Question

How many different structures are possible for each of the following complex ions? (a) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{5}\right]^{3+}\) (b) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{3+}\) (c) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]^{3+}\) (d) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+}\)

Short answer

(a) 1 arrangement, (b) 2 arrangements, (c) 2 arrangements, (d) 3 arrangements

Step-by-step solution

Understanding the structure of complex ions

Every complex ion has a central metal atom (in this case Co) surrounded by ligands (here, H2O and NH3) attached by coordinate bonds. The arrangement of these ligands around the metal atom gives the geometry of the complex ion. Here each complex has a total of 6 ligands, which gives an octahedral geometry.

Calculating possible arrangements for (a)

In (a) \([\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{5}\right]^{3+}\), there's only one molecule of H2O. So it has only one possible position in the octahedral shape. So there's only one possible arrangement for this complex.

Calculating possible arrangements for (b)

In (b) \([\operatorname{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{3+}\), there are two molecules of H2O. These can be either opposite to each other (giving 'trans' structure) or adjacent to each other (giving 'cis' structure). So there are two possible arrangements for this complex.

Calculating possible arrangements for (c)

In (c) \([\operatorname{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]^{3+}\), there are three molecules of H2O. These can either form a meridian (giving 'mer' structure) or a facial triangle (giving 'fac' structure). So there are two possible arrangements for this complex.

Calculating possible arrangements for (d)

In (d) \([\operatorname{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+}\), there are four molecules of H2O. Similar to step 3, these can be arranged in 'cis' or 'trans' configuration. Also here, 'cis' configuration has two possibilities, adjacent H2O or opposite H2O. So there are three possible arrangements for this complex.

Key concepts

Octahedral Complexes

When diving into the realm of coordination chemistry, one of the most fundamental geometric arrangements we encounter is the octahedral complex. This specific form is established when six ligands symmetrically surround a central metal ion, much like the vertices of an octahedron - a figure with eight faces. Each ligand attaches to the metal through a coordinate bond, meaning both electrons in the bond originate from the same atom, the ligand in this case.

Imagine placing a ball in the center of a room, with a friend standing at each corner. Just like your friends, ligands in an octahedral complex can assume different arrangements, changing the complex's properties. This geometry allows for varied structures even with the same types of ligands, offering a playground for exploration in fields like biochemistry and material sciences where such complexes perform crucial roles.

Coordination Chemistry

Coordination chemistry explores how molecules or ions, known as ligands, assemble around a central atom to create complex structures. Think of it as a dance where the central metal ion is the lead, and the ligands are the followers. They form coordination compounds by coordinating covalent bonds where the ligands donate a pair of electrons to the metal ion, a gracious dance of chemical bonding.

The critical detail here is the coordination number, primarily the number of points at which ligands attach to the central ion. For octahedral complexes, the coordination number is six. The nature and order of these ligands give rise to a vast array of chemical behaviors. Some complexes can change color, reactivity, or even magnetic properties based simply on how the ligands are arranged around the central metal atom.

Ligand Arrangements

Ligand arrangements in a complex influence the overall structure and function of the molecule. In octahedral complexes, the spatial arrangement of the ligands is particularly fascinating because it yields different isomers for the same chemical formula. An isomer is a compound with the same formula but different structural configurations.

In octahedral complexes, ligands can be opposite each other, creating a 'trans' configuration, or adjacent to each other, forming a 'cis' configuration. Further, if three identical ligands occupy one face or meridian of the octahedron, they are said to be in a 'fac' or 'mer' arrangement, respectively. Each of these isomers may have distinct chemical and physical properties. For instance, two complexes could possess the same types of ligands and yet behave entirely differently in a reaction or display different colors due to the arrangement of the ligands around the central atom. Learning to predict and understand these arrangements sparks a deeper comprehension of how molecules function and interact in various chemical contexts.