Question

(a) Does \(C S_{2}\) have a dipole moment? If so, in which direction does the net dipole point? (b) Does \(\mathrm{SO}_{2}\) have a dipole moment? If so, in which direction does the net dipole point?

Short answer

(a) CS₂ does not have a dipole moment due to its linear geometry that causes the dipole moments of the S-C bonds to cancel each other out. (b) SO₂ has a dipole moment due to its bent geometry. The net dipole points from the more electronegative oxygen atoms towards the less electronegative sulfur atom.

Step-by-step solution

1. Draw the Lewis structure for CS₂

First, count the number of valence electrons in the molecule: Carbon (C) has 4 valence electrons, and Sulfur (S) has 6, so we have: 4 + 2(6) = 16 total valence electrons. Draw the Lewis structure with carbon in the center and a sulfur atom on either side. Each sulfur atom forms a double bond with the central carbon atom, making the central carbon atom have an octet of electrons. The sulfur atoms also have an octet of electrons.

2. Determine the molecular geometry for CS₂ using VSEPR theory

VSEPR theory states that electron groups (including lone pairs and single, double, and triple bonds) will take positions in space in order to minimize repulsion. In CS₂, there are two electron groups around the central carbon atom, and both are bonding groups (double bonds to S atoms). According to VSEPR theory, with two electron groups and no lone pairs on the central atom, the molecule will have a linear geometry.

3. Determine if CS₂ has a net dipole moment

Since the molecule has a linear geometry, the two sulfur atoms are symmetrically placed on either side of the central carbon atom. This means that each S-C bond has a dipole moment, but they cancel each other out, so there is no net dipole moment. Consequently, CS₂ does not have a dipole moment.

4. Draw the Lewis structure for SO₂

First, count the number of valence electrons in the molecule: Sulfur (S) has 6 valence electrons, and Oxygen (O) has 6, so we have: 6 + 2(6) = 18 total valence electrons. Draw the Lewis structure with sulfur in the center and an oxygen atom on either side. There is a double bond between the sulfur atom and one oxygen atom, and a single bond between the sulfur atom and the other oxygen atom. The sulfur atom has a lone electron pair.

5. Determine the molecular geometry for SO₂ using VSEPR theory

In SO₂, there are three electron groups around the central sulfur atom (two bonding groups and one lone pair). According to VSEPR theory, with three electron groups and one lone pair on the central atom, the molecule will have a bent geometry.

6. Determine if SO₂ has a net dipole moment

SO₂ has a bent geometry, which results in the two oxygen atoms being placed asymmetrically around the central sulfur atom. This creates a net dipole moment in the molecule, pointing from the more electronegative oxygen atoms (with the higher electron density) to the less electronegative sulfur atom (with the lower electron density). In conclusion: (a) CS₂ does not have a dipole moment. (b) SO₂ has a dipole moment, and the net dipole points from the oxygen atoms towards the sulfur atom.

Key concepts

Lewis Structures

Lewis structures are a handy way of representing molecules to show the arrangement of different atoms and the bonds between them. To construct a Lewis structure, you first need to know the number of valence electrons each atom contributes. Valence electrons are the electrons in the outer shell of an atom that are involved in forming bonds.

For example, in the molecule CS₂, carbon has 4 valence electrons and each sulfur atom has 6, giving a total of 16 valence electrons. You arrange these electrons around the central atom, which is usually the one that can form the most bonds, to satisfy the octet rule. The octet rule states that atoms are most stable when they have eight electrons in their outermost shell. In CS₂, carbon forms four bonds with two sulfur atoms, each creating a double bond, thereby filling the octet for carbon.

Lewis structures are essential for visualizing the molecule's shape and seeing which atoms are connected. They form the basis for predicting and understanding molecular geometry and polarity.

VSEPR Theory

VSEPR (Valence Shell Electron Pair Repulsion) theory is a useful model used to predict the shape of individual molecules. It is based on the idea that pairs of valence electrons around a central atom will arrange themselves to minimize repulsion, leading to predictable shapes.

In the CS₂ molecule, the VSEPR model predicts a linear shape. Here’s why: It has two double bonds, each forming an electron group around the central carbon atom. These groups will position themselves opposite each other to minimize repulsion, resulting in a linear geometry with bond angles of 180 degrees. The linear arrangement means any dipoles present in the molecule are symmetrically opposite and thus cancel out, leading to no net dipole moment.

In contrast, SO₂ has a bent shape due to its three electron groups (two bonded atoms and one lone pair). This arrangement is asymmetric, resulting in a net dipole moment pointing from the oxygen atoms towards the central sulfur.

Molecular Geometry

Molecular geometry is all about the 3D arrangement of the atoms in a molecule. This arrangement is crucial as it affects the molecule’s functionality, properties, and reactivity.

For instance, CS₂ exhibits linear geometry as per its Lewis structure and VSEPR predictions. The carbon in the center forms straight-line connections with the sulfur atoms on either side. Because of this alignment, any polar bonds cancel each other, resulting in no overall dipole moment.

SO₂, however, displays bent geometry because of the lone pair on sulfur. The presence of unbounded electron pairs compresses the bond angle, causing the molecule to bend. This lack of symmetry allows dipole moments to add up, making SO₂ polar. Understanding the geometry helps to infer the physical properties, such as boiling points and polarity, which are important in chemical reactions.

Valence Electrons

Valence electrons play a central role in predicting how atoms interact to form molecules. These electrons are the key players in chemical bonding because they are located in the atom's outermost shell.

When considering the molecule CS₂, carbon contributes four valence electrons while each sulfur supplies six. Thus, CS₂ has a total of 16 valence electrons. Distributing these electrons correctly to form bonds and complete the octet for each atom is a crucial step in drawing the Lewis structure.

In SO₂, sulfur provides 6 valence electrons, while each oxygen also offers 6, amounting to 18 valence electrons. These electrons must be arranged to fulfill the octet rule, but due to the presence of a lone pair on sulfur, the molecule's geometry is altered. Valence electrons and their rearrangement determine how chemical bonding occurs and the resulting structure of the molecule.