Problem 97 - Chemistry

Question

Solid \(\mathrm{PCl}_{5}\) exists as \(\left[\mathrm{PCl}_{4}^{+}\right]\left[\mathrm{PCl}_{6}^{-}\right] .\) Draw Lewis structures for these ions. Describe the hybridization state of the \(\mathrm{P}\) atoms.

Step-by-Step Solution

Answer

The Lewis structure of \(\left[\mathrm{PCl}_{4}^{+}\right]\) ion shows P atom at the center surrounded by 4 Cl atoms with single bonds, indicating a \(sp^{3}\) hybridization state. The Lewis structure of \(\left[\mathrm{PCl}_{6}^{-}\right]\) ion shows the P atom surrounded by 6 Cl atoms with single bonds, pointing to a \(sp^{3}d^{2}\) hybridization state.

Step 1: Draw the Lewis Structure for \(\left[\mathrm{PCl}_{4}^{+}\right]\)

A Lewis structure is the graphic representation of the electron distribution around atoms. In \(\left[\mathrm{PCl}_{4}^{+}\right]\), phosphorus (P) forms 4 bonds with Chlorine (Cl). The Lewis structure would show Phosphorus in the middle surrounded by the 4 Chlorine atoms, indicating the single bonds between them. Since it's a positively charged ion, we will be missing one electron from P’s usual five.

Step 2: Draw the Lewis Structure for \(\left[\mathrm{PCl}_{6}^{-}\right]\)

For \(\left[\mathrm{PCl}_{6}^{-}\right]\), Phosphorus is bonded to 6 Chlorine atoms, also represented by single bonds between each P-Cl. The negative charge here indicates an additional electron added to the structure, making the total number of valence electrons for P to be 6 in this case.

Step 3: Determine the Hybridization State

The hybridization of an atom in a molecule can be determined by the number of atomic orbitals that mix to form the hybrid orbitals. In \(\left[\mathrm{PCl}_{4}^{+}\right]\), the P atom forms four sigma bonds with four Cl atoms, so it is in a \(sp^{3}\) hybridization state. In \(\left[\mathrm{PCl}_{6}^{-}\right]\), the P atom forms six sigma bonds with six Cl atoms, so we need to have six hybrid orbitals formed implying a \(sp^{3}d^{2}\) hybridization state.

Key Concepts

Hybridization

Understanding hybridization is key to predicting the shape and bond angles in a molecule. It's the process where atomic orbitals mix to form new hybrid orbitals that are used in chemical bonding. When drawing or predicting molecular structures, hybridization tells us how the elements are 'spaced' around a central atom, like phosphorus (P) in our PCl₅ ions.

In the case of PCl₄⁺, we're looking at a positively charged ion where phosphorus has lost one electron. The phosphorus atom forms four single bonds to the chlorine atoms, leading to hybridization of its sp³ orbitals. This means one s orbital and three p orbitals combine to form four new equivalent orbitals directed toward the corners of a tetrahedron.

For PCl₆^-, the addition of an extra electron allows phosphorus to bind to six chlorines. Here, the hybridization involves not only an s and p orbitals but also includes d orbitals, resulting in sp³d² hybridization. This geometry forms an octahedral structure, ensuring maximum separation between bond pairs.

PCl5

Phosphorus pentachloride ( PCl₅) can exist as two ions: PCl₄⁺ and PCl₆^-. These two ions illustrate different molecular geometries and examples of hybridization.

• PCl₄⁺: In this ion, the phosphorus atom is surrounded by four chlorine atoms, forming a tetrahedral structure. The positive charge indicates it has one less electron, affecting its Lewis structure.
• PCl₆^-: For this ion, phosphorus is central and bonded with six chlorines, adopting an octahedral geometry. The negative charge here shows that an additional electron is present, minimizing electron pair repulsion.

These structural differences arise from the ability of phosphorus to expand its valence shell using d orbitals. Thus, PCl₅ not only gives insight into chemical bonds but also presents a classic case for studying electron count and geometry in complex molecules.

Sigma Bonds

Sigma (\( \sigma \)) bonds are the primary type of covalent bonds in molecules like PCl₅. They are formed by the head-on overlap of atomic orbitals, allowing for free rotation along the bond axis, which is essential for the structural flexibility of molecules.

In PCl₄⁺, each of the four phosphorus-chlorine bonds is a sigma bond formed using sp³ hybrid orbitals. This single electron cloud gives rise to a strong, stable interaction between the atoms.

• Each bond originates from the overlap of hydrogen's s orbital with the sp³ hybrid orbital of phosphorus.
• This smooth overlap and sharing of electrons stabilize the molecular structure, producing the characteristic tetrahedral shape.

In the more complex PCl₆^- scenario, hybridization reaches sp³d², accommodating six sigma bonds between phosphorus and chlorine. These bonds endure due to the optimal overlap across the octahedral formation, showcasing how varying sigma bond configurations influence molecular geometry.