Question

Carbon and sulfur form compounds with each other with the formulas \(\mathrm{CS}_{2}\) and \(\mathrm{C}_{3} \mathrm{S}_{2}\) . Draw a Lewis structure for each compound that has a formal charge of zero for all atoms in the structure.

Short answer

The Lewis structures for the two compounds are as follows: For CS₂: :S - C - S: .. .. For C₃S₂: :S - C = C = C - S: .. ..

Step-by-step solution

Determine the total number of valence electrons for each compound

First, we need to find the total number of valence electrons for each compound. Carbon (C) has 4 valence electrons and sulfur (S) has 6 valence electrons. For CS₂: There is 1 carbon atom and 2 sulfur atoms in the molecule, so the total number of valence electrons is: (1 x 4) + (2 x 6) = 4 + 12 = 16. For C₃S₂: There are 3 carbon atoms and 2 sulfur atoms in the molecule, so the total number of valence electrons is: (3 x 4) + (2 x 6) = 12 + 12 = 24.

Draw the Lewis structure for CS₂

We can start by placing Carbon (the central atom) in the center, surrounded by the two sulfur atoms. Then, we can distribute the 16 valence electrons to create a stable Lewis structure with the formal charge of zero for each atom. 1. Connect the central carbon atom to each sulfur atom using single bonds, using 2 electrons per bond (4 electrons total): S - C - S 2. Complete the octets for each sulfur atom by adding lone pairs of electrons: S: 6 - 2 = 4 remaining electrons (2 lone pairs) S - C - S: 16 - 4 = 12 remaining electrons 3. Distribute the remaining 12 electrons to complete the octets: :S - C - S: .. .. The formal charges for all atoms are zero, and we have reached a stable Lewis structure for CS₂.

Draw the Lewis structure for C₃S₂

For C₃S₂, we can start by placing the carbon atoms in the center with the two sulfur atoms bonded to the outermost carbons. Then, we can distribute the 24 valence electrons to create a stable Lewis structure with the formal charge of zero for each atom. 1. Connect the carbons and sulfurs using single bonds, using 2 electrons per bond (8 electrons total): S - C - C - C - S 2. Complete the octets for each sulfur atom by adding lone pairs of electrons: S: 6 - 2 = 4 remaining electrons (2 lone pairs) S - C - C - C - S: 24 - 8 = 16 remaining electrons 3. Distribute the remaining 16 electrons to complete the octets: :S - C - C - C - S: .. . . .. By connecting the central carbon atoms with double bonds, each atom attains a formal charge of zero. The final Lewis structure for C₃S₂ is: :S - C = C = C - S: .. .. We have now found Lewis structures for both CS₂ and C₃S₂, with the formal charge of zero for all atoms in the structure.

Key concepts

Formal Charge

Understanding formal charges is essential for crafting accurate Lewis structures. Formal charge helps us determine how the electrons are distributed across different atoms in a molecule. In a Lewis structure, we aim for a formal charge of zero to achieve a stable configuration. To calculate the formal charge for an atom:

• Start with the number of valence electrons the atom naturally possesses.
• Subtract the number of non-bonding electrons (lone pairs) around the atom.
• Subtract half the number of bonding electrons shared with other atoms (since electrons in bonds are shared between two atoms).

The formula is as follows:\[\text{Formal Charge} = \text{Valence Electrons} - (\text{Lone Pair Electrons} + \frac{1}{2} \times \text{Bonding Electrons})\]Achieving a formal charge of zero ensures the most stable and neutral distribution of electrons in the molecule. This is the goal when drawing Lewis structures, as it represents a minimal energy state for the molecule.

Valence Electrons

Valence electrons are the outermost electrons of an atom, and they play a crucial role in chemical bonding and reactions. In the Lewis structure model, these electrons are represented as either dots around the atom or as lines between atoms when participating in bonds. Employing valence electrons efficiently is key when forming molecules like \(\mathrm{CS}_2\) and \(\mathrm{C}_3\mathrm{S}_2\).
Each element in the periodic table has a specific number of valence electrons based on its group number. For example, carbon, found in group 14, has 4 valence electrons, while sulfur, in group 16, possesses 6 valence electrons. To determine the total number of valence electrons in a compound:

• Multiply the number of each type of atom by its valence electrons.
• Add these values together to get the total number of electrons that should be used in creating the Lewis structure.

For example, the \(\mathrm{CS}_2\) molecule has a total of 16 valence electrons, calculated as\[(1 \times 4) + (2 \times 6) = 4 + 12 = 16\]Valence electrons guide the construction of the molecule's bonds and influence the molecular stability.

Molecular Geometry

Molecular geometry concerns the three-dimensional arrangement of atoms within a molecule. It determines how atoms are spatially oriented around a central atom, largely influencing a molecule’s physical and chemical properties. Lewis structures help us predict molecular geometry by illustrating which atoms are bonded and where lone pairs reside. These structures allow us to use models such as VSEPR (Valence Shell Electron Pair Repulsion) to predict shapes based on repulsions between electron pairs.In molecules like \(\mathrm{CS}_2\), where carbon is the central atom bonded linearly to two sulfurs, the geometry is linear. However, in another configuration with elements such as \(\mathrm{C}_3\mathrm{S}_2\), it's important to note how atoms like carbon are often found in chains, affecting the molecule's ultimate shape.

• Linear Geometry: This occurs when there are no lone pairs on the central atom, leading to bond angles of 180 degrees, as in \(\mathrm{CS}_2\).
• Different Geometries: Result from the presence of lone pairs affecting bond angles around central atoms. For instance, if lone pairs were present, they would adjust angles away from a perfect linear shape.

Understanding molecular geometry not only aids in drawing Lewis structures accurately but also in anticipating the impacts on reactivity and interaction of the molecule with others in chemical reactions.