Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

vIn \(\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{2-}\), the number of \(\pi\) bonds is (a) 2 (b) 3 (c) 4 (d) 6

Step-by-Step Solution

Answer

The number of π bonds is 4.

Step 1: Identify the Molecular Structure

Start by identifying the components of \( \left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{2-} \) molecule: it is composed of a central silver (Ag) atom bonded to two cyanide (CN) groups. Cyanide is a linear molecule with the structure C≡N, where C is bonded to N with a triple bond consisting of one sigma (σ) bond and two pi (π) bonds.

Step 2: Assess the Bonds in Cyanide

Since each CN group has a C≡N bond, and it includes one σ bond and two π bonds, identify the total number of π bonds per CN unit. Each CN has two π bonds.

Step 3: Calculate Total Pi Bonds for the Molecule

There are two cyanide groups in \( \left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{2-} \), and since each CN contains two π bonds, multiply the number of CN groups by the number of π bonds per cyanide: \( 2 \times 2 = 4 \) π bonds in the molecule.

Key Concepts

Coordination Compounds

A coordination compound is a complex structure that consists of a central metal atom bonded to surrounding molecules or ions called ligands. This bonding typically involves a dative bond, also known as a coordinate covalent bond. In this type of bond, both electrons come from the same molecule. It is quite common in transition metals due to their ability to accommodate additional electrons.

In the compound \( [\mathrm{Ag}(\mathrm{CN})_2]^{2-} \), silver (Ag) serves as the central metal, coordinating with two cyanide (CN) groups. Cyanide acts as a bidentate ligand, meaning it can bind to the metal, providing electron pairs. This forms a stable complex due to the overlap of the empty orbitals of the Ag atom with the filled orbitals of the cyanide ions.

• Central metal: Silver (Ag)
• Ligands: Cyanide groups (CN)
• Bonding Type: Coordinate covalent bonds

Coordination compounds are fundamental in various chemical reactions, including catalysis and drug design, as they can stabilize metals in unusual oxidation states.

Molecular Structure

The molecular structure of \( [\mathrm{Ag}(\mathrm{CN})_2]^{2-} \) is characterized by its linear geometry. This is due to the linear arrangement of the cyanide ions around the central silver atom. The straightforward line formation occurs because each cyanide group is bonded to the metal with a simple, linear covalent bond.

Cyanide itself is a linear molecule where the carbon and nitrogen are connected by a triple bond, represented as C≡N. This includes one sigma (σ) bond and two pi (π) bonds. Linear structures allow for effective overlap of \( p \) orbitals to form pi bonds, which strengthens the molecule.

• Structure of CN: Linear with a C≡N bond
• Type of bonds: 1 σ bond and 2 π bonds within CN
• Molecule geometry: Linear

Understanding molecular structures is crucial for predicting the behavior of molecules in chemical reactions, such as reactivity and interaction with other molecules.

Cyanide Group

The cyanide group (CN) is a fascinating part of chemistry due to its toxic nature and simplicity in structure. It consists of a carbon atom triple-bonded to a nitrogen atom. This triple bond is a robust and stable arrangement with one sigma and two pi bonds, making CN a group that strongly holds electron density between the two atoms.

This bond strength allows cyanide to participate in stable coordination compounds by donating lone pairs to metal atoms. Moreover, the linear shape of CN facilitates the formation of these complexes, as seen in \( [\mathrm{Ag}(\mathrm{CN})_2]^{2-} \), where it contributes significantly to the geometrical structure.

• Cyanide formula: CN
• Bond characteristics: Triple bond with high strength
• Functional role: Acts as a strong ligand in coordination compounds

Understanding cyanide's role in molecular compounds is essential, particularly in the context of industrial processes and biological systems where cyanides are present.