Question

Name the proper three-dimensional molecular shapes for each of the following molecules or ions, showing lone pairs as needed: $(\mathbf{a}){\mathrm{ClO}}_2^{-}(\mathbf{b}){\mathrm{SO}}_4^{2-}(\mathbf{c}){\mathrm{NF}}_3(\mathbf{d}){\mathrm{CCl}}_2{\mathrm{Br}}_2(\mathbf{e}){\mathrm{SF}}_4^{2+}$

Short answer

The molecular shapes for the given molecules and ions are as follows: (a) ClO₂⁻ has a linear shape, (b) SO₄²⁻ has a tetrahedral shape, (c) NF₃ has a trigonal pyramidal shape, (d) CCl₂Br₂ has a tetrahedral shape, and (e) SF₄²⁺ has a see-saw shape.

Step-by-step solution

(a) Clo₃⁻ ion: Determine the central atom and valence electrons

In the ClO₂⁻ ion, the central atom is chlorine (Cl) because oxygen (O) is more electronegative, so chlorine will have oxygen atoms surrounding it. Chlorine has 7 valence electrons, each oxygen atom has 6 valence electrons, and there is one extra electron due to the negative charge of the ion. Therefore, the total number of valence electrons is: $7+2\times 6+1=20$.

(a) Clo₃⁻ ion: Determine the bonding and lone electron pairs

The total number of electron pairs is 20 ÷ 2 = 10. Each oxygen bonded to chlorine contributes one bonding electron pair, thus using 2 electron pairs. The remaining 10 - 2 = 8 electron pairs are lone pairs and distributed evenly to the oxygen atoms. This means each oxygen atom has three lone pairs while the chlorine does not have any.

(a) Clo₃⁻ ion: Predict the molecular shape

Since Cl is surrounded by 2 atoms and 0 lone pairs, its electron pair geometry is linear. Therefore, the molecular shape of ClO₂⁻ is linear.

(b) SO₄²⁻ ion: Determine the central atom and valence electrons

In the SO₄²⁻ ion, the central atom is sulfur (S), surrounded by four oxygen (O) atoms. Sulfur has 6 valence electrons, each oxygen atom has 6 valence electrons, and there are two extra electrons due to the negative charge of the ion. Therefore, the total number of valence electrons is: $6+4\times 6+2=32$.

(b) SO₄²⁻ ion: Determine the bonding and lone electron pairs

The total number of electron pairs is 32 ÷ 2 = 16. Each oxygen atom contributes one bonding electron pair, so there are 4 bonding electron pairs. The other 16 - 4 = 12 electron pairs are lone pairs and are distributed evenly to the oxygen atoms. Each oxygen atom has three lone pairs.

(b) SO₄²⁻ ion: Predict the molecular shape

Since the sulfur atom is surrounded by 4 atoms and no lone pairs, its electron pair geometry is tetrahedral. Therefore, the molecular shape of SO₄²⁻ is tetrahedral.

(c) NF₃ molecule: Determine the central atom and valence electrons

In the NF₃ molecule, the central atom is nitrogen (N), surrounded by three fluorine (F) atoms. Nitrogen has 5 valence electrons and each fluorine atom has 7 valence electrons. Therefore, the total number of valence electrons is: $5+3\times 7=26$.

(c) NF₃ molecule: Determine the bonding and lone electron pairs

The total number of electron pairs is 26 ÷ 2 = 13. Each fluorine atom contributes one bonding electron pair, so there are 3 bonding electron pairs. The other 13 - 3 = 10 electron pairs are lone pairs. Nitrogen has one lone pair, and each fluorine atom has three lone pairs.

(c) NF₃ molecule: Predict the molecular shape

Since the nitrogen atom is surrounded by 3 atoms and 1 lone pair, its electron pair geometry is tetrahedral. However, due to the presence of a lone pair, the molecular shape of NF₃ is trigonal pyramidal.

(d) CCl₂Br₂ molecule: Determine the central atom and valence electrons

In the CCl₂Br₂ molecule, the central atom is carbon (C) surrounded by two chlorine (Cl) atoms and two bromine (Br) atoms. Carbon has 4 valence electrons, each chlorine atom has 7 valence electrons, and each bromine atom has 7 valence electrons as well. Therefore, the total number of valence electrons is: $4+2\times 7+2\times 7=32$.

(d) CCl₂Br₂ molecule: Determine the bonding and lone electron pairs

The total number of electron pairs is 32 ÷ 2 = 16. Each chlorine and bromine atom shares a bonding electron pair with carbon, so there are 4 bonding electron pairs. The other 16 - 4 = 12 electron pairs are lone pairs and are distributed between the chlorine and bromine atoms. Each chlorine and bromine atom has three lone pairs.

(d) CCl₂Br₂ molecule: Predict the molecular shape

Since carbon is surrounded by 4 atoms and no lone pairs, its electron pair geometry is tetrahedral. Therefore, the molecular shape of CCl₂Br₂ is tetrahedral.

(e) SF₄²⁺ ion: Determine the central atom and valence electrons

In the SF₄²⁺ ion, the central atom is sulfur (S), which is surrounded by four fluorine (F) atoms. Sulfur has 6 valence electrons, each fluorine atom has 7 valence electrons, and there are two additional valence electrons due to the positive charge of the ion. Therefore, the total number of valence electrons is: $6+4\times 7-2=34$.

(e) SF₄²⁺ ion: Determine the bonding and lone electron pairs

The total number of electron pairs is 34 ÷ 2 = 17. Each fluorine atom contributes one bonding electron pair, so there are 4 bonding electron pairs. The other 17 - 4 = 13 electron pairs are lone pairs. Sulfur has one lone pair, and each fluorine atom has three lone pairs.

(e) SF₄²⁺ ion: Predict the molecular shape

Since the sulfur atom is surrounded by 4 atoms and 1 lone pair, its electron pair geometry is trigonal bipyramidal. However, due to the presence of one lone pair, the molecular shape of SF₄²⁺ is see-saw.

Key concepts

Valence shell electron pair repulsion theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a fundamental concept in chemistry that helps predict the shape of molecules. It is based on the idea that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion. This arrangement is due to the negative charge of electron pairs repelling each other.

VSEPR theory considers two types of electron pairs: bonding pairs (those involved in forming bonds with another atom) and lone pairs (those not involved in bonding). Every central atom of a molecule contains electron pairs that determine the molecule's geometry by the unique way they repel each other.

Using VSEPR, chemists can predict the three-dimensional arrangement of atoms in a molecule, which is critical for understanding its chemical properties and reactivity. For example, a molecule like ClO₂⁻ has a linear shape due to the arrangement of its electron pairs, while a molecule like SO₄²⁻ has a tetrahedral shape. Understanding these shapes enables us to predict how these molecules behave during chemical reactions.

Lone pairs in molecular shapes

Lone pairs refer to pairs of valence electrons on an atom that are not involved in bonding and do not contribute to the molecular structure through covalent bonds. However, they play a crucial role in defining the shape of a molecule.

Because lone pairs occupy space around the central atom, they affect the overall geometry of the molecule. Lone pairs tend to repel more strongly than bonded pairs. This is because lone pairs are localized closer to the central atom and only have one nucleus pulling them, unlike bonding pairs which are shared between two nuclei and therefore, are pulled in opposite directions.

This pronounced repulsion can alter the bond angles in a molecule. For instance, take the NF₃ molecule: it has three bonding pairs and one lone pair on the nitrogen atom. The lone pair's presence makes the molecular shape trigonal pyramidal, even though the electron pair geometry is tetrahedral. Similarly, in the case of the SF₄²⁺ ion, the lone pair results in a see-saw shape instead of a perfect trigonal bipyramidal geometry.

Tetrahedral molecular geometry

Tetrahedral molecular geometry is one of the most common molecular shapes and is characterized by a central atom surrounded by four atoms in such a way that they are positioned at the corners of a tetrahedron. This geometry leads to bond angles of approximately 109.5°, which allows for the most efficient spacing among the atoms, minimizing repulsion among the electron pairs.

A classic example of a tetrahedral molecule is methane ${\text{CH}}_4$, where the carbon atom is at the center, surrounded by hydrogen atoms symmetrically. In cases like SO₄²⁻, the sulfur atom serves as the central atom bonded to four oxygen atoms, resulting in a tetrahedral shape.

This particular geometry is important because it provides insight into molecular symmetry and can influence the physical properties and reactivity of the molecule. In essence, when predicting how molecules with a tetrahedral shape will interact chemically, knowing the spatial arrangement helps us understand how these molecules might bind or interact with others.