Carbon disulfide (\(\text{CS}_2\)) is composed of one carbon atom and two sulfur atoms. Its three-dimensional arrangement in space is fundamentally linear. The shape of a molecule dictates its physical and chemical properties, such as its polarity and solubility. Understanding this geometry requires a systematic approach, starting with how the atoms share electrons and culminating in a prediction of the molecular structure.
Drawing the Lewis Structure
The first step in understanding any molecule’s shape involves determining its two-dimensional electron arrangement, known as the Lewis structure. Carbon (\(\text{C}\)) is in Group 14, providing four valence electrons, while each of the two sulfur (\(\text{S}\)) atoms is in Group 16, contributing six valence electrons. This results in a total of 16 valence electrons that must be accounted for in the structure.
Carbon is the central atom because it is less electronegative than sulfur. The arrangement starts by connecting the central carbon to each sulfur atom with a single bond, using four of the total valence electrons. Distributing the remaining 12 electrons to the outer sulfur atoms satisfies their octets, but leaves the central carbon atom with only four valence electrons.
To achieve a stable octet for all atoms, a pair of non-bonding electrons from each sulfur atom shifts to form a double bond with the central carbon. The final Lewis structure shows the carbon atom double-bonded to a sulfur atom on each side (\(\text{S=C=S}\)). This structure uses all 16 valence electrons, satisfies the octet rule for all three atoms, and leaves the central carbon atom with no lone pairs.
Predicting the Shape with VSEPR Theory
The two-dimensional Lewis structure is translated into a three-dimensional shape using the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory is based on the idea that groups of electrons, called electron domains, will repel each other and arrange themselves around the central atom to be as far apart as possible. An electron domain is defined as any bond—single, double, or triple—or any lone pair around the central atom.
In carbon disulfide, the central carbon atom is surrounded by two double bonds. Since each double bond counts as a single electron domain, the carbon atom has a total of two electron domains. These two domains maximize their separation by moving to opposite sides of the central carbon atom, resulting in an angle of \(180^\circ\) between them.
The electron domain geometry describes the arrangement of all electron groups, which is linear for \(\text{CS}_2\) due to the two domains. The molecular geometry, which describes only the arrangement of the atoms, is also linear because the central carbon atom has no lone pairs. The resulting structure is a perfectly straight line, with the sulfur-carbon-sulfur bond angle being exactly \(180^\circ\).
Hybridization and Molecular Polarity
The linear geometry of carbon disulfide is a direct consequence of the central carbon atom’s orbital hybridization. Because the central carbon atom only needs to accommodate two electron domains, it undergoes \(sp\) hybridization.
This process involves mixing one \(s\) orbital and one \(p\) orbital to create two equivalent \(sp\) hybrid orbitals. These two \(sp\) orbitals orient themselves \(180^\circ\) apart to form the two sigma (\(\sigma\)) bonds with the sulfur atoms, consistent with the linear geometry. The remaining two unhybridized \(p\) orbitals are used to form the two pi (\(\pi\)) bonds that complete the double bonds.
The molecule’s overall electrical property, its polarity, is also determined by this precise linear shape. Although the carbon-sulfur bonds are weakly polar due to a slight difference in electronegativity, the molecule as a whole is nonpolar. The linear arrangement ensures that the dipole moment created by the electrons in the bond on one side is exactly canceled out by the equal and opposite pull on the other side. This perfect symmetry results in a net dipole moment of zero, classifying carbon disulfide as a nonpolar molecule.