Question

Draw the \(d\) -orbital splitting diagrams for the octahedral complex ions of each of the following. a. \(\mathrm{Fe}^{2+}\) (high and low spin) b. \(\mathrm{Fe}^{3+}\) (high spin) c. \(\mathrm{Ni}^{2+}\)

Short answer

The d-orbital splitting diagrams for the given metal ions in octahedral complexes are as follows: a. \(\mathrm{Fe}^{2+}\) (high spin): \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\) \(\square\uparrow\) \(\square\) \(\mathrm{Fe}^{2+}\) (low spin): \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\) \(\square\) b. \(\mathrm{Fe}^{3+}\) (high spin): \(\square\uparrow\downarrow\) \(\square\uparrow\) \(\square\uparrow\) \(\square\) \(\square\) c. \(\mathrm{Ni}^{2+}\) (low spin): \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\)

Step-by-step solution

Understanding Octahedral d-Orbital Splitting

In an octahedral complex, the central metal ion is surrounded by six ligands forming an octahedral arrangement. Due to the presence of these ligands, the energy of the five d-orbitals is split into two groups: those with higher energy (d\(_{x^2-y^2}\), d\(_{z^2}\)) and those with lower energy (d\(_{xy}\), d\(_{xz}\), d\(_{yz}\)). The energy difference between these two groups is represented by the symbol \(\Delta_\mathrm{o}\). The concept of high-spin and low-spin complexes deals with the arrangement of unpaired electrons in d-orbitals. A high-spin complex has more unpaired electrons, while a low-spin complex has fewer unpaired electrons.

Determine the Electron Configuration of the Given Metal Ions

Before drawing the d-orbital splitting diagrams, let's find the electron configurations of the given metal ions: a. \(\mathrm{Fe}^{2+}\): The electron configuration for the neutral iron atom (Fe) is \([\mathrm{Ar}]\ 3\mathrm{d}^6\ 4\mathrm{s}^2\). \(\mathrm{Fe}^{2+}\) would have lost two electrons, so its electron configuration would be \([\mathrm{Ar}]\ 3\mathrm{d}^4\). b. \(\mathrm{Fe}^{3+}\): Similarly, \(\mathrm{Fe}^{3+}\) would have lost three electrons, so its electron configuration would be \([\mathrm{Ar}]\ 3\mathrm{d}^3\). c. \(\mathrm{Ni}^{2+}\): The electron configuration for the neutral nickel atom (Ni) is \([\mathrm{Ar}]\ 3\mathrm{d}^8\ 4\mathrm{s}^2\). \(\mathrm{Ni}^{2+}\) would have lost two electrons, so its electron configuration would be \([\mathrm{Ar}]\ 3\mathrm{d}^6\).

Draw the d-Orbital Splitting Diagram for \(\mathrm{Fe}^{2+}\) (High Spin and Low Spin)

Since \(\mathrm{Fe}^{2+}\) has four electrons in the 3d orbitals, we can draw the high-spin and low-spin splitting diagrams as follows: For the high-spin complex: Electrons fill the lower-energy orbitals first, followed by the higher-energy orbitals. The high-spin diagram would have two unpaired electrons in the lower energy orbitals and two unpaired electrons in the higher energy orbitals. \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\) \(\square\uparrow\) \(\square\) For the low-spin complex: Electrons prefer to pair up in the lower-energy orbitals before occupying the higher-energy orbitals. The low-spin diagram would have two paired and two unpaired electrons in the lower energy orbitals and no electrons in the higher energy orbitals. \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\) \(\square\)

Draw the d-Orbital Splitting Diagram for \(\mathrm{Fe}^{3+}\) (High Spin)

Since \(\mathrm{Fe}^{3+}\) has three electrons in the 3d orbitals, the high-spin splitting diagram would be: \(\square\uparrow\downarrow\) \(\square\uparrow\) \(\square\uparrow\) \(\square\) \(\square\)

Draw the d-Orbital Splitting Diagram for \(\mathrm{Ni}^{2+}\)

Since \(\mathrm{Ni}^{2+}\) has six electrons in the 3d orbitals, the splitting diagram (which is a low-spin complex) would be: \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\uparrow\downarrow\) \(\square\) Now we have the d-orbital splitting diagrams for the given metal ions \(\mathrm{Fe}^{2+}\), \(\mathrm{Fe}^{3+}\), and \(\mathrm{Ni}^{2+}\) in octahedral complexes.

Key concepts

Octahedral Complex Ions

When we talk about octahedral complex ions, imagine a central metal ion snugly surrounded by six equally distanced ligands forming an octagon-like structure. This arrangement exerts electrostatic forces on the d-orbitals of the central metal, causing a split in energy levels between them. Since different orbitals experience these forces to varying degrees, we end up with two distinct sets of d-orbitals - those that will absorb more energy (higher energy) and those that absorb less (lower energy).

Understanding this concept is a bedrock for further grasping the ideas behind high-spin and low-spin complexes and predicting the magnetic properties and colors of these complexes. Moreover, the nature of the ligands (whether they are strong or weak field ligands) plays a significant part in determining the degree of splitting, which in turn affects whether the complex will be high-spin or low-spin.

Electron Configuration

The term electron configuration refers to the distribution of electrons in the orbitals around an atomic nucleus. Starting off with a simple 'address' of where each electron resides, it follows set rules like the Pauli exclusion principle (no two electrons can have the same four quantum numbers) and Hund's rule (every orbital in a subshell is singly occupied before any one orbital is doubly occupied).

For transition metals in complex ions, such as Fe²⁺ and Fe³⁺, the electron configuration gets a bit trickier due to variable oxidation states. When these ions are placed in an octahedral field, the d-orbital electrons are forced to reorganize based on the newly created high- and low-energy levels, a process directly linked to the magnetic properties and colors of the complexes. This electron arrangement is key to understanding the d-orbital splitting and resulting magnetic properties.

High-Spin and Low-Spin Complexes

Diving into high-spin and low-spin complexes might feel complex, pun intended, but it's essential in predicting chemical behaviors. High-spin complexes occur when the energy required to pair up electrons in the same d-orbital (intra-orbital pairing energy) is higher than the energy difference created by the ligands' splitting effect, symbolized by \( \Delta_\mathrm{o} \). As such, electrons remain unpaired longer and occupy higher-energy orbitals sooner, resulting in more unpaired electrons and, usually, magnetic complexes.

In contrast, low-spin complexes form under the opposite conditions—when the energy difference due to splitting is greater than the energy required to pair electrons. Thus, electrons pair up early in the lower-energy orbitals, leading to fewer unpaired electrons and often diamagnetic complexes. Recognizing whether a complex is high-spin or low-spin is crucial, as this affects its reactivity, magnetic properties, and even the color observed in spectroscopic analysis.