TM.16 LIGAND FIELD THEORY

In document General Chemistry (Page 80-86)

The valence bond model described in Section TM.11 and the crystal field theory described in Section TM.12 each explain some aspects of the chemistry of the transition metals, but neither model is good at predicting all of the properties of transition metal complexes. A third model, based on molecular orbital theory, was therefore developed that is known as ligand field theory. Ligand field theory is more powerful than either the valence bond or crystal field theories. Unfortunately, it is also more abstract.

The ligand field model for an octahedral transition metal complex such as the Co(NH3)63ion assumes that the 3d, 4s, and 4p orbitals on the metal overlap with one or-bital on each of the six ligands to form a total of 15 molecular oror-bitals, as shown in Figure TM.22. Six of the orbitals are bonding molecular orbitals, whose energies are much lower than those of the original atomic orbitals. Another six are antibonding molecular orbitals, whose energies are higher than those of the original atomic orbitals. Three are best de-scribed as nonbonding molecular orbitals, because they have essentially the same energy as the 3d atomic orbitals on the metal.

FIGURE TM.22 The molecular orbitals in this ligand field diagram for

Co(NH3)63were generated by allow-ing the valence-shell 3d, 4s, and 4p or-bitals on the transition metal to overlap with an orbital on each of the six lig-ands that contribute pairs of nonbond-ing electrons to form an octahedral complex.

3d

O

E

Metal orbitals

4s 4p

Ligand orbitals

Ligand field theory enables the 3d, 4s, and 4p orbitals on the metal to overlap with or-bitals on the ligand to form the octahedral covalent bond skeleton that holds the complex together. At the same time, the model generates a set of five orbitals in the center of the

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diagram that are split into t2g and egsubshells, as predicted by the crystal field theory. As a result, we don’t have to worry about “inner-shell” versus “outer-shell” metal complexes.

In effect, we can use the 3d orbitals in two different ways. We can use them to form the covalent bond skeleton and then use them again to form the orbitals that hold the elec-trons that were originally in the 3d orbitals of the transition metal.

KEY TERMS

Actinide

Bidentate ligand Chelating ligand Chiral

Cis

Complex ion

Coordination compound Coordination number Crystal field theory Dextrorotatory

Diamagnetic Electron pair

acceptor/donor High-spin

Isomers Lanthanide Levorotatory Lewis acid/base Ligand

Ligand field theory

Low-spin

Main-group elements Monodentate

Optically active Paramagnetic

Spectrochemical series Trans

Transition metals Valence bond theory

PROBLEMS

Transition Metals and Coordination Complexes

1. Identify the subshell of atomic orbitals filled among the transition metals in the fifth row of the periodic table.

2. Describe some of the ways in which transition metals differ from main-group metals such as aluminum, tin, and lead. Describe ways in which they are similar.

3. Use the electron configurations of Zn2, Cd2, and Hg2to explain why those ions of-ten behave as if they were main-group metals.

4. Use the electronegativities of cobalt and nitrogen to predict whether the CoON bond in the Co(NH3)63ion is best described as ionic, polar covalent, or covalent.

5. Define the terms coordination number and ligand.

Werner’s Model of Coordination Complexes

6. Werner wrote the formula of one of his coordination complexes as CoCl36 NH3. To-day, we write that compound as [Co(NH3)6]Cl3to indicate the presence of Co(NH3)63

and Clions. Write modern formulas for the compounds Werner described as CoCl35 NH3, CoCl34 NH3, and CoCl35 NH3H2O.

7. What is the charge on the cobalt ion in the following complex [Co(NH3)6]Cl3? 8. Explain why aqueous solutions of CoCl36 NH3conduct electricity better than

aque-ous solutions of CoCl34 NH3.

9. Explain why Ag ions precipitate three chloride ions from an aqueous solution of CoCl36 NH3but only one chloride ion from an aqueous solution of CoCl34 NH3. 10. Predict the number of Clions that could precipitate from an aqueous solution of the

Co(en)2Cl2complex.

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11. Predict the number of ions formed when the NiSO44 NH32 H2O complex dissociates in water.

Typical Coordination Numbers

12. Use the examples in Table TM.1 to identify at least one factor that influences the co-ordination number of a transition metal ion.

13. Determine both the coordination number and the charge on the transition metal ion in each of the following complexes.

(a) CuF42 (b) Cr(CO)6 (c) Fe(CN)64 (d) Pt(NH3)2Cl2

14. Determine both the coordination number and the charge on the transition metal ion in each of the following complexes.

(a) Co(SCN)42 (b) Fe(acac)3 (c) Ni(en)2(H2O)22 (d) Co(NH3)5(H2O)3 The Electron Configuration of Transition Metal Ions

15. Write the electron configuration of the following transition metal ions.

(a) V2 (b) Cr2 (c) Mn2 (d) Fe2 (e) Ni2 16. Explain why the Co2ion can be described as a d7ion.

17. Which of the following ions can be described as d5? (a) Cr2 (b) Mn2 (c) Fe3 (d) Co3 (e) Cu

18. Explain the difference between the symbols Cr3and Cr(VI).

19. Which of the following is not an example of a d0 transition metal complex?

(a) TiO2 (b) VO2 (c) Cr2O72 (d) MnO4

20. Explain why manganese becomes more electronegative when it is oxidized from Mn2

to Mn(VII).

21. Use electronegativities to predict whether the MnOO bond in MnO4is best described as covalent or ionic.

Lewis Acid–Lewis Base Approach to Bonding in Complexes

22. Describe what to look for when deciding whether an ion or molecule is a Lewis acid.

23. Explain how Lewis acids, such as the Co3ion, pick up Lewis bases, or ligands, to form coordination complexes.

24. Which of the following are Lewis acids?

(a) Fe3 (b) BF3 (c) H2 (d) Ag (e) Cu2

25. Which of the following are Lewis bases, and therefore potential ligands?

(a) CO (b) O2 (c) Cl (d) N2 (e) NH3

26. Which of the following are Lewis bases, and therefore potential ligands?

(a) CN (b) SCN (c) CO32 (d) NO (e) S2O32

Typical Ligands

27. Define the terms monodentate, bidentate, tridentate, and tetradentate. Give an example of each category of ligands.

28. Use Lewis structures to explain why carbon monoxide could act as a bridge between a pair of transition metals, but it can’t be a chelating ligand that coordinates to the same metal twice.

29. Draw the structures of the following coordination complexes.

(a) Fe(acac)3 (b) Co(en)33 (c) Fe(EDTA) (d) Fe(CN)64 1012T_mod02_1-34 1/19/05 18:57 Page 31

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Nomenclature of Complexes 30. Name the following complexes.

(a) Cu(NH3)42 (b) Mn(H2O)62 (c) Fe(CN)64 (d) Ni(en)32 (e) Cr(acac)3

31. Name the following complexes.

(a) Pt(NH3)2Cl2 (b) Ni(CO)4 (c) Co(en)33

32. Name the following complexes.

(a) Na3[Co(NO2)6] (b) Na2[Zn(CN)4] (c) [Co(NH3)4Cl2]Cl (d) [Ag(NH3)2]Cl 33. Write the formulas for the following compounds.

(a) hexamminechromium(III) chloride

(b) chloropentamminechromium(III) chloride (c) trisethylenediamminecobalt(III) chloride (d) potassium tetranitritodiamminecobaltate(III) Isomers

34. Which of the following octahedral complexes can form cis/trans isomers?

(a) Co(NH3)63 (b) Co(NH3)5Cl2 (c) Co(NH3)5(H2O)3 (d) Co(NH3)4Cl2 (e) Co(NH3)4(H2O)23

35. Predict the structures of the cis/trans isomers of Ni(en)2(H2O)22.

36. The octahedral Mo(PH3)3(CO)3 complex can exist as a pair of isomers. Predict the structures of the compounds.

37. Which of the following square-planar complexes can form cis/trans isomers?

(a) Cu(NH3)42 (b) Pt(NH3)2Cl2 (c) RhCl3(CO) (d) IrCl(CO)(PH3)2

38. Explain why square-planar complexes with the generic formula MX2Y2 can form cis/trans isomers, but tetrahedral complexes with the same generic formula cannot.

39. Explain why square-planar complexes with the generic formula MX3Y can’t form cis/trans isomers.

40. Use the fact that Rh(CO)(H)(PH3)2 forms cis/trans isomers to predict whether the geometry around the transition metal is square planar or tetrahedral.

41. Compounds are optically active when the mirror image of the compound cannot be su-perimposed on itself. Draw the mirror images of the following complex ions and de-termine which of the ions are chiral.

(a) Cu(NH3)42(a square-planar complex) (b) Co(NH3)62(an octahedral complex) (c) Ag(NH3)2(a linear complex) (d) Cr(en)33(an octahedral complex)

42. Explain why neither of the cis/trans isomers of Pt(NH3)2Cl2 is chiral.

43. Explain why the cis isomer of Ni(en)2(H2O)22 is chiral, but the trans isomer is not.

44. Explain why the cis isomer of Ni(en)2(H2O)22 is chiral, but the cis isomer of Ni(NH3)4(H2O)22is not.

45. Which of the following octahedral complexes are chiral?

(a) Cr(acac)3 (b) Cr(C2O4)33 (c) Cr(CN)63 (d) Cr(CO)4(NH3)2

The Valence Bond Approach to Bonding in Complexes

46. Describe the difference between the valence bond model for the Co(NH3)63complex ion and the valence bond model for the Ni(NH3)62complex ion.

47. Apply the valence bond model of bonding in transition metal complexes to Ni(CO)4, Fe(CO)5, and Cr(CO)6. (Hint: Assume that the valence electrons on transition metals in complexes in which the metal is in the zero oxidation state are concentrated in the d orbitals.)

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48. Use the results of the previous problem to explain why the transition metal is sp3 hy-bridized in Ni(CO)4, dsp3 hybridized in Fe(CO)5, and d2sp3 hybridized in Cr(CO)6. 49. Use valence bond theory to explain the 2 charge on the Fe(CO)42ion. Predict the charge on the equivalent Co(CO)4xion. Use acid–base chemistry to predict the charge on the HFe(CO)4x ion.

50. Use Lewis structures to explain what happens in the following reaction.

2 CrO42(aq) 2 H(aq) 88nm88 Cr2O72(aq) H2O(l )

Predict the charge on the product of the following reaction. Explain why this transition-metal compound is a gas at room temperature.

MnO42(aq) 2 H(aq) 88nm88 Mn2O7x

(l ) H2O(l )

51. Apply the valence bond model of bonding in transition metal complexes to the Zn(NH3)42and Fe(H2O)63 complex ions.

52. Use the assumption that transition metals often pick up enough ligands to fill their va-lence shell to predict the charge on the Mn(CO)5x ion.

53. Use the assumption that transition metals often pick up enough ligands to fill their va-lence shell to predict the charge on the HgI4x ion.

54. Use the assumption that transition metals often pick up enough ligands to fill their va-lence shell to predict the coordination number of the Cd2ion in the Cd(OH)x2ion.

55. Explain why Zn2ions form both Zn(CN)42and Zn(NH3)42ions.

Crystal Field Theory

56. Describe what happens to the energies of the 3d atomic orbitals in an octahedral crys-tal field.

57. Describe what happens to the energies of the 3d atomic orbitals in a tetrahedral crys-tal field.

58. Which of the 3d atomic orbitals in an octahedral crystal field belong to the t2g set of orbitals? Which belong to the egset?

59. In an octahedral field what do the orbitals in a t2g set have in common? What do the orbitals in the eg set have in common?

60. The 3d orbitals are split into t2g and egsets in both octahedral and tetrahedral crystal fields. Is there any difference between the orbitals that go into the t2gset in octahedral and in tetrahedral crystal fields?

61. Explain why t for a tetrahedral complex is much smaller than o for the analogous octahedral complex.

62. Use the splitting of the 3d atomic orbitals in an octahedral crystal field to explain the stability of the oxidation states corresponding to d3 and d6 electron configurations in the Cr(NH3)63 and Fe(CN)64complex ions.

63. The difference between the energies of the t2gand egsets of atomic orbitals in an octa-hedral or tetraocta-hedral crystal field depends on both the metal atom and the ligands that form the complex. Which of the following metal ions would give the largest difference?

(a) Rh3 (b) Cr3 (c) Fe3 (d) Co2 (e) Mn2

64. Which of the following ligands would give the largest value of o? (a) CN (b) NH3 (c) H2O (d) OH (e) F

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High-Spin versus Low-Spin Complexes

65. Describe the difference between a high-spin and a low-spin d6complex.

66. What factors determine whether a complex is high-spin or low-spin?

67. Explain why the Mn(H2O)62 ion is a high-spin complex.

68. One of the Fe(H2O)62and Fe(CN)64complex ions is high-spin and the other is low-spin. Which is which?

69. Use the relative magnitudes of oand t to explain why there are no low-spin tetra-hedral complexes.

70. Compare the positions of the Co2 with Co3 and Fe2 with Fe3 ions in the spec-trochemical series. Explain why the value of  generally increases with the charge on the transition metal ion.

71. Compare the positions of the Co3, Rh3, and Ir3ions in the spectrochemical series.

What happens to the value of  as we go down a column among the transition metals?

The Colors of Transition Metal Complexes

72. Describe the characteristic colors of aqueous solutions of the following transition metal ions.

(a) Cu2 (b) Fe3 (c) Ni2 (d) CrO42 (e) MnO4

73. Explain why so many of the pigments used in oil paints, such as vermilion (HgS), cad-mium red (CdS), cobalt yellow [K3Co(NO2)6], chrome yellow (PbCrO4), Prussian blue (Fe4[Fe(CN)6]3), and cobalt blue (CoOAl2O3), contain transition metal ions.

74. Explain why Cu(NH3)42 complexes have a deep-blue color if they don’t absorb blue light. What light do they absorb?

75. CrO42ions are bright yellow. In what portion of the visible spectrum do the ions ab-sorb light?

76. When CrO42reacts with acid to form Cr2O72 ions, the color shifts from bright yel-low to orange. Does this mean that the light absorbed shifts toward a higher or a yel-lower frequency?

77. Ni2 forms a complex with the dimethylglyoxime (DMG) ligand that absorbs light in the blue-green portion of the spectrum. What is the color of the Ni(DMG)2complex?

78. Explain why a white piece of paper looks as if it has a faint pink color to a person who has been working for several hours at a computer terminal that has a green screen.

Ligand Field Theory

79. Describe how ligand field theory eliminates the difference between inner-shell com-plexes, such as the Co(NH3)63ion, and outer-shell complexes, such as the Ni(NH3)62

ion.

80. Explain how ligand field theory allows the valence-shell d orbitals on the transition metal to be used simultaneously to form the skeleton structure of the complex and to hold the electrons that were originally in the d orbitals on the transition metal.

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In document General Chemistry (Page 80-86)