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Chapter 24: Problem 17

Describe how the crystal field theory explains the fact that so many transition metal compounds are colored.

Short Answer

Expert verified
The crystal field theory explains the color of transition metal compounds by the interaction between the transition metal ion and its ligands. Ligands cause d orbital splitting in the metal ion, creating different energy levels. When light shines on the compound, the energy of the light is absorbed to promote an electron from a lower energy d orbital (t2g) to a higher energy d orbital (eg), a process that corresponds to a specific wavelength of light, which is perceived as color. The color varies, as the energy gap between t2g and eg orbitals varies according to the type of metal ion, ligand, and geometry of the complex.

Step by step solution

01

Understanding Crystal Field Theory

In the field of inorganic chemistry, the crystal field theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by surrounding charged particles. This explains the colors of transition metal complexes.
02

Explaining d Orbital Splitting

When ligands approach the central metal ion, the degeneracy of the five d orbitals is broken as the ligands push the d orbitals that point directly at them. Those d orbitals end up with a higher energy and they are referred to as 'eg', while the ones experiencing lesser repulsion, usually on the 'x', 'y', and 'z' axes are referred to as 't2g' orbitals.
03

Detailing Electronic Transitions

When light is shone on the complex, the energy of the light is absorbed and used to promote an electron from a lower energy d orbital (t2g) to a higher energy d orbital (eg). These transitions are visible to us as color. The specific energy difference between the t2g and eg orbitals determines the color that we see, as it corresponds to a specific wavelength of light.
04

Explaining the Variability in Color

The energy difference between the eg and t2g orbitals, can vary based on the type of metal ion, the type of ligand, and the geometry of the complex, making compounds of transition metals display a wide array of colors.

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Most popular questions from this chapter

Write a series of equations to show the stepwise displacement of \(\mathrm{H}_{2} \mathrm{O}\) ligands in \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) by ethylenediamine, for which \(\log K_{1}=4.34, \log K_{2}=3.31\), and \(\log K_{3}=2.05 .\) What is the overall formation constant, \(\beta_{3}=K_{f},\) for \(\left[\mathrm{Fe}(\mathrm{en})_{3}\right]^{3+} ?\)

Estimate the total \(\left[\mathrm{Cl}^{-}\right]\) required in a solution that is initially \(0.10 \mathrm{M} \mathrm{CuSO}_{4}\) to produce a visible yellow color. \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}+4 \mathrm{Cl}^{-} \rightleftharpoons\left[\mathrm{CuCl}_{4}\right]^{2-}+4 \mathrm{H}_{2} \mathrm{O}\) \(K_{f}=4.2 \times 10^{5}\) Assume that \(99 \%\) conversion of \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}\) to \(\left[\mathrm{CuCl}_{4}\right]^{2-}\) is sufficient for this to happen, and ignore the presence of any mixed aqua- chloro complex ions.

The number of unpaired electrons in the complex ion \(\left[\operatorname{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) is (a) \(5 ;(\mathrm{b}) 4 ;(\mathrm{c}) 3 ;(\mathrm{d}) 2 ;(\mathrm{e}) 1\).

Acetyl acetone undergoes an isomerization to form a type of alcohol called an enol. The enol, abbreviated acacH, can act as a bidentate ligand as the anion acac^-. Which of the following compounds are optically active: \(\operatorname{Co}(\mathrm{acac})_{3} ;\) trans\(\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ; \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ?\)

Which of these general structures for a complex ion would you expect to exhibit cis and trans isomerism? Explain. (a) tetrahedral (b) square-planar (c) linear
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