Question

The compound \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) only exists as one isomer. Why does this support the statement that the \(\mathrm{H}\) and \(\mathrm{Cl}\) atoms in the compound are arranged tetrahedrally around the carbon rather than in a square planar structure?

Short answer

The lack of isomers for \(\mathrm{CH}_{2}\mathrm{Cl}_{2}\) supports a tetrahedral arrangement because a square planar structure would result in different possible isomers due to non-equivalent positions for the \(\mathrm{H}\) and \(\mathrm{Cl}\) atoms.

Step-by-step solution

Understanding Molecular Geometry

Recognize that the molecular geometry of a compound is determined by the arrangement of electron pairs around the central atom according to the VSEPR theory. For a molecule with four electron pairs (single bonds in this case), the geometry that minimizes repulsion is tetrahedral.

Comparing Tetrahedral and Square Planar Geometries

Consider the two possible geometries for a molecule with four atoms bonded to a central atom: tetrahedral and square planar. The tetrahedral geometry has bond angles of approximately 109.5 degrees, while a square planar has 90-degree angles between adjacent atoms and 180-degree angles across the central atom.

Understanding Isomers

Recognize that isomers are different molecules with the same molecular formula but different arrangements of atoms in space. If the compound had a square planar geometry, there would be different positions for the hydrogen and chlorine atoms to occupy, resulting in the possibility of different isomers.

Applying the Concept of Isomers to \(\mathrm{CH}_{2}\mathrm{Cl}_{2}\)

Since \(\mathrm{CH}_{2}\mathrm{Cl}_{2}\) exists only as one isomer, it indicates that all positions around the carbon atom are equivalent. This equivalence of positions is a characteristic of the tetrahedral geometry and does not apply to a square planar geometry, which would have allowed for different isomers.

Key concepts

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory is central to understanding molecular geometry. According to this theory, electron pairs in the outermost shell of an atom will arrange themselves as far apart as possible to minimize repulsion between them. These electron pairs include both bonding pairs, which are shared with other atoms to form chemical bonds, and lone pairs, which are not shared and belong exclusively to one atom.

When we consider a compound such as methane (CH4), the carbon atom, which is at the center, has four bonding pairs of electrons. These pairs repel one another and position themselves at the corners of a tetrahedron to be as far apart as possible. This leads to a tetrahedral molecular shape, known for its equal bond angles and symmetric distribution, which forms the basis of understanding more complex molecular geometries.

Isomers

Isomers are compounds that share the same chemical formula but differ in the arrangement of their atoms in space. There are several types of isomers, such as structural isomers, where the atoms are connected in different orders, and stereoisomers, which have the same sequence of bonded atoms but differ in the three-dimensional orientation of their atoms.

For instance, butane (C4H10) can exist as two different structural isomers: the straight-chain n-butane and the branched-chain isobutane. Isomers can demonstrate vastly different chemical and physical properties despite having the same molecular formula, a fascinating aspect of chemical structure and reactivity.

Tetrahedral Geometry

Tetrahedral geometry is a specific molecular shape where a central atom is surrounded by four other atoms, with each of these atoms located at the corners of an imaginary tetrahedron. This arrangement is a consequence of the VSEPR theory to minimize repulsion, as it provides equal bond angles of approximately 109.5 degrees between all the bonding pairs.

In the context of the CH2Cl2 molecule, this geometrical form explains why the molecule exists as a single isomer. All four positions around the central carbon atom are equivalent, which wouldn't be possible if the molecule had a square planar geometry. Tetrahedral geometry is a foundation in understanding many organic and inorganic compounds and their reactivity patterns.

Electron Pair Repulsion

Electron pair repulsion is a natural phenomenon arising from the negative charge of electrons. Since like charges repel each other, electron pairs in an atom's valence shell push apart from one another to the farthest allowable distances within the confined three-dimensional space around the nucleus. This repulsion dictates the resulting geometry of the molecule.

The concept of electron pair repulsion is strongly tied to VSEPR theory and effectively predicts the shapes of countless molecules. It's essential to remember that the repulsion strength between two lone pairs is greater than the repulsion between a lone pair and a bonding pair, which in turn is stronger than the repulsion between two bonding pairs. This principle helps us understand why certain molecular shapes form over others.