The coordination complex \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) forms colorless, diamagnetic crystals that melt at \(90^{\circ} \mathrm{C}\) . (a) What is the oxidation number of chromium in this compound? (b) Given that \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is diamagnetic, what is the electron configuration of chromium in this compound? (c) Given that \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is colorless, would you expect CO to be a weak-field or strong-field ligand? (d) Write the name for \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) using the nomenclature rules for coordination compounds.

Understanding the oxidation number of elements in compounds like coordination complexes is fundamental for grasping their chemistry. The oxidation number represents the charge that an atom would have if the compound was composed of ions. It is pivotal for predicting reactivity, understanding electron transfer, and writing chemical formulas correctly.

In the coordination compound \[\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\], the oxidation number of chromium is determined by considering the charge of the ligands bonded to it. Since carbonyl (CO) is a neutral ligand, it has an oxidation number of 0. The complex itself doesn't carry an overall charge; thus, chromium's oxidation number is 0. This means there are no net electron transfers from the chromium to the ligands, keeping its electron configuration unchanged.

The electron configuration tells us how electrons are distributed within the orbitals of an atom. For transition metals, electron configurations can offer insight into the atom's chemical behaviors, including bonding and magnetism.

The electron configuration of an isolated chromium atom is \[\text{[Ar]} 4s^1 3d^5\]. However, in the complex \[\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\], chromium maintains its electrons because its oxidation number is 0. The complex is noted to be diamagnetic, which means all electrons are paired. This implies that one electron from the 4s orbital is promoted to the 3d orbital, leading to a new configuration of \[\text{[Ar]} 4s^0 3d^6\] with all paired electrons. This configuration explains the observed diamagnetic property of the compound.

Ligand field theory aids in understanding the color and magnetic properties of coordination compounds. It is an adaptation of molecular orbital theory that looks at the effect ligands have on the d-orbitals of a transition metal ion.

In the context of \[\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\], we observe that the compound is colorless and all its electrons are paired, which is indicative of a strong-field ligand. Carbon monoxide is, indeed, a strong-field ligand and causes a larger splitting in the chromium's d-orbitals. This prevents electrons from being unpaired and promotes a low-spin configuration, where electrons pair up in the lower energy orbitals, hence no electron transition is possible to absorb visible light, resulting in the compound being colorless.

The rules for naming chemical compounds, including coordination complexes, allows for the clear communication of a compound's composition. The nomenclature involves systematic naming of the ligands followed by the central metal with its oxidation state when it is not zero.

For \[\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\], the ligands are named first followed by the central metal. Since the oxidation number of chromium is 0, it is not indicated in the compound's name. Thus, the correct nomenclature for the coordination complex is hexacarbonylchromium, reflecting the six CO ligands (hexacarbonyl) and the chromium center without the need for numeric oxidation state indicators.