Problem 50 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following compound is both paramagnetic and coloured? (a) \(\left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{TiCl}_{6}\right]\) (b) \(\mathrm{VOSO}_{4}\) (c) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) (d) \(\mathrm{K}_{3}\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\)

Step-by-Step Solution

Answer

Compound \(\mathrm{VOSO}_{4}\) is both paramagnetic and colored.

Step 1: Identify Paramagnetic Compounds

Paramagnetism occurs in compounds with unpaired electrons. Analyze each compound for the presence of unpaired electrons in the metal ions.

Step 2: Check for Color

Colored compounds generally have transitions in the visible light region, often due to d-d transitions or charge transfer.

Step 3: Analyze Compound (a)

The compound \((\mathrm{NH}_{4})_{2}[\mathrm{TiCl}_{6}]\) contains \(\mathrm{Ti}^{4+}\), which has no unpaired electrons (it is \(3d^0\)) and is colorless, making it neither paramagnetic nor colored.

Step 4: Analyze Compound (b)

The compound \(\mathrm{VOSO}_{4}\) contains \(\mathrm{VO}^{2+}\), which has an electronic configuration of \(3d^1\) with one unpaired electron, making it paramagnetic. This compound is also colored, typically blue, due to d-d transitions.

Step 5: Analyze Compound (c)

\(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\) contains \(\text{Cr}^{6+}\), which has no unpaired electrons (it is \(3d^0\)) and is colored due to charge transfer transitions rather than paramagnetism.

Step 6: Analyze Compound (d)

\(\mathrm{K}_{3}[\mathrm{Cu}(\mathrm{CN})_{4}]\) has \(\mathrm{Cu}^+\) which has a \(3d^{10}\) configuration with no unpaired electrons, making it diamagnetic and generally colorless.

Key Concepts

Paramagnetism

Paramagnetism is a key concept in inorganic chemistry referring to the magnetic properties of materials with unpaired electrons. When electrons are unpaired, they generate a magnetic dipole. This means the compound is attracted to an external magnetic field.

• Silver, gold, and copper are examples of diamagnetic compounds, which lack unpaired electrons.
• In contrast, compounds like \( ext{VOSO}_4\) with unpaired electrons in metal ions are paramagnetic.

Understanding paramagnetism helps predict how compounds will interact with magnetic fields. It’s especially important in areas such as catalysis and electronic applications.

Unpaired Electrons

Unpaired electrons exist when one or more electrons occupy an atomic or molecular orbital by themselves. These electrons are key players in determining whether a compound is paramagnetic.

• The presence of unpaired electrons leads to magnetic characteristics that can be detected with experimental techniques.
• For example, \( ext{VO}^{2+}\) has a \(3d^1\) electronic configuration.

This single unpaired electron makes the compound paramagnetic and affects other properties, including reactivity and color.

d-d Transitions

d-d transitions are electronic transitions that occur between the d-orbitals of a metal ion. These transitions involve the absorption of visible light, which often gives rise to colorful compounds.

• Metal ions in complexes display a variety of colors due to these transitions.
• Compounds like \( ext{VOSO}_4\) exhibit blue coloration due to d-d transitions.

These transitions are a result of electron movement within the d-orbitals, which are split in energy levels by surrounding ligands.

Charge Transfer

Charge transfer occurs when an electron moves from one atom or molecular orbital to another within a compound, often between a ligand and a metal. This transfer of charge can create color, even in the absence of unpaired electrons.

• These transitions typically involve a full transfer of electron density, contrasting with the partial exchange seen in d-d transitions.
• An example is \(\text{K}_2\text{Cr}_2\text{O}_7\), which is colorful due to charge transfer rather than unpaired electrons.

Charge transfer is crucial for understanding the vivid colors of many metal-containing compounds and their electronic properties.

Electronic Configuration

Electronic configuration refers to the arrangement of electrons in an atom's orbitals. This arrangement dictates many properties, including magnetism and color.

• Elements with configurations like \(3d^0\) or \(3d^{10}\), such as \(\text{Ti}^{4+}\) or \(\text{Cu}^{+}\), are generally colorless and diamagnetic.
• In contrast, configurations with unpaired electrons, such as \(3d^1\) or \([3d^5, 4s^1]\), lead to paramagnetism and color.

Understanding electronic configurations helps predict the physical and chemical behavior of compounds, making it a foundational aspect of inorganic chemistry.