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Chapter 23: Problem 49

In crystal-field theory, ligands are modeled as if they are point negative charges. What is the basis of this assumption, and how does it relate to the nature of metal-ligand bonds?

Short Answer

Expert verified
In crystal-field theory, ligands are modeled as point negative charges to simplify the analysis of electrostatic interactions between the ligand's electron cloud and the positively charged metal ion. This assumption allows us to focus on the energy splitting of d-orbitals and, despite its limitations, helps to understand some key aspects of the electronic structure and properties of transition metal complexes. The nature of metal-ligand bonds is more complex than simple electrostatic attraction, involving other interactions like covalent bonding. However, the assumption of ligands as point negative charges can still provide useful information on the electrostatic component of metal-ligand bonds in many transition metal complexes.

Step by step solution

01

Crystal-Field Theory

Crystal-field theory is a model used to describe the electronic structure of transition metal complexes and the effect of ligands on their properties. This theory is based on the idea that ligands, which are molecules or ions surrounding a metal ion, create an electric field that influences the distribution of d-electrons in the metal ion. This electric field leads to the splitting of energy levels of different d-orbitals, which has important consequences for the electronic structure, properties, and reactivity of the complex.
02

Modeling Ligands as Point Negative Charges

In crystal-field theory, ligands are often represented as point negative charges. This simplification is based on the assumption that the interactions between the ligand's negatively charged electron cloud and the positively charged metal ion are the main factors governing the energy splitting of d-orbitals. By modeling ligands as point negative charges, we can focus on the electrostatic interactions and neglect other complex interactions, such as covalent bonding, that may also be present in the metal-ligand bond. This assumption has its limitations, and the actual interactions in the metal-ligand bond are usually more complex than simple electrostatic attraction. Nonetheless, considering ligands as point negative charges allows us to understand and predict some essential aspects of the electronic structure and properties of transition metal complexes.
03

Relation to Metal-Ligand Bonds

The assumption of ligands as point negative charges relates to the nature of metal-ligand bonds in that it allows us to analyze the electrostatic interactions between the ligand's negatively charged electron cloud and the positively charged metal ion. This electrostatic interaction is a crucial component of many metal-ligand bonds, especially in ionic complexes, and it plays a significant role in determining the energy levels of metal ion d-orbitals. However, it is essential to recognize that electrostatic interactions are not the only component of metal-ligand bonds, and other types of interactions, such as covalent bonding or orbital mixing, may contribute to the metal-ligand bond. Therefore, this simplification is not always applicable to every metal complex, and a more advanced theory (such as molecular orbital theory) may be required to provide a more accurate description of the metal-ligand bond in some cases. Nonetheless, for many transition metal complexes, considering ligands as point negative charges helps to understand and predict their electronic structure, properties, and reactivity.

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Most popular questions from this chapter

The lanthanide contraction explains which of the following periodic trends? (a) The atomic radii of the transition metals first decrease and then increase when moving horizontally across each period. (b) When forming ions the transition metals lose their valence s orbitals before their valence \(d\) orbitals. (c) The radii of the period 5 transition metals (Y-Cd) are very similar to the radii of the period 6 transition metals (Lu-Hg).

Solutions of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral), and \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral) are colored. One is pink, one is blue, and one is yellow. Based on the spectrochemical series and remembering that the energy splitting in tetrahedral complexes is normally much less than that in ectahedral ones, assign a color to each complex.

Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin (Hb) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{array}{ll} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\mathrm{e}}=-70 \mathrm{~kJ} \\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\mathrm{a}}=-80 \mathrm{~kJ} \end{array} $$ Using these data, estimate the equilibrium constant at \(298 \mathrm{~K}\) for the equilibrium $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$

(a) If a complex absorbs light at \(610 \mathrm{~nm}\), what color would you expect the complex to be? (b) What is the energy in Joules of a photon with a wavelength of \(610 \mathrm{~nm}\) ? (c) What is the energy of this absorption in \(\mathrm{kJ} / \mathrm{mol}\) ?

(c) When the coordinated water to the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase is deprotonated, what ligands are bound to the Zn(II) center? Assume the three nitrogen ligands are unaffected. (d) The \(\mathrm{F} K_{a}\) of \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{d}\right]^{2+}\) is 10 . Suggest an explanation for the difference between this \(\mathrm{pK} \mathrm{K}_{\text {and }}\) that of carbonic anhydrase. (e) Would you expect carbonic anhydrase to have a decp color, like hemoglobin and other metalion containing proteins do? Explain. Two different compounds have the formulation \(\mathrm{CoBr}\left(\mathrm{SO}_{4}\right) \cdot 5 \mathrm{NH}_{3}\). Compound \(\mathrm{A}\) is dark violet, and compound B is red-violet. When compound \(A\) is treated with \(\mathrm{AgNO}_{3}(\mathrm{Gq})\), no reaction occurs, whereas compound \(\mathrm{B}\)
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