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Chapter 24: Problem 19

If the ion \(\mathrm{Co}^{2+}\) is linked with strong-field ligands to produce an octahedral complex, the complex has one unpaired electron. If \(\mathrm{Co}^{2+}\) is linked with weak-field ligands, the complex has three unpaired electrons. How do you account for this difference?

Short Answer

Expert verified
The difference in the number of unpaired electrons when \(\mathrm{Co}^{2+}\) is linked with strong-field versus weak-field ligands is due to the relative energy gap (\(\Delta\)) between the five d-orbitals created by these ligands. In a strong-field case, the energy gap is large and the electrons prefer to occupy higher energy orbitals rather than pair up, leading to one unpaired electron. In a weak-field case, the energy gap is less, hence, the fourth, fifth and sixth electrons occupy lower energy orbitals, resulting in three unpaired electrons.

Step by step solution

01

Explanation for Complex with Strong-Field Ligands

When a cobalt ion (\(\mathrm{Co}^{2+}\)) forms an octahedral complex with strong-field ligands, the ligands cause a large splitting of the d-orbitals. As a consequence, the energy difference (\(\Delta\)) between the d-orbitals is large. In the case of \(\mathrm{Co}^{2+}\), which has 7 d-electrons ([Ar] 3d^7 electron configuration), after 3 electrons fill the lower energy orbitals (t_2g), the next electron occupies one of the higher energy orbitals (e_g) to minimize total spin. Therefore, there will be only one unpaired electron.
02

Explanation for Complex with Weak-Field Ligands

When the \(\mathrm{Co}^{2+}\) ion is bonded with weak-field ligands, the splitting of the d-orbitals is relatively small. This scenario is also known as 'high-spin' due to the greater number of unpaired electrons. Here, the two high-energy orbitals (e_g) are not much higher in energy than the three low-energy orbitals (t_2g), so the fourth electron also fills into the t_2g set. Thus, the \(\mathrm{Co}^{2+}\) ion in a weak-field complex has three unpaired electrons.
03

Conclusion

Therefore, the number of unpaired electrons in an octahedral complex of \(\mathrm{Co}^{2+}\) depends on the type of ligands (strong or weak field) the ion is bonded with. This is in accordance with Crystal Field Theory, which suggests that the distribution of the d-electrons and consequently, the number of unpaired electrons, is influenced by the energy difference between the d-orbitals in a metal complex.

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Most popular questions from this chapter

Which of these octahedral complexes would you expect to exhibit geometric isomerism? Explain. (a) \(\left[\mathrm{CrOH}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\) (b) \(\left[\mathrm{CrCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{3}\right]^{+}\) (c) \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\) (d) \(\left[\mathrm{CrCl}_{4}(\mathrm{en})\right]^{-}\) (e) \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\)

Supply acceptable names for the following. (a) \(\left[\mathrm{Co}(\mathrm{OH})\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)\right]^{2+}\) (b) \(\left[\mathrm{Co}(\mathrm{ONO})_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]\) (c) \(\left[\operatorname{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]\left[\mathrm{PtCl}_{6}\right]\) (d) \(\left[\mathrm{Fe}(\mathrm{ox})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{-}\) (e) \(\mathrm{Ag}_{2}\left[\mathrm{HgI}_{4}\right]\)

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\(\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ; \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ?\)

The most soluble of the following solids in \(\mathrm{NH}_{3}(\mathrm{aq})\) is (a) \(\mathrm{Ca}(\mathrm{OH})_{2} ;\) (b) \(\mathrm{Cu}(\mathrm{OH})_{2} ;\) (c) \(\mathrm{BaSO}_{4} ;\) (d) \(\mathrm{MgCO}_{3}\) (e) \(\overline{\mathrm{Fe}_{2} \mathrm{O}_{3}}\).

The amino acid glycine \(\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}\right.,\) denoted Hgly) binds as an anion and is a bidentate ligand. Draw and name all possible isomers of \(\left[\mathrm{Co}(\mathrm{gly})_{3}\right]\) How many isomers are possible for the compound $$\left[\mathrm{Co}(\mathrm{gly})_{2} \mathrm{Cl}\left(\mathrm{NH}_{3}\right)\right]\left[\text {Hint:} \mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2}^{-}\text {is }\right.$$ the glycinate anion.]
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