Problem 91 - Chemistry The Central Science In Si Units

Question

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.

Step-by-Step Solution

Answer

(a) The oxidation number of chromium is 0. (b) The electron configuration is \([\mathrm{Ar}] \ 3d^{6} \ 4s^{0}\). (c) CO is a strong-field ligand. (d) It's named "hexacarbonylchromium(0)".

Step 1: Determine the Oxidation Number of Chromium

In the coordination complex \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\), carbon monoxide \((\mathrm{CO})\) is a neutral ligand, contributing no charge to the overall complex charge. Therefore, the oxidation number of chromium must balance the overall charge of the complex, which is zero. The oxidation number of chromium is thus 0.

Step 2: Analyze the Diamagnetic Property to Determine Electron Configuration

The complex \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is diamagnetic, indicating that all electrons are paired. In its ground state, a neutral chromium atom \((\mathrm{Cr})\) has an electron configuration of [Ar] 3d\(^5\) 4s\(^1\). Considering that the oxidation state is 0 and the complex is coordinatively saturated with six CO ligands, chromium must fully pair its \(3d\) electrons to form 3d\(^6\). Hence, the electron configuration of chromium in this complex is \([\mathrm{Ar}] \ 3d^{6} \ 4s^{0}\).

Step 3: Assess the Field Strength of the Ligand

\(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is colorless, which is typical for complexes where the ligands cause the \(d-d\) transitions to shift out of the visible spectrum. CO is known to be a strong-field ligand, which contributes to this behavior by causing a large split in the d-orbital energies, thus making \(d-d\) transitions fall in the UV range, not visible light.

Step 4: Name the Coordination Complex

Using nomenclature rules for coordination compounds, the complex \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) is named "hexacarbonylchromium(0)". The prefix "hexa-" indicates six CO ligands, "carbonyl" for the CO ligand, and "chromium" followed by the oxidation state in parentheses.

Key Concepts

Oxidation Numbers

Coordination chemistry often involves determining oxidation numbers, especially in complexes. In \([\mathrm{Cr}(\mathrm{CO})_{6}]\), each carbon monoxide (CO) ligand is neutral. This means it does not alter the overall charge of the complex. Thus, the complex's charge remains zero. To define the oxidation number of chromium (Cr), we analyze the charge balance. Since the complex does not have a net charge, the oxidation number of Cr must also be 0 to maintain charge neutrality. This is a crucial concept, as it helps predict the behavior and interactions of the metal atom within the complex.

Electron Configuration

In coordination complexes, knowing the electron configuration is key to understanding their properties. For \([\mathrm{Cr}(\mathrm{CO})_{6}]\), knowing it is diamagnetic helps. Diamagnetism implies that all of its electrons are paired. The neutral chromium atom has the configuration \[\text{[Ar]} \, 3d^{5} \, 4s^{1}\]. However, in the complex, the oxidation state of Cr is 0, suggesting no electron loss or gain from ligands. Therefore, Cr must adjust its d-orbitals to accommodate the CO ligands. It achieves a \[3d^6 \, 4s^0\] configuration by pairing all d-orbital electrons. This shift is important, as electron pairing affects if the complex will be attracted to a magnetic field.

Ligand Field Theory

Ligand Field Theory (LFT) is an important concept to explain the coloration and magnetism in coordination compounds. In \([\mathrm{Cr}(\mathrm{CO})_{6}]\), the complex is colorless. This absence of color indicates \(d-d\) transitions do not occur in visible light. CO, being a strong-field ligand, causes a large split in the d-orbital energy levels (7"). A strong \(\Delta\) means that the light needed to promote electrons is outside the visible spectrum, often in the UV range. This theory is powerful for predicting other properties, such as bond strength and magnetism in related complexes.

Nomenclature in Chemistry

Naming coordination compounds follows precise rules. The IUPAC system is used to ensure clarity and consistency in chemical communication. For \([\mathrm{Cr}(\mathrm{CO})_{6}]\), we begin with the prefix 7hexa-8 to denote six CO ligands. The term 7carbonyl8 describes the CO ligand specifically. 7Chromium8 denotes the central metal atom. Finally, 7(0)8 in parentheses indicates the metal9s zero oxidation state. Thus, the name is 7hexacarbonylchromium(0).8 Recognizing these components aids in understanding the elements and charges in complex structures.