Problem 60 - General Chemistry

Question

Obtain the distribution of \(d\) electrons in the complex ions listed below, using crystal field theory. Each ion is either tetrahedral or square planar. On the basis of the number of unpaired electrons (given in parentheses), decide the correct geometry. a. \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{NO}_{2}\right)_{2}\right]^{2+}\) b. \(\left[\mathrm{MnCl}_{4}\right]^{2-}\) c. \(\left[\mathrm{NiCl}_{4}\right]^{2-}(2)\) d. \(\left[\mathrm{AuF}_{4}\right]^{-}(0)\)

Step-by-Step Solution

Answer

a: Square planar, b: Tetrahedral, c: Tetrahedral, d: Square planar.

Step 1: Identify the d-Electron Count

First, determine the oxidation state of the metal in each complex ion and then calculate the number of d-electrons by subtracting the oxidation state from the group number of the metal in the periodic table.

Step 2: Determine the Geometry

Use the given number of unpaired electrons and the possible geometry (tetrahedral or square planar) to determine the electron distribution among the orbitals. Tetrahedral complexes typically have more unpaired electrons due to smaller splitting, whereas square planar complexes exhibit larger splitting and often result in paired electrons.

Step 3: Analyzing Each Complex

a. For \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{NO}_{2}\right)_{2}\right]^{2+}\): Pt has oxidation state of +2 leading to 8 d-electrons and a square planar geometry with no unpaired electrons.b. For \(\left[\mathrm{MnCl}_{4}\right]^{2-}\): Mn is +2, giving 5 d-electrons with a tetrahedral geometry, resulting in 5 unpaired electrons.c. For \(\left[\mathrm{NiCl}_{4}\right]^{2-}(2)\): Ni is +2, yielding 8 d-electrons, and with two unpaired electrons, it is tetrahedral. d. For \(\left[\mathrm{AuF}_{4}\right]^{-}(0)\): Au is +3, giving 8 d-electrons, square planar as there are no unpaired electrons.

Key Concepts

Electron Distribution

Understanding how electrons are distributed in complex ions is crucial for predicting their chemical properties. In crystal field theory, the distribution of these electrons among different orbitals influences the ion's magnetic and spectroscopic characteristics.
Metal ions have several d orbitals, typically five, which can hold up to 10 electrons. Depending on the surrounding ligands, these d orbitals split into different energy levels. The arrangement and nature of these energy levels - whether the ion forms a tetrahedral or square planar complex - determine how the electrons fill the available orbitals.

• Tetrahedral Geometry: Typically shows lower energy differences between orbitals, leading to more unpaired electrons.
• Square Planar Geometry: Has a larger energy difference, often causing electrons to pair up in the lower energy orbitals, leaving few or no unpaired electrons.

These arrangements play a key role in determining the ion's color, magnetic properties, and reactivity.

Oxidation State

The oxidation state of a metal ion in a complex is crucial for calculating electron distribution. It refers to the charge left on the metal after accounting for its bonded ligands.
To find the oxidation state of a metal in a complex:

• Identify the overall charge of the complex ion.
• Determine the known charges of the ligands surrounding the metal.
• Calculate the metal's charge such that the sum of the metal and ligand charges equals the overall ion charge.

For example, in \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{NO}_{2}\right)_{2}\right]^{2+}\), the charge of Pt is balanced by four neutral ammonia and nitrite ligands, resulting in Pt having a +2 oxidation state.
This helps us understand how many electrons are "available'' to participate in bonding and how they're distributed among the d orbitals.

Coordination Geometry

Coordination geometry refers to the spatial arrangement of ligands around the central metal ion in a complex. It dictates not just the structure, but also the chemical properties of the complex.
In crystal field theory, the two common geometries are:

• Tetrahedral: Occurs when four ligands are positioned symmetrically around the central atom. It typically involves smaller crystal field splitting, which often leads to more unpaired electrons.
• Square Planar: A less common but significant coordination geometry. It involves larger crystal field splitting, leading electrons to prefer pairing at the lower energy levels.

The geometry can be inferred from the number of unpaired electrons: a lesser number suggests a square planar geometry while more unpaired electrons indicate a tetrahedral formation.

d-Electron Count

The d-electron count of a metal ion is a fundamental property that reflects its electronic configuration and is pivotal in determining the behavior of the ion in a complex.
To determine the d-electron count:

• Identify the group number of the metal atom in the periodic table, which gives the total number of its valence electrons.
• Subtract the oxidation state of the metal ion from its group number.

For example, Ni is in Group 10. In \(\left[\mathrm{NiCl}_{4}\right]^{2-}\), Ni has an oxidation state of +2, leading to a d-electron count of 8.
This number helps in predicting how the d orbitals might be filled in various geometries and whether the metal complex will exhibit any unpaired electrons, influencing its magnetic and optical properties.