Question

Dichloroethylene $\left({\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2\right)$ has three forms (isomers), each of which is a different substance. (a) Draw Lewis structures of the three isomers, all of which have a carbon-carbon double bond. (b) Which of these isomers has a zero dipole moment? (c) How many isomeric forms can chloroethylene, ${\mathrm{C}}_2{\mathrm{H}}_3\mathrm{Cl}$, have? Would they be expected to have dipole moments?

Short answer

The three isomers of dichloroethylene are cis-1,2-dichloroethylene, trans-1,2-dichloroethylene, and 1,1-dichloroethylene. Among them, trans-1,2-dichloroethylene has a zero dipole moment due to its symmetrical structure. Chloroethylene has two isomers: cis-chloroethylene (nonzero dipole moment) and trans-chloroethylene (zero dipole moment).

Step-by-step solution

Draw Lewis structures of three isomers of dichloroethylene with a carbon-carbon double bond

To draw the three isomers, we need to consider possible arrangements of hydrogen and chlorine atoms around the two carbon atoms, which are connected through a double bond. Here are the Lewis structures of the three isomers: 1. cis-1,2-dichloroethylene: Cl \ C = C / \ H Cl 2. trans-1,2-dichloroethylene: Cl \ C = C / \ Cl H 3. 1,1-dichloroethylene: Cl \ C = C / \ Cl H

Identify the isomer with a zero dipole moment

A molecule has a zero dipole moment when the vector sum of all individual bond dipoles in the molecule is zero. In other words, the molecular structure is symmetrical enough to cancel out the polarities. The trans-1,2-dichloroethylene has a symmetrical structure, with chlorine atoms on opposite sides of the double bond, which leads to a zero dipole moment.

Find the number of isomers for chloroethylene

In order to find the number of possible isomers of chloroethylene, we need to consider the possible places for the chlorine atom and hydrogen atoms around the two carbon atoms, which are connected through a double bond. Here are the two isomers of chloroethylene: 1. cis-chloroethylene: Cl \ C = C / \ H H 2. trans-chloroethylene: Cl \ C = C / \ H H

Determine if the isomers of chloroethylene have dipole moments

Similar to the dichloroethylene case, a molecule has a dipole moment if the structure is not symmetrical enough to cancel out the polarities of individual bonds. In the case of chloroethylene isomers: 1. cis-chloroethylene has a nonzero dipole moment because the polarities do not cancel each other out due to the presence of the hydrogen and chlorine atoms on the same side of the double bond. 2. trans-chloroethylene has a zero dipole moment since the structure is symmetrical, with the hydrogen atoms on opposite sides of the double bond, which leads to a cancellation of the polarities.

Key concepts

Lewis structures

When visualizing molecules, Lewis structures play a crucial role. These diagrams are a simple way of showing how atoms are connected and where electrons are distributed around individual atoms in a molecule. For dichloroethylene, which has the formula ${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$, the Lewis structure is drawn with a double bond between the two carbon atoms, reflecting the sharing of four electrons. The remaining valence electrons are used to complete the octets of the chlorine and hydrogen atoms.The key is to distribute the atoms and electrons in a way that reflects the potential isomers of the molecule. With dichloroethylene, we have three possibilities: cis-1,2-dichloroethylene, where the chlorines are on the same side of the double bond; trans-1,2-dichloroethylene, with chlorines on opposite sides; and 1,1-dichloroethylene, with both chlorines bonded to the same carbon. Each has unique spatial arrangements of atoms, despite having the same molecular formula, leading to different physical and chemical properties.

Dipole moment

The dipole moment is a measure that shows whether a molecule has a polar character and can be seen as an indication of the molecule's overall symmetry. If the centers of positive and negative charges coincide, the molecule exhibits no net dipole moment and is considered nonpolar; otherwise, it is polar.For molecules like dichloroethylene, having a carbon-carbon double bond means that the position of surrounding atoms is crucial in determining the dipole moment. The trans-1,2-dichloroethylene isomer has a zero dipole moment due to its symmetrical structure, as the chlorines are on opposite ends, resulting in a balance of charge distribution. On the contrary, cis-1,2-dichloroethylene and 1,1-dichloroethylene each have a nonzero dipole moment because their structures are asymmetrical, and the polarities of individual bonds do not cancel out.

Molecular symmetry

Molecular symmetry relates to the spatial arrangement of atoms in a molecule and how these arrangements affect the molecule's physical properties, including its dipole moment. A molecule with a center of symmetry, meaning that parts of it are mirror images over a certain axis, often has a zero dipole moment because the individual dipole moments of bonds are arranged so that they can cancel each other out.In the case of the trans-1,2-dichloroethylene isomer, its linear symmetry leads to a zero dipole moment—the individual dipole moments from the C-Cl bonds are equal in magnitude but opposite in direction, resulting in net zero molecule polarity. However, the cis-1,2-dichloroethylene isomer does not have this symmetry, and its dipole moments do not cancel each other.

Geometric isomerism

Geometric isomerism arises from the rigid structure of double bonds in molecules, which prevents the atoms from rotating freely around the bond axis. This leads to distinct isomers, known as geometric isomers, which can have differing physical and chemical properties despite having the same molecular formula.In dichloroethylene, geometric isomerism creates three distinct isomers, cis-1,2-dichloroethylene with chlorines on the same side, trans-1,2-dichloroethylene with chlorines on the opposite sides, and 1,1-dichloroethylene with both chlorines attached to the same carbon. The cis and trans notations are used to describe the relative positions of groups attached to the carbons double-bonded to one another. This form of isomerism is crucial in organic chemistry as it can affect boiling points, solubility, and reactivity.