Problem 60 - Chemistry and Chemical Reactivity

Question

For a tetrahedral complex of a metal in the first transition series, which of the following statements concerning energies of the \(3 d\) orbitals is correct? (a) The five \(d\) orbitals have the same energy. (b) The \(d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\) orbitals are higher in energy than the \(d_{x y} d_{y y}\) and \(d_{x y}\) orbitals. (c) The \(d_{x z} d_{y z}\) and \(d_{x y}\) orbitals are higher in energy than the \(d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\) orbitals.

Step-by-Step Solution

Answer

(c) is the correct statement.

Step 1: Understanding the Tetrahedral Field Theory

In a tetrahedral complex, the approach of ligands causes a rearrangement in the energy levels of the metal's "d" orbitals. Unlike octahedral complexes, where the "d_{z^2}" and "d_{x^2-y^2}" orbitals are higher in energy, in tetrahedral complexes, it is the other way around.

Step 2: Identify Energy Levels in Tetrahedral Complexes

In the tetrahedral geometry, the "d_{x y}", "d_{y z}", and "d_{x z}" orbitals are higher in energy than the "d_{x^2-y^2}" and "d_{z^2}" orbitals. This is due to the different spatial distribution of ligands and orbitals compared to octahedral complexes.

Step 3: Evaluating Given Statements

(a) is incorrect because in tetrahedral complexes, the "d" orbitals split into different energy levels. (b) is incorrect since the "d_{x^2-y^2}" and "d_{z^2}" orbitals are lower. (c) is correct because the "d_{x z}", "d_{y z}", and "d_{x y}" orbitals are indeed higher in energy.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) is a powerful tool in understanding the behavior of transition metal complexes. It explains how the presence of ligands affects the energy levels of a metal's d-orbitals.
In a coordination complex, ligands are ions or molecules that donate electron pairs to the metal center. This interaction causes the d-orbitals of the metal to split into different energy levels. The type of splitting depends on the geometry of the complex, such as tetrahedral or octahedral.

• In octahedral complexes, the d-orbitals split into two groups: the higher-energy "e_g" set and the lower-energy "t_2g" set.
• In tetrahedral complexes, the situation is reversed, and the "t_2" orbitals are higher in energy than the "e" orbitals.

This splitting leads to colorful compounds and affects the magnetic properties of the metal complex. CFT helps predict these properties by considering how different ligands influence the metal's d-orbitals.

Transition Metals

Transition metals are elements found in the d-block of the periodic table. They are characterized by having partially filled d-orbitals, which allows them to form various oxidation states and colorful compounds.
The unique characteristics of transition metals include:

• The ability to form complex ions with different coordination numbers and geometries, such as tetrahedral and octahedral.
• Variable oxidation states, which occur because they can lose different numbers of d-electrons.
• The catalytic activity, often related to the presence of partially filled d-orbitals that can facilitate electron exchanges.

These properties make transition metals crucial for many biological processes, industrial applications, and the creation of various modern materials.

d-Orbital Splitting

d-Orbital splitting is a key concept in Crystal Field Theory that describes how d-orbitals of a metal ion are influenced by ligands. In a free metal atom, d-orbitals have equal energy, but when surrounded by ligands, they split into different energy levels.
In tetrahedral complexes:

• The "d_{xz}", "d_{yz}", and "d_{xy}" orbitals have higher energy and are grouped as "t_2".
• The "d_{x^2-y^2}" and "d_{z^2}" orbitals have lower energy and are grouped as "e".

This difference in energy levels is important for predicting the color and magnetic properties of the complex. In octahedral complexes, the arrangement and energy ordering of these orbitals is reversed. This intricate balance of energy levels explains many properties of the transition metal complexes.