Question

Complete the following statements for the complex ion \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{-}\). (a) The oxidation number of \(\mathrm{Cr}\) is ________ (b) The coordination number of \(\mathrm{Cr}\) is __________ (c) _______ is a bidentate ligand.

Short answer

(a) +3; (b) 6; (c) \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\)

Step-by-step solution

Identify Components in the Complex Ion

The complex ion is \([\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{H}_{2}\mathrm{O})_{2}]^{-}\). It consists of one chromium ion \(\mathrm{Cr}\), two oxalate ions \((\mathrm{C}_{2}\mathrm{O}_{4})^{2-}\), and two water molecules \((\mathrm{H}_{2}\mathrm{O})\).

Determine Oxidation Number of Chromium

To find the oxidation number of \(\mathrm{Cr}\), set up an equation using known charges: the overall charge of the complex \([-1]\), oxalate ions \((\mathrm{C}_2\mathrm{O}_4)^{2-}\) each contributing \(-2\) charge, and water contributing \(0\) charge (neutral ligand). The equation is: \(x + 2(-2) + 2(0) = -1\) where \(x\) is the oxidation number of \(\mathrm{Cr}\). Solving for \(x\) gives \(x = +3\).

Determine Coordination Number of Chromium

The coordination number refers to the number of ligand donor atoms directly bonded to the central metal ion. Oxalate \((\mathrm{C}_2\mathrm{O}_4)\) is a bidentate ligand, contributing two donor atoms each, and water \((\mathrm{H}_2\mathrm{O})\) is a monodentate ligand, contributing one. Hence, the coordination number is calculated as \(2 \times 2 + 2 \times 1 = 6\).

Identify Bidentate Ligand

In the complex ion, the oxalate ion \((\mathrm{C}_2\mathrm{O}_4)^{2-}\) can form two bonds with the central metal ion, making it a bidentate ligand. Water \((\mathrm{H}_2\mathrm{O})\) is monodentate.

Key concepts

Oxidation Number

The oxidation number of an element in a compound indicates the charge the atom would have if the compound was composed of ions. To determine the oxidation number of chromium \( \mathrm{Cr} \) in the complex ion \( \left[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{H}_{2}\mathrm{O})_{2}\right]^{-} \), we need to keep in mind the charges contributed by each component:

• The overall charge of the complex is \(-1\).
• Each oxalate ion \((\mathrm{C}_2\mathrm{O}_4)^{2-}\) contributes a \(-2\) charge, totaling \(-4\) for two oxalate ions.
• Water, \((\mathrm{H}_2\mathrm{O})\), is neutral and contributes \(0\) charge.

By setting up the equation \( x + 2(-2) + 2(0) = -1 \), where \( x \) is the oxidation number of chromium, we solve for \( x \):
\[ x - 4 = -1 \]
Thus, \( x = +3 \). Therefore, the oxidation number of chromium in this complex is +3, indicating it loses three electrons compared to its elemental state.

Coordination Number

The coordination number of a complex ion is a count of the number of ligand atoms that are attached directly to the central metal ion. Each attachment point is considered separately. In the case of the \( [\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_2(\mathrm{H}_2\mathrm{O})_2]^{-} \) complex ion:

• Oxalate \((\mathrm{C}_2\mathrm{O}_4)\) is a bidentate ligand, meaning each oxalate ion forms two bonds with the metal center. Thus, two oxalate ions contribute a total of four bonds.
• Water \((\mathrm{H}_2\mathrm{O})\) is a monodentate ligand, forming just one bond with the metal ion. Two water molecules contribute two additional bonds.

Adding these contributions gives the total coordination number. In this case:
\[ 2 \times 2 + 2 \times 1 = 6 \]
Chromium in this complex has a coordination number of 6, signifying the number of coordinate covalent bonds formed with ligands.

Bidentate Ligand

Ligands are molecules or ions that donate pairs of electrons to a central metal in a complex ion, forming coordinate covalent bonds. They can be categorized by the number of attachment points to the metal. A bidentate ligand is one that forms two bonds with the central metal. In the given complex \( \left[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{H}_{2}\mathrm{O})_{2}\right]^{-} \):

• The oxalate ion \((\mathrm{C}_2\mathrm{O}_4)^{2-}\) is recognized as a bidentate ligand.
• It has two oxygen atoms each with lone electron pairs that can coordinate with the central chromium ion.
• This enables the oxalate ion to wrap around and attach simultaneously at two sites on the metal.

This dual attachment not only helps stabilize the metal complex but also gives insight into the spatial arrangement and geometry of the entire complex ion.