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Chapter 23: Problem 52

The lobes of which \(d\) orbitals point directly between the ligands in (a) octahedral geometry, (b) tetrahedral geometry?

Short Answer

Expert verified
(a) In octahedral geometry, the \(d_{xy}, d_{yz}\), and \(d_{xz}\) orbitals point directly between the ligands. (b) In tetrahedral geometry, the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals point directly between the ligands.

Step by step solution

01

Understand the geometries of the d orbitals

There are five d orbitals: \(d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2},\) and \(d_{z^2}\). The \(d_{xy}, d_{yz},\) and \(d_{xz}\) orbitals have four lobes in the xy, yz, and xz planes, respectively. The \(d_{x^2-y^2}\) orbital has four lobes in the x and y directions, and the \(d_{z^2}\) orbital has a doughnut-shaped lobe in the xy plane and two additional lobes along the z-axis. Step 2: Analyze the octahedral geometry
02

Analyze the octahedral geometry

In octahedral geometry, there are six ligands surrounding the central atom, with each ligand located at the corners of an octahedron. The x, y, and z axes bisect the angles formed by the ligands, which means the ligands are placed along the diagonals of the axes. Step 3: Identify the d orbitals for octahedral geometry
03

Identify the d orbitals for octahedral geometry

Since the ligands are located along the diagonals of the axes in octahedral geometry, the d orbitals that point directly between the ligands are the ones that have lobes between these diagonals. In this case, the \(d_{xy}, d_{yz}\), and \(d_{xz}\) orbitals have lobes pointing directly between the ligands in octahedral geometry. Step 4: Analyze the tetrahedral geometry
04

Analyze the tetrahedral geometry

In tetrahedral geometry, there are four ligands surrounding the central atom, with each ligand located at the corners of a tetrahedron. The ligands are not located along the x, y, and z axes but rather between these axes. Step 5: Identify the d orbitals for tetrahedral geometry
05

Identify the d orbitals for tetrahedral geometry

Since the ligands are located between the axes in tetrahedral geometry, the d orbitals that point directly between the ligands are the ones that have lobes along the axes. In this case, the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals have lobes pointing directly between the ligands in tetrahedral geometry. #Answer#: (a) For octahedral geometry, the \(d_{xy}, d_{yz}\), and \(d_{xz}\) orbitals have lobes pointing directly between the ligands. (b) For tetrahedral geometry, the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals have lobes pointing directly between the ligands.

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Most popular questions from this chapter

A palladium complex formed from a solution containing bromide ion and pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\) (a good electron-pair donor), is found on elemental analysis to contain 37.6\(\%\) bromine, 28.3\(\%\) carbon, 6.60\(\%\) nitrogen, and 2.37\(\%\) hydrogen by mass. The compound is slightly soluble in several organic solvents; its solutions in water or alcohol do not conduct electricity. It is found experimentally to have a zero dipole moment. Write the chemical formula, and indicate its probable structure.

A manganese complex formed from a solution containing potassium bromide and oxalate ion is purified and analyzed. It contains \(10.0 \% \mathrm{Mn}, 28.6 \%\) potassium, \(8.8\%\) carbon, and 29.2\(\%\) bromine by mass. The remainder of the compound is oxygen. An aqueous solution of the complex has about the same electrical conductivity as an equimolar solution of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] .\) Write the formula of the compound, using brackets to denote the manganese and its coordination sphere.

Sketch the structure of the complex in each of the following compounds and give the full compound name: (a) \(\operatorname{cis}-\left[\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{Na}_{2}\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{5}\right]\) (c) \(\operatorname{trans} \mathrm{NH}_{4}\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\) (d) \(\operatorname{cis}-\left[\operatorname{Ru}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]\)

Draw the crystal-field energy-level diagrams and show the placement of \(d\) electrons for each of the following: (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (four unpaired electrons), \((\mathbf{b})\left[\operatorname{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (a high-spin complex), (c) \(\left[\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2+}\) (a low-spin complex) \((\mathbf{d})\left[\operatorname{Ir} \mathrm{Cl}_{6}\right]^{2-}\) (a low-spin complex) \((\mathbf{e})\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\) \((\mathbf{f})\left[\mathrm{NiF}_{6}\right]^{4-}.\)

Given the colors observed for \(\mathrm{VO}_{4}^{3-}\) (orthovanadate ion), \(\mathrm{CrO}_{4}^{2-}\) (chromate ion), and \(\mathrm{MnO}_{4}^{-}\) (permanganate ion (see Exercise \(23.84 ),\) what can you say about how the energy separation between the ligand orbitals and the empty \(d\) orbitals changes as a function of the oxidation state of the transition metal at the center of the tetrahedral anion?
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