Question

Predict the electron pair geometry, the molecular shape, and the bond angle for a carbon disulfide molecule, \(\mathrm{CS}_{2}\), using VSEPR theory.

Short answer

The electron pair geometry and molecular shape of \( \text{CS}_2 \) is linear with a bond angle of \( 180^\circ \).

Step-by-step solution

Identifying the Central Atom

In the molecule \( \text{CS}_2 \), carbon \( (\text{C}) \) is the central atom because it is less electronegative than sulfur and typically forms the backbone of organic molecules.

Counting Valence Electrons

Carbon has 4 valence electrons and each sulfur has 6. Adding them gives a total of \( 4 + 6 + 6 = 16 \) valence electrons.

Determining Electron Pair Geometry

Carbon forms double bonds with each sulfur, using 8 of the 16 valence electrons, leaving no lone pairs on the carbon. Hence, with 2 regions of electron density, the electron pair geometry is linear.

Predicting Molecular Shape

With no lone pairs on the central atom and two double-bonded regions, the molecular shape of \( \text{CS}_2 \) is also linear, following the linear electron pair geometry.

Calculating Bond Angles

In a linear geometry, the bond angle between the double bonds on carbon is \( 180^\circ \). Hence, the \( \text{S-C-S} \) bond angle is \( 180^\circ \).

Key concepts

Electron Pair Geometry

The concept of electron pair geometry is central to understanding molecular structures. It refers to the spatial arrangement of all electron pairs—bonding and non-bonding—around the central atom.
In the case of a carbon disulfide (\(\text{CS}_2\)) molecule, VSEPR (Valence Shell Electron Pair Repulsion) theory is utilized to predict this arrangement.
According to VSEPR, electrons repel each other and thus arrange themselves as far apart as possible in three-dimensional space to minimize these repulsions.
Given a total of 16 valence electrons, carbon forms double bonds with each sulfur. This results in two regions of electron density: one for each double bond.
Since there are no lone pairs on the central carbon, the electron pair geometry of \(\text{CS}_2\) is linear. All electron regions are distributed symmetrically across a straight line, enabling the molecule to achieve its minimal energy configuration

Molecular Shape

Molecular shape refers to the arrangement of atoms in a molecule, determined by the electron pair geometry and the presence of any lone pairs.
In \(\text{CS}_2\), the absence of lone pairs on the carbon atom simplifies things—the molecular shape follows directly from its linear electron pair geometry.
Each sulfur atom is double-bonded to the carbon atom in such a way that the molecule stretches out into a straight line.
Because there are no lone pairs to alter the configuration, both the electron pair geometry and molecular shape in this molecule coincide as linear.
Common examples of linear molecules include other simple diatomic molecules like \(\text{CO}_2\), which share similar geometrical characteristics.

Bond Angle

The bond angle is the angle formed between two adjacent bonds originating from a central atom.
In VSEPR theory, the bond angle becomes predictable once you comprehend the electron pair geometry.
For the molecule \(\text{CS}_2\), which has a linear shape, the bond angle is clearly defined.
The sulfur-carbon-sulfur (\(\text{S-C-S}\)) bond angle measures \(180^\circ\). This is consistent with the linear electron pair geometry of the molecule, where the two double bonds spread out linearly around the central carbon atom, ensuring maximal separation due to electron repulsion.
Bond angles like \(180^\circ\) are indicative of a lack of steric hindrance or lone pairs, providing stability to the molecule.