Problem 87 - Chemistry The Central Science In Si Units

Question

Consider the following \(\mathrm{XF}_{4}\) ions: \(\mathrm{PF}_{4}^{-}, \mathrm{BrF}_{4}^{-}, \mathrm{ClF}_{4}^{+}\), and \(\mathrm{AlF}_{4}^{-}\). (a) Which of the ions have more than an octet of electrons around the central atom? (b) For which of the ions will the electron-domain and molecular geometries be the same? (c) Which of the ions will have an octahedral electron-domain geometry? (d) Which of the ions will exhibit a see-saw molecular geometry?

Step-by-Step Solution

Answer

(a) P, Br, Cl exceed octet; (b) AlF4-; (c) None; (d) PF4⁻.

Step 1: Determine Total Valence Electrons

Calculate the total number of valence electrons for each ion, considering the charge. For example, for \( \mathrm{PF}_4^- \), phosphorus has 5 valence electrons and each fluorine has 7, plus one extra for the negative charge, totaling 34 electrons.

Step 2: Apply the Octet Rule

For each ion, determine if the central atom exceeds the octet rule. Elements beyond period 2, like phosphorus, bromine, and chlorine, can have expanded octets. For these ions, check if they have more than 8 electrons around the central atom.

Step 3: Determine Electron-Domain and Molecular Geometries

Use VSEPR theory to determine both the electron-domain and molecular geometries. The electron-domain geometry considers all electron pairs, while the molecular geometry considers only bonded atoms. Ionic charge can influence this.

Step 4: Identify Same Electron-Domain and Molecular Geometries

Identify ions where the geometrical configurations are the same. This often occurs when there are no lone pairs on the central atom.

Step 5: Analyze Octahedral Electron-Domain Geometry

Identify which ions could potentially have an octahedral electron-domain geometry by having 6 electron domains around the central atom.

Step 6: Identify See-Saw Molecular Geometry

Since the see-saw shape arises from a trigonal bipyramidal electron-domain geometry with one lone pair, find ions with 5 electron domains and determine if they exhibit see-saw geometry.

Key Concepts

Octet Rule

The Octet Rule is a fundamental concept in chemistry that refers to the tendency of atoms to prefer having eight electrons in their valence shell. This electron configuration is typically associated with increased stability. For most elements, this corresponds to having a full outer shell, similar to the noble gases.

In typical scenarios, atoms achieve an octet by sharing, gaining, or losing electrons through the formation of covalent or ionic bonds. However, it's important to note that the Octet Rule has some exceptions.

• Atoms in the first two periods of the periodic table follow the Octet Rule quite strictly.
• Elements like phosphorus, sulfur, chlorine, and others in periods greater than two can "expand" their octet.

In the case of molecules like \(\mathrm{PF}_{4}^{-}\), the central phosphorus atom can accommodate more than eight electrons, exhibiting an expanded octet.

Electron-Domain Geometry

Electron-Domain Geometry is the arrangement of electron groups (both bonding and lone pairs) around a central atom. This concept is closely associated with the VSEPR theory, which stands for Valence Shell Electron Pair Repulsion theory.

The VSEPR theory helps to predict the 3D shape of molecules based on the idea that electron pairs repel each other and therefore arrange themselves as far apart as possible.

• Each electron domain can include bonds (single, double, or triple), as well as lone pairs.
• Different numbers of electron domains will lead to different geometric configurations.

For instance, a molecule with six electron domains around the central atom will typically have an octahedral geometry, as seen in \(\mathrm{BrF}_{4}^{-}\).

Molecular Geometry

Molecular Geometry refers specifically to the spatial arrangement of atoms in a molecule. Unlike electron-domain geometry, which considers all electron pairs, molecular geometry only concerns itself with atoms.

This difference becomes especially important when lone pairs are present, as they can alter the apparent shape of the molecule.

• For example, a molecule with a trigonal bipyramidal electron-domain geometry that includes a lone pair will often have a see-saw shape as a molecular geometry.
• This alteration is due to the lone pair's extra space requirement, pushing bonding pairs closer together in three-dimensional space.

\(\mathrm{ClF}_{4}^{+}\) is a scenario where electron-domain and molecular geometries are analyzed separately to understand the resulting molecule's shape.

Expanded Octet

The concept of an Expanded Octet applies to elements that can hold more than eight electrons in their valence shell, defying the traditional octet rule. This is possible because certain elements have empty d-orbitals into which extra electrons can be placed.

Expanded octets typically occur in elements found in period 3 or beyond on the periodic table.

• Examples include phosphorus and sulfur, which can form compounds with up to 10 or 12 electrons in their valence shells.
• Molecules like \(\mathrm{PF}_{4}^{-}\) demonstrate this phenomenon by accommodating more than the standard eight electrons around the central atom.

This allows for more complex molecular shapes and configurations, making the study of these compounds particularly intriguing.