Question

Explain why \(\mathrm{Mn}^{3+}\) forms high-spin and low-spin octahedral complexes but \(\mathrm{Mn}^{4+}\) does not.

Short answer

Question: Explain the difference in behavior between Mn³⁺ and Mn⁴⁺ in forming high-spin and low-spin octahedral complexes. Answer: Mn³⁺ can form both high-spin and low-spin octahedral complexes due to its 3d⁴ configuration, which allows for the accommodation of electrons in both the t2g and eg orbitals. In contrast, Mn⁴⁺ cannot form distinct high-spin and low-spin octahedral complexes as its 3d³ configuration leads to the presence of electrons only in the lower energy t2g orbitals, resulting in no significant difference between the two configurations.

Step-by-step solution

Determine the electronic configurations of Mn³⁺ and Mn⁴⁺

The electronic configuration of manganese (Mn) in its ground state is [Ar] 3d⁵ 4s². In order to find the electronic configuration for Mn³⁺, we remove three electrons from the manganese atom. First, the two 4s electrons are removed, and then one more electron from the 3d orbitals. This results in the electronic configuration for Mn³⁺ as [Ar] 3d⁴. For Mn⁴⁺, we remove four electrons, taking one more electron from the 3d orbitals, giving us an electronic configuration of [Ar] 3d³.

Analyze Mn³⁺ in forming high-spin and low-spin octahedral complexes

In octahedral complexes, the ligands approach the central metal ion and cause the energy levels of the d-orbitals to split into two sets: a lower energy level (t2g) containing three orbitals and a higher energy level (eg) containing two orbitals. For high-spin complexes, the ligand's effect on the d-orbitals is weak, and so electrons prefer to occupy all five d-orbitals singly before starting to pair up in the lower energy t2g orbitals. In the case of Mn³⁺ with its 3d⁴ configuration, there are enough unpaired electrons to distribute into the t2g orbitals and partially fill one of the eg orbitals, making it possible for the Mn³⁺ ion to form a high-spin complex. In low-spin complexes, the ligand has a stronger effect on the d-orbitals, causing the energy difference between the t2g and eg orbitals to be larger. Electrons will then pair up in the lower energy t2g orbitals before moving to the eg orbitals. Mn³⁺ can also form low-spin octahedral complexes because the four d-electrons can be accommodated by the lower energy t2g orbitals.

Analyze Mn⁴⁺ in forming high-spin and low-spin octahedral complexes

When it comes to Mn⁴⁺, the situation is different. Mn⁴⁺ has an electronic configuration of [Ar] 3d³, which means there are fewer electrons to fill the d-orbitals. In both high-spin and low-spin octahedral complexes, the three unpaired electrons will first populate the t2g orbitals. In this case, there is no difference between the high-spin and low-spin configurations because all the electrons are already in the lower energy t2g orbitals. Consequently, Mn⁴⁺ cannot form high-spin and low-spin octahedral complexes as there is no significant difference between the two. In conclusion, Mn³⁺ can form both high-spin and low-spin octahedral complexes due to its 3d⁴ configuration, which allows for the accommodation of electrons in both the t2g and eg orbitals. On the other hand, Mn⁴⁺ cannot form distinct high-spin and low-spin octahedral complexes as its 3d³ configuration leads to the presence of electrons only in the lower energy t2g orbitals, making the two configurations essentially the same.

Key concepts

Electronic Configuration of Transition Metal Ions

Understanding the electronic configuration of transition metal ions is crucial when evaluating their chemical behavior. The element manganese (Mn) has a standard electronic configuration of [Ar] 3d⁵ 4s². When manganese forms cations such as Mn³⁺ and Mn⁴⁺, it does so by losing electrons.

When Mn loses three electrons to become Mn³⁺, the configuration becomes [Ar] 3d⁴. This is because the two 4s electrons are removed first, followed by one more from the 3d orbitals. Similarly, when it loses an additional electron to form Mn⁴⁺, its configuration is [Ar] 3d³. The number and arrangement of these d electrons play a pivotal role in the magnetic properties and the types of complexes that the ion can form.

High-Spin and Low-Spin Complexes

The distinction between high-spin and low-spin complexes lies in the strength of the ligands' field. This field influences the energy separation between the two sets of d-orbitals in an octahedral complex, known as t2g and eg.

In high-spin complexes, weak field ligands cause a smaller energy gap between t2g and eg orbitals. This smaller gap allows electrons to occupy higher energy eg orbitals to minimize electron pairing, resulting in more unpaired electrons and hence a high-spin complex. In contrast, low-spin complexes have strong field ligands, inducing a greater energy separation, which enables electrons to pair up in the lower energy t2g orbitals before the higher eg orbitals are utilized.

Mn³⁺, with its four d-electrons, can form both types of complexes. Electrons can either fill the t2g and eg orbitals in a high-spin configuration or pair up within the t2g in a low-spin configuration. Mn⁴⁺, however, remains in a low-spin-like state regardless of ligand strength due to having only three d-electrons to fill the lower t2g orbitals.

Ligand Field Theory

Ligand field theory (LFT) is a sophisticated theory that explains the electronic structures of transition metal complexes. It considers the interaction between the ligands and the d-orbitals of the central metal ion. In an octahedral field, the d-orbitals are split into two sets where three orbitals (t2g) have a lower energy level, and two orbitals (eg) have a higher energy level.

According to LFT, the split is influenced by the ligand's electric field, which can vary greatly depending on the nature of the liganship. For instance, ligands such as fluoride and water are considered weak field ligands and result in a smaller split. In contrast, strong field ligands like cyanide cause a larger split between t2g and eg.

This theory provides insight into why Mn³⁺ can exhibit both high-spin and low-spin configurations. The strength of the ligand's field can significantly alter the energy layout and thus the electron distribution in the d-orbitals. On the other hand, Mn⁴⁺, with one less electron, cannot take advantage of this variable energy landscape due to its limited number of electrons, resulting in only one possible arrangement.