# 24.E: Exercises

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## 24.1: Werner’s Theory of Coordination Compounds

### Conceptual Problems

1. Give two reasons a metal can bind to only a finite number of ligands. Based on this reasoning, what do you predict is the maximum coordination number of Ti? of Ac?
2. Can a tetrahedral MA2B2 complex form cis and trans isomers? Explain your answer.
3. The group 12 elements are never found in their native (free) form but always in combination with one other element. What element is this? Why? Which of the group 12 elements has the highest affinity for the element you selected?

1. The group 12 metals are rather soft and prefer to bind to a soft anion such as sulfide rather than to a hard anion like oxide; hence they are usually found in nature as sulfide ores. Because it is the softest of these metals, mercury has the highest affinity for sulfide.

### Structure and Reactivity

1. Complexes of metals in the +6 oxidation state usually contain bonds to which two Lewis bases? Why are these bonds best described as covalent rather than ionic? Do Ca, Sr, and Ba also form covalent bonds with these two Lewis bases, or is their bonding best described as ionic?
2. Cr, Mn, Fe, Co, and Ni form stable CO complexes. In contrast, the earlier transition metals do not form similar stable complexes. Why?
3. The transition metals Cr through Ni form very stable cyanide complexes. Why are these complexes so much more stable than similar compounds formed from the early transition metals?
4. Of Co(en)33+, CoF63, Co(NH3)63+, and Co(dien)23+, which species do you expect to be the most stable? Why?
5. Of Ca2+, Ti2+, V2+, Mn2+, Fe2+, Co2+, Ni2+, and Zn2+, which divalent metal ions forms the most stable complexes with ligands such as NH3? Why?
6. Match each Lewis base with the metal ions with which it is most likely to form a stable complex:

Lewis bases: NH3, F, RS, OH, and Cl

Metals: Sc3+, Cu+, W6+, Mg2+, V3+, Fe3+, Zr4+, Co2+, Ti4+, Au+, Al3+, and Mn7+

1. Of ReF2, ReCl5, MnF6, Mn2O7, and ReO, which are not likely to exist?
2. Of WF2, CrF6, MoBr6, WI6, CrO3, MoS2, W2S3, and MoH, which are not likely to exist?

1. Metals in the +6 oxidation state are stabilized by oxide (O2−) and fluoride (F). The M−F and M−O bonds are polar covalent due to extreme polarization of the anions by the highly charged metal. Ca, Sr, and Ba can be oxidized only to the dications (M2+), which form ionic oxides and fluorides.
1. Cyanide is a relatively soft base, and the early transition-metal cations are harder acids than the later transition metals.
1. The formation of complexes between NH3 and a divalent cation is largely due to electrostatic interactions between the negative end of the ammonia dipole moment and the positively charged cation. Thus the smallest divalent cations (Ni2+, Zn2+, and Cu2+) will form the most stable complexes with ammonia.
1. Re2+ is a very soft cation, and F and O2− are very hard bases, so ReO and ReF2 are unlikely to exist. MnF6 is also unlikely to exist: although fluoride should stabilize high oxidation states, in this case Mn6+ is probably too small to accommodate six F ions.

## 24.2: Ligands

### Problems

1. Do ligands act like Lewis acids or Lewis bases? Why?
2. Do ligands form ionic bonds with the central metal atom?
3. What are chelating agents?
4. What is a monodentate ligand?
5. Describe polydentate ligands and provide an example.

1. Ligands act like Lewis bases because they share their electron pairs (electron donors) with the central metal atom.
2. No, ligands do not form ionic bonds the with the central metal atom. Rather, they form covalent bonds with the central metal atom because they share electron pairs.
3. Chelating agents are ligands that have two or more atoms with donating electron pairs that are able to attach a metal ion at the same time. These chelating ligands are monodentate and tridentate ligands
4. A monodentate ligand is a ligand that uses only one pair of electrons to bond to the central metal atom or ion.
5. Polydentate ligands are ligands which are able to donate more than two electron pairs to the central metal they bond to. EDTA is an example of a polydentate ligand.
6. Hexadentate ligands are ligands which have six lone pairs of electrons which can all bond to the central metal atom.
7. tetraamminecopper(II) sulfate
8. Tris(ethylenediamine)cobalt(II) nitrate

### Problems

Write the name of the following complexes (Chapter 24 / Custom Edition Chapter 21 Exercises):

1. [CoCl3(NH3)3]
2. [Co(ONO)3(NH3)3]
3. [Fe(ox)2(H2O)2]-
4. Ag2[HgI4]

1. triamminetrichlorocobalt(III)
2. triamminetrinitrito-O-cobalt(III); or triamminetrinitritocobalt(III)
4. silver(I) tetraiodomercurate(II)

## 24.4: Isomerism

### Problems

1. Write the Coordination Isomer for: [Co(NH3)6][Cr(CN)6]
2. Write the corresponding linkage isomer as well as names of the two complexes for: [CoCl(NO2)(NH3)4Cl]
3. What is the coordination isomer of: [Cr(NH3)6][Fe(CN)6]
4. Write the Ionization isomer for: [CoBr(NH3)5]SO4
5. Explain a polydentate ligand.

1. [Cr(NH3)6][Co(CN)6]
2. [CoCl(ONO)(NH3)4Cl]
3. [Fe(NH3)6][Cr(CN)6]
4. [CoSO4(NH3)5]Br
5. A polydentate ligand is a ligand that can bind to the central atom of a complex compound at many places at one time.

## 24.5: Bonding in Complex Ions: Crystal Field Theory

### Conceptual Problems

1. Describe crystal field theory in terms of its
1. assumptions regarding metal–ligand interactions.
2. weaknesses and strengths compared with valence bond theory.
1. In CFT, what causes degenerate sets of d orbitals to split into different energy levels? What is this splitting called? On what does the magnitude of the splitting depend?
2. Will the value of Δo increase or decrease if I ligands are replaced by NO2 ligands? Why?
3. For an octahedral complex of a metal ion with a d6 configuration, what factors favor a high-spin configuration versus a low-spin configuration?
4. How can CFT explain the color of a transition-metal complex?

Structure and Reactivity

1. Do strong-field ligands favor a tetrahedral or a square planar structure? Why?
2. For each complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.
1. [TiCl6]3−
2. [CoCl4]2−
1. For each complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.
1. [Cu(NH3)4]2+
2. [Ni(CN)4]2−
1. The ionic radii of V2+, Fe2+, and Zn2+ are all roughly the same (approximately 76 pm). Given their positions in the periodic table, explain why their ionic radii are so similar.

1. d9, square planar, neither high nor low spin, single unpaired electron
2. d8, square planar, low spin, no unpaired electrons

## 24.8: Aspects of Complex-Ion Equilibria

### Conceptual Problems

1. What is the difference between Keq and Kf?
2. Which would you expect to have the greater tendency to form a complex ion: Mg2+ or Ba2+? Why?
3. How can a ligand be used to affect the concentration of hydrated metal ions in solution? How is Ksp affected? Explain your answer.
4. Co(II) forms a complex ion with pyridine (C5H5N). Which is the Lewis acid, and which is the Lewis base? Use Lewis electron structures to justify your answer.

### Numerical Problems

1. Fe(II) forms the complex ion [Fe(OH)4]2− through equilibrium reactions in which hydroxide replaces water in a stepwise manner. If log K1 = 5.56, log K2 = 4.21, log K3 = −0.10, and log K4 = −1.09, what is Kf? Write the equilibrium equation that corresponds to each stepwise equilibrium constant. Do you expect the [Fe(OH)4]2− complex to be stable? Explain your reasoning.
2. Zn(II) forms the complex ion [Zn(NH3)4]2+ through equilibrium reactions in which ammonia replaces coordinated water molecules in a stepwise manner. If log K1 = 2.37, log K2 = 2.44, log K3 = 2.50, and log K4 = 2.15, what is the overall Kf? Write the equilibrium equation that corresponds to each stepwise equilibrium constant. Do you expect the [Zn(NH3)4]2+ complex to be stable? Explain your reasoning.
3. Although thallium has limited commercial applications because it is toxic to humans (10 mg/kg body weight is fatal to children), it is used as a substitute for mercury in industrial switches. The complex ion [TlBr6]3− is highly stable, with log Kf = 31.6. What is the concentration of Tl(III)(aq) in equilibrium with a 1.12 M solution of Na3[TlBr6]?

[Fe(H2O)6]2+(aq) + OH(aq) ⇌ [Fe(H2O(aq))5(OH)] + (aq) + H2O log K1 = 5.56
[Fe(H2O)5(OH)] + (aq) + OH(aq) ⇌ [Fe(H2O)4(OH)2](aq) + H2O(aq) log K2 = 9.77
[Fe(H2O)4(OH)2](aq) + OH(aq) ⇌ [Fe(H2O)3(OH)3](aq) + H2O(aq) log K3 = 9.67
[Fe(H2O)3(OH)3](aq) + OH(aq) ⇌ [Fe(OH)4]2−(aq) + 3H2O(l) log K4 = 8.58
[Fe(H2O)6]2+(aq) + 4OH(aq) ⇌ [Fe(OH)4]2−(aq) + 6H2O(l)
log Kf = log K1 + log K2 + log K2 + log K4
= 33.58

Thus, Kf = 3.8 × 1033. Because [Fe(OH)4]2− has a very large value of Kf, it should be stable in the presence of excess OH.

## 24.11: Applications of Coordination Chemistry

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