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Chapter 21: Problem 90

Consider the pseudo-octahedral complex ion of \(\mathrm{Cr}^{3+}\), where \(\mathrm{A}\) and \(\mathrm{B}\) represent ligands. Ligand A produces a stronger crystal field than ligand B. Draw an appropriate crystal field diagram for this complex ion (assume the A ligands are on the \(z\) -axis).

Short Answer

Expert verified
To draw the crystal field energy diagram for the pseudo-octahedral complex ion of \(\mathrm{Cr}^{3+}\) with ligand A producing a stronger crystal field than ligand B, split the d-orbitals into two energy levels: the higher energy level for the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals and the lower energy level for the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals. Label the respective orbitals and indicate that the A ligands (stronger crystal field) are along the z-axis, while the B ligands (weaker crystal field) are along the x and y axes. The diagram should represent the influence of ligands A and B on the d-orbital energies for the complex ion.

Step by step solution

01

Recall Octahedral Crystal Field Splitting

In an octahedral crystal field splitting, the d-orbitals are split into two groups because of the interaction with the ligands. With ligands along the x, y, and z axes, the d-orbitals (\(d_{z^2}\) and \(d_{x^2-y^2}\)) along the axes will experience a higher energy than those (\(d_{xy}\), \(d_{xz}\), and \(d_{yz}\)) in between the axes. This leads to a splitting of the 5 d-orbitals into two sets - one with two orbitals (\(d_{z^2}\) and \(d_{x^2-y^2}\)) and the other with three orbitals (\(d_{xy}\), \(d_{xz}\), and \(d_{yz}\)).
02

Comparing the Two Ligands

Ligand A produces a stronger crystal field than ligand B meaning that the energy difference between d-orbitals along the z-axis and those in between the x and y axes is greater when A ligands are present along the z-axis. Thus, the order of energy for the d-orbitals would be \(d_{z^2}\) (and \(d_{x^2-y^2}) > d_{xz}\), \(d_{yz}\), \(d_{xy}\).
03

Draw the Crystal Field Diagram

To draw the crystal field energy diagram for this complex ion: 1. Draw two horizontal lines representing the two sets of energy levels, with the higher one for the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals and the lower one for the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals. 2. Label the two lines with the respective orbitals. 3. Indicate that the A ligands (stronger crystal field) are along the z-axis, and the B ligands (weaker crystal field) are along the x and y axes. The crystal field energy diagram represents the influence of ligands A and B on the d-orbital energies for the given pseudo-octahedral complex ion.

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Most popular questions from this chapter

Which of the following statement(s) is(are) true? a. The coordination number of a metal ion in an octahedral complex ion is 8 . b. All tetrahedral complex ions are low-spin. c. The formula for triaquatriamminechromium(III) sulfate is \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}\) d. The electron configuration of \(\mathrm{Hf}^{2+}\) is \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\). e. Hemoglobin contains \(\mathrm{Fe}^{3+}\).

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