A Lewis structure is a diagram that represents the covalent bonding within a molecule or polyatomic ion, showing how atoms are connected and where valence electrons are located. Atoms share electrons to achieve a stable octet of eight electrons. The molecule under examination is Carbon Disulfide (\(\text{CS}_2\)), a colorless liquid used as an industrial solvent. Deriving the Lewis structure for \(\text{CS}_2\) reveals the specific arrangement of atoms and electrons, providing insight into the molecule’s overall shape.
Calculating Total Valence Electrons and Drawing the Skeleton
The first step is to determine the total number of valence electrons. Carbon (Group 14) contributes four valence electrons, and each Sulfur atom (Group 16) contributes six. Since \(\text{CS}_2\) contains one carbon and two sulfur atoms, the total number of valence electrons is calculated as \(4 + (2 \times 6) = 16\).
Next, arrange the atoms into a skeletal structure. Because carbon is less electronegative than sulfur, the carbon atom occupies the central position, flanked by the two sulfur atoms, forming an S-C-S arrangement. Connect the central carbon to each sulfur atom with a single covalent bond (S-C-S). This initial framework uses four of the 16 available valence electrons (two electrons per bond), leaving 12 electrons to be distributed.
Distributing Electrons and Satisfying the Octet Rule
The remaining 12 valence electrons are first distributed to the terminal sulfur atoms to satisfy their octets. Each sulfur atom currently has two electrons from the single bond, requiring six more electrons (three lone pairs). Placing six lone pair electrons on the first sulfur atom and six on the second utilizes all 12 remaining valence electrons, fulfilling the octet for both terminal atoms.
However, the central carbon atom only possesses four electrons from the two single bonds, failing to satisfy its octet. The octet rule requires eight electrons around each atom. Since all available electrons have already been placed, a rearrangement is necessary to provide the central carbon with the four additional electrons it needs.
The solution involves converting lone pairs from the terminal atoms into additional shared bonding pairs. A lone pair from the left sulfur is moved to form a second bond with the carbon atom, creating a double bond (\(\text{S}=\text{C}\)). To complete the carbon octet, a lone pair from the right sulfur is also moved to form a second double bond, resulting in the final arrangement \(\text{S}=\text{C}=\text{S}\). This structure successfully satisfies the octet rule for all three atoms: carbon is surrounded by four bonds (eight electrons), and each sulfur atom retains two lone pairs plus the two double bonds (eight electrons total).
The Final Lewis Structure and Molecular Geometry
The most stable Lewis structure for Carbon Disulfide is \(\text{S}=\text{C}=\text{S}\), where each sulfur atom has two remaining lone pairs. This structure is preferred because the formal charge on every atom is zero, indicating a highly stable arrangement. A structure with zero or minimized formal charges is generally the most accurate representation.
This final structure, with the central carbon atom double-bonded to the two sulfur atoms, serves as the basis for predicting the molecule’s three-dimensional shape using the Valence Shell Electron Pair Repulsion (VSEPR) theory. VSEPR theory states that electron domains around a central atom will arrange themselves to be as far apart as possible to minimize electrostatic repulsion.
In \(\text{CS}_2\), the central carbon atom has two regions of high electron density: the double bond to the left sulfur and the double bond to the right sulfur. Since double bonds count as a single electron domain, the central carbon is surrounded by only two electron domains with no lone pairs on the central atom itself.
The greatest separation possible for two domains is a straight line, resulting in a bond angle of \(180^\circ\). Consequently, both the electron domain geometry and the molecular geometry for \(\text{CS}_2\) are classified as linear.