Problem 35 - Chemistry: An Atoms-Focused Approach

Question

Why is the \(d_{x y}\) orbital higher in energy than the \(d_{x z}\) and \(d_{y z}\) orbitals in a square planar crystal field?

Step-by-Step Solution

Answer

Answer: In a square planar crystal field, the \(d_{xy}\) orbital is higher in energy due to increased repulsion it experiences from the ligands, as it is aligned directly with them. Conversely, the \(d_{xz}\) and \(d_{yz}\) orbitals have their lobes directed between the ligands, resulting in less repulsion and lower energy levels.

Step 1: Understand the square planar crystal field

A square planar crystal field refers to the arrangement of ligands surrounding a central transition metal atom. In this arrangement, four ligands are positioned at the corners of a square, with the central metal atom in the middle. This arrangement causes the \(d\) orbitals of the central atom to split into two different energy levels.

Step 2: Explain the effect of the crystal field on the d orbitals energy levels

In a crystal field, the ligands are considered as negatively charged point charges that interact with the positively charged transition metal ion. The interaction between the charges causes repulsion, which then affects the energy of the \(d\) orbitals. In a square planar crystal field, the interaction between the ligands and the central metal atom causes the \(d_{xy}\) orbital to be at a higher energy level than the \(d_{xz}\) and \(d_{yz}\) orbitals. This is due to the fact that the \(d_{xy}\) orbital is aligned with the ligands, and thus experiences greater repulsion. On the other hand, the \(d_{xz}\) and \(d_{yz}\) orbitals have their lobes directed between the ligands, resulting in less repulsion and lower energy levels.

Step 3: Show the effect on the energy levels diagrammatically

In a square planar crystal field, the crystal field splitting diagram can be represented as follows: - The \(d_{xy}\) orbital is at a higher energy level due to direct alignment with the ligands. - The \(d_{xz}\) and \(d_{yz}\) orbitals are at a lower energy level because their lobes are directed between the ligands, experiencing less repulsion. The energy level diagram would look like this: Higher energy: \(d_{xy}\) Lower energy: \(d_{xz}\), \(d_{yz}\) In conclusion, the \(d_{xy}\) orbital is higher in energy than the \(d_{xz}\) and \(d_{yz}\) orbitals in a square planar crystal field due to the increased repulsion it experiences from the ligands. The \(d_{xz}\) and \(d_{yz}\) orbitals, having their lobes directed between the ligands, experience less repulsion, resulting in lower energy levels.