/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 The lobes of which \(d\) orbital... [FREE SOLUTION] | 91影视

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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

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) \(\operatorname{cis}-\left[\operatorname{Ru}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]\)

(a) A compound with formula \(\mathrm{RuCl}_{3}\) \(\cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess AgNO \(_{3}(a q)\) forms 2 mol of solid AgCl per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3}\) \(\cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates 3 mol of AgCl per mole of complex. What has happened in the ensuing time?

Explain why the transition metals in periods 5 and 6 have nearly identical radii in each group.

(a) Using Werner's definition of valence, which property is the same as oxidation number, primary valence or secondary valence? (b) What term do we normally use for the other type of valence? (c) Why can \(\mathrm{NH}_{3}\) serve as a ligand but BH \(_{3}\) cannot?

If the lobes of a given \(d\)-orbital point directly at the ligands, will an electron in that orbital have a higher or lower energy than an electron in a \(d\)-orbital whose lobes do not point directly at the ligands?
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