Problem 3 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the coordination number of metal in [Co(en) \(_{2}\) \(\left.\mathrm{Cl}_{2}\right] ?\) (a) 3 (b) 4 (c) 5 (d) 6

Step-by-Step Solution

Answer

The coordination number of cobalt in \([\text{Co(en)}_{2}\text{Cl}_{2}]\) is 6.

Step 1: Understanding the Coordination Number

The coordination number of a metal is defined as the number of ligand donor atoms to which the metal is directly bonded.

Step 2: Identifying the Metal and Ligands

In the complex \([\text{Co(en)}_{2}\text{Cl}_{2}]\), cobalt (Co) is the central metal atom. The ligands are ethylenediamine (\text{en}) and chloride ions (\text{Cl}^{-}).

Step 3: Counting the Donor Atoms from Ligands

Ethylenediamine (\(\text{en}\)) is a bidentate ligand, meaning each molecule provides two donor atoms. Since two \(\text{en}\) ligands are present, they contribute a total of 4 donor atoms. Each \(\text{Cl}^-\) is a monodentate ligand, contributing one donor atom each, adding up to 2 donor atoms from two chloride ions.

Step 4: Summing Up the Donor Atoms

Add the donor atoms: 4 (from \(\text{en}\)) + 2 (from \(\text{Cl}^-\)) = 6. This sum is the coordination number of the cobalt atom in the complex.

Key Concepts

Ligands

In coordination chemistry, ligands are crucial components. They are ions or molecules that bond to a metal atom to form a coordination complex. Each ligand has at least one donor atom that forms a coordinate bond with the metal center. This bond involves the sharing of a lone pair of electrons from the donor atom on the ligand to an empty orbital on the metal.
In the example of the complex \( [\text{Co(en)}_2\text{Cl}_2] \), ligands are ethylenediamine (\( \text{en} \)) and chloride ions. Ligands determine many properties of the metal complex, including its reactivity and geometry. They can be categorized based on the number of donor atoms they have and the way they bind to the metal.

Bidentate Ligand

A bidentate ligand is a specific type of ligand that can form two coordinate bonds with a metal center at once. This happens because the ligand has two donor atoms that can donate a pair of electrons. Bidentate ligands are known to provide greater stability to a complex than monodentate ligands, due to the chelate effect, which involves the formation of rings that incorporate the metal.
In our given complex, ethylenediamine is a bidentate ligand. Each molecule of ethylenediamine can form a bond with the cobalt atom through two nitrogen atoms. This means that for every ethylenediamine molecule present, there are two donor atoms contributing to the coordination number. Thus, in the coordination complex \( [\text{Co(en)}_2\text{Cl}_2] \), two ethylenediamine molecules collectively provide four donor atoms.

Monodentate Ligand

Monodentate ligands are those which can form only one coordinate bond with the central metal atom. They are simpler compared to multidentate ligands, having just one donor atom which allows for a single point of attachment to the metal.
Chloride ions (\( \text{Cl}^- \)) in \( [\text{Co(en)}_2\text{Cl}_2] \) act as monodentate ligands. Each chloride ion contributes just a single pair of electrons to form a bond with the cobalt atom. Two chloride ions present in the complex lead to two donor bonds with the metal.
The combination of monodentate and bidentate ligands can affect the overall stability and structure of the coordination complex, which is essential for its functionality in various chemical applications.

Donor Atoms

Donor atoms are the specific atoms within a ligand that directly form coordinate bonds with the central metal atom in a complex. These atoms have lone pairs of electrons which they can donate to the metal, thus forming coordinate covalent bonds.
Determining the coordination number of a metal involves counting these donor atoms. It gives insight into the geometry and possible reactivity of the complex.
In our cobalt-containing complex \( [\text{Co(en)}_2\text{Cl}_2] \), the ethylenediamine (\( \text{en} \)) ligand contributes four donor atoms (two from each nitrogen in two \( \text{en} \) molecules), and the two chloride ions each bring one donor atom, totaling six donor atoms. This total corresponds to the coordination number of six, which indicates that the cobalt ion has made connections with six donor atoms in its environment.