Question

Dichlorobenzene, \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\), exists in three forms (isomers) called ortho, meta, and para: Which of these has a nonzero dipole moment? Explain.

Short answer

Ortho-dichlorobenzene and meta-dichlorobenzene have nonzero dipole moments as their bond dipoles do not cancel each other out. In contrast, para-dichlorobenzene has a zero dipole moment because the bond dipoles are equal in magnitude and opposite in direction, leading to their cancellation.

Step-by-step solution

Draw the Lewis structures of the three isomers

We will begin by drawing Lewis structures for ortho-dichlorobenzene (1,2-dichlorobenzene), meta-dichlorobenzene (1,3-dichlorobenzene), and para-dichlorobenzene (1,4-dichlorobenzene). Ortho-dichlorobenzene: ``` Cl | / \ --C---C-- |\ / \ | C Cl |/ \_/ --C---C-- \ H ``` Meta-dichlorobenzene: ``` Cl | / \ --C---C-- |\_ /_\ | C C-Cl | \_/_| |--C---C- ``` Para-dichlorobenzene: ``` Cl | / \ --C---C-- |/_\_/\ | C-Cl |:_:_:| --C---C-- ```

Analyze the molecular geometry

Now that we have the Lewis structures, we need to analyze the molecular geometry of each isomer and determine if they have a nonzero dipole moment or not. Ortho-dichlorobenzene: The two Cl atoms are adjacent to each other, leading to two bond dipoles that don't cancel each other out. These bond dipoles add up in the plane of the molecule, resulting in a nonzero dipole moment. Meta-dichlorobenzene: The two Cl atoms are opposite to each other on the benzene ring, resulting in bond dipoles that are not equal in magnitude but opposite in direction. This means that the bond dipoles partially cancel each other out, leading to a nonzero dipole moment. Para-dichlorobenzene: The two Cl atoms are positioned diametrically opposite to one another on the benzene ring. As a result, the bond dipoles are equal in magnitude and opposite in direction, meaning they completely cancel out each other. Thus, this isomer has a zero dipole moment.

Determine which isomers have nonzero dipole moments

Based on our analysis, we can conclude that ortho-dichlorobenzene (1,2-dichlorobenzene) and meta-dichlorobenzene (1,3-dichlorobenzene) have nonzero dipole moments, whereas para-dichlorobenzene (1,4-dichlorobenzene) has a zero dipole moment.

Key concepts

Lewis Structures

When embarked on the journey of understanding molecules, Lewis structures are the fundamental diagrams we create to visually map out the valence electrons and their bonds within a molecule. For instance, when we observe the different isomers of dichlorobenzene, Lewis structures aide us in showcasing the specific placements of chlorine (Cl) atoms attached to the benzene ring. This representation is critical as it allows us to visualize the distinct structures of ortho-, meta-, and para-dichlorobenzene.

Despite the similarities in their molecular formulas, it's the Lewis structures that unveil the unique arrangement of atoms. In ortho-dichlorobenzene, the two Cl atoms sit next to each other, while in meta-dichlorobenzene, they are separated by a single benzene carbon. Para-dichlorobenzene showcases the Cl atoms at opposite ends of the benzene ring. These varying placements are not mere aesthetics – they have a profound impact on the molecule's characteristics and are pivotal when determining properties like the dipole moment.

Molecular Geometry

Molecular geometry goes beyond the simple connections between atoms; it deals with the three-dimensional arrangement of atoms in a molecule. By understanding the molecular geometry of different isomers of dichlorobenzene, we unlock the reasons behind their varying dipole moments.

The genuine shape of the molecule matters. For ortho-dichlorobenzene, the Cl atoms' proximity leads to a non-symmetrical arrangement creating a notable dipole moment. Conversely, para-dichlorobenzene's symmetrical geometry allows the opposing dipoles to cancel each other out, resulting in a molecule with no overall dipole moment. Meta-dichlorobenzene, sitting between these two extremes, has a less symmetrical shape than para but is more balanced than ortho, resulting in a nonzero yet smaller dipole moment.

Chemical Isomerism

Chemical isomerism is the phenomenon where compounds with the same molecular formula exhibit different chemical structures. This concept helps us to understand why molecules like dichlorobenzene, which share the same number of each type of atom, can have wildly differing physical and chemical properties.

Isomers like ortho-, meta-, and para-dichlorobenzene are prime examples of structural isomerism, specifically positional isomers, where the position of the substituent groups (in this case, chlorine atoms) varies on the benzene ring. Each position results in a distinctive distribution of electrons and thus contributes to different reactivity, boiling points, and as we've explored, dipole moments. Understanding isomerism is crucial for chemistry students not only to ace their assignments but also to later grasp the complexities of organic chemistry and the behavior of molecules in various environments.