend and twist, leading to a configuration that averages out to be nonpolar. This flexibilty means that, over time, the molecule tends not to have a persistent dipole moment, contributing to its nonpolar nature.
In cis-dichloroethylene, the bond geometry is less flexible because of its double bond. The molecule adopts a fixed cis configuration where both chlorine atoms reside on one side of the molecule, leading to polar characteristics. This geometrical rigidity emphasizes the dipole moment, as there is a clear delineation between the positively and negatively charged sides of the molecule.