Problem 8 - Chemistry in 30 days

Question

Co-ordination number and oxidation number of \(\mathrm{Cr}\) in \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) are respectively (a) 4 and \(+2\) (b) 6 and \(+3\) (c) 3 and \(+3\) (d) 3 and 0

Step-by-Step Solution

Answer

The co-ordination number is 6 and the oxidation number of Cr is +3.

Step 1: Identify the ligand and its charges

The ligand in the coordination compound is \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\) (oxalate ion), which carries a charge of \(-2\). There are three oxalate ligands bound to the chromium atom in the complex.

Step 2: Determine co-ordination number

The co-ordination number corresponds to the number of ligand donor atoms attached to the central metal ion. Since each oxalate ion is a bidentate ligand and can coordinate through two donor atoms, three oxalate ions coordinate with the chromium, giving a co-ordination number of \(6\).

Step 3: Calculate oxidation number of chromium

To find the oxidation number of \(\mathrm{Cr}\), assess the overall charge of the complex ion \([\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}\). The potassium ions (\(\mathrm{K}^+\) have a \(+1\) charge each). Given that the whole compound is neutral, the charge of the complex ion \([\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]\) is \(-3\). Let \(x\) be the oxidation number of \(\mathrm{Cr}\). The equation becomes: \(x + 3(-2) = -3\). Solving this, \(x = +3\).

Key Concepts

Oxidation Number

The oxidation number is an essential concept in coordination chemistry. It represents the charge that an atom would have if all bonds were ionic. In the case of the complex \( \mathrm{K}_{3}[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}] \), we'll find the oxidation number of chromium (Cr). The compound contains three potassium ions (\( \mathrm{K}^{+} \)), each with a charge of \( +1 \). This indicates that the overall charge from potassium is \( +3 \).

The oxalate ion (\( \mathrm{C}_{2}\mathrm{O}_{4}^{2-} \)) is the ligand, and each carries a \( -2 \) charge. Since there are three oxalate ions, they contribute a total charge of \( -6 \). The metal complex \( [\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-} \) must therefore have an overall charge of \( -3 \), balancing the compound to neutral.

To find the oxidation number of \( \mathrm{Cr} \), assign \( x \) as the unknown value. The equation translates to \( x + 3(-2) = -3 \). Solving this, we find that \( x = +3 \). Thus, the oxidation number of chromium in this compound is \( +3 \). This helps in determining the electron flow and bond types in the complex.

Coordination Number

The coordination number is the total number of ligand donor atoms attached to the central metal atom in a coordination complex. In \( \mathrm{K}_{3}[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}] \), the chromium (Cr) atom acts as the central metal. Understanding the coordination number helps describe the geometry and bonding environment around the central metal ion.

Each oxalate ion \( (\mathrm{C}_{2}\mathrm{O}_{4}^{2-}) \) is a bidentate ligand, meaning it can attach to the central metal at two different points. Since there are three oxalate ions present in this complex, each contributing two coordination sites, the total coordination number becomes \( 3 \times 2 = 6 \).

Hence, the coordination number of chromium in this compound is 6. This contributes greatly to understanding the molecule's structure, often leading to an octahedral geometry, a common structure for coordination compounds.

Bidentate Ligands

Bidentate ligands are molecules that bind to a metal atom using two donor atoms, thereby forming two bonds with the central metal ion. The term "bidentate" comes from Latin where 'bi-' means two and 'dentate' means teeth or binding sites.

The oxalate ion \( (\mathrm{C}_{2}\mathrm{O}_{4}^{2-}) \) acts as a bidentate ligand in the coordination compound \( \mathrm{K}_{3}[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}] \). Each oxalate ion is capable of donating electrons to the metal through two of its oxygen atoms, thus creating two points of attachment per ligand.

Bidentate ligands like oxalate are crucial in forming stable complexes. They wrap around the central atom, increasing the stability due to the chelate effect. This effect arises as forming rings through these two donor sites makes dissociation from the metal less probable, often resulting in more stable coordination complexes. Understanding the behavior of bidentate ligands is key in manipulating and designing coordination compounds for various applications in chemistry.