Problem 52 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

a. Zn^2+: t2g: ↑↓↑↓↑↓ eg: ↑↓↑↓ b. Co^2+ low spin: t2g: ↑↓↑↓↑ eg: empty c. Co^2+ high spin: t2g: ↑↑↑↑↑ eg: empty d. Ti^3+: t2g: ↑ empty empty eg: empty empty

Step 1: (Step 1: Understand Octahedral d-Orbital Splitting)

In an octahedral complex, the d orbitals split into two groups with different energy levels when surrounded by ligands. The energy difference between these groups is called the crystal field splitting energy (∆). The three lower-energy orbitals are referred to as t2g orbitals (dxy, dyz, and dxz), while the two higher-energy orbitals are eg orbitals (dx^2-y^2 and dz^2).

Step 2: (Step 2: Determine the d-electron configuration for each ion)

To draw the d-orbital splitting diagrams, we need to know the number of d-electrons for each ion: a. Zn^2+ (Zn: atomic number 30) - [Ar] 4s^2 3d^10 -> Zn^2+: [Ar] 3d^10 - 10 d electrons b. Co^2+ (Co: atomic number 27) - [Ar] 4s^2 3d^7 -> Co^2+: [Ar] 3d^5 - 5 d electrons c. Ti^3+ (Ti: atomic number 22) - [Ar] 4s^2 3d^2 -> Ti^3+: [Ar] 3d^1 - 1 d electron

Step 3: (Step 3: Draw the d-orbital splitting diagram for Zn^2+)

Since the Zn^2+ ion has 10 d electrons, all of the d orbitals are fully occupied. The diagram will show all the t2g and eg orbitals filled with two electrons each: t2g: ↑↓↑↓↑↓ eg: ↑↓↑↓

Step 4: (Step 4: Draw the d-orbital splitting diagram for Co^2+ high spin and low spin)

Since the Co^2+ ion has 5 d electrons, the electrons can either occupy the t2g orbitals (low spin) or distribute themselves among both t2g and eg orbitals (high spin), depending on the strength of the crystal field. For Co^2+ low spin: t2g: ↑ ↓ ↑ ↓ ↑ eg: empty For Co^2+ high spin: t2g: ↑ ↑ ↑ ↑ ↑ eg: empty

Step 5: (Step 5: Draw the d-orbital splitting diagram for Ti^3+)

Since the Ti^3+ ion has only 1 d electron, it will occupy the lowest energy t2g orbital. The diagram will show the following electron distribution: t2g: ↑ empty empty eg: empty empty