Consider the following three complexes: (Complex 1) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SCN}\right]^{2+}\) (Complex 2) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{2+}\) (Complex 3) \(\mathrm{CoClBr} \cdot 5 \mathrm{NH}_{3}\) Which of the three complexes can have (a) geometric isomers, (b) linkage isomers, (c) optical isomers, (d) coordination-sphere isomers?

(a) Geometric isomers occur when ligands are arranged differently around a central metal ion. In this case, we are specifically looking for cis/trans isomers for octahedral complexes, where cis isomers have adjacent same ligands and trans isomers have opposite same ligands. (b) Linkage isomers occur when a ligand can bind to the central metal ion through different atoms. This typically involves ligands with multiple potential binding sites, such as SCN⁻ which can bind through either the sulfur (S) or nitrogen (N) atoms. (c) Optical isomers are non-superimposable mirror images of each other and typically occur when a complex has an asymmetric arrangement of ligands. This means it cannot be completely superimposed onto its mirror image. (d) Coordination-sphere isomers involve the swapping of a ligand inside the coordination sphere with one outside the coordination sphere. This results in two isomers with different arrangements of ligands inside and outside the coordination sphere. Now that we understand each type of isomer, let's analyze each complex.

Complex 1 is given as \([\text{Co}(\text{NH}_3)_5\text{SCN}]^{2+}\). (a) Geometric isomers: This complex has an octahedral geometry with five NH₃ and one SCN⁻ ligand. Due to the different types of ligands, there are no cis/trans isomers, so it cannot have geometric isomers. (b) Linkage isomers: Since the SCN⁻ ligand can bind through S or N, this complex can have linkage isomers. (c) Optical isomers: The presence of five NH₃ and one SCN⁻ in an octahedral configuration does not give an asymmetric arrangement. Therefore, it cannot have optical isomers. (d) Coordination-sphere isomers: This complex does not have any ligands outside its coordination sphere, so it cannot have coordination-sphere isomers.

Complex 2 is given as \([\text{Co}(\text{NH}_3)_3\text{Cl}_3]^{2+}\). (a) Geometric isomers: This complex has an octahedral geometry with three NH₃ and three Cl⁻ ligands. It can have both cis and trans isomers, so it can have geometric isomers. (b) Linkage isomers: Neither the NH₃ nor the Cl⁻ ligands have multiple binding sites, so it cannot have linkage isomers. (c) Optical isomers: The presence of three NH₃ and three Cl⁻ ligands in an octahedral configuration can give an asymmetric arrangement. Therefore, it can have optical isomers. (d) Coordination-sphere isomers: This complex does not have any ligands outside its coordination sphere, so it cannot have coordination-sphere isomers.

Complex 3 is given as \(\text{CoClBr} \cdot 5\text{NH}_3\). (a) Geometric isomers: This complex has an octahedral geometry with one Cl⁻, one Br⁻, and four NH₃ ligands. Due to the different types of ligands, there are no cis/trans isomers, so it cannot have geometric isomers. (b) Linkage isomers: Neither the Cl⁻, Br⁻ nor the NH₃ ligands have multiple binding sites, so it cannot have linkage isomers. (c) Optical isomers: The presence of one Cl⁻, one Br⁻, and four NH₃ ligands in an octahedral configuration can give an asymmetric arrangement. Therefore, it can have optical isomers. (d) Coordination-sphere isomers: This complex has five NH₃ ligands outside the coordination sphere, which can swap with the Cl⁻ or Br⁻ ligands. Therefore, it can have coordination-sphere isomers. In conclusion, the complexes have the following isomers: - Complex 1: linkage isomers - Complex 2: geometric and optical isomers - Complex 3: optical and coordination-sphere isomers