Problem 67 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are diamagnetic? (1) \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) (2) \(\mathrm{K}_{3}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]\) (3) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (4) \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]\) Select the correct answer using the codes given below: (a) 1 and 2 (b) 2,3 and 4 (c) 1,3 and 4 (d) 2 and 4

Step-by-Step Solution

Answer

The diamagnetic compounds are (1), (3), and (4); option (c) is correct.

Step 1: Understand Diamagnetism

Diamagnetic materials are those that do not have unpaired electrons. To find out whether a compound is diamagnetic, we analyze its metal ion's electronic configuration in its coordination complex.

Step 2: Analyze Compound (1)

For K₄[Fe(CN)₆], the oxidation state of Fe is +2. The electronic configuration of Fe²⁺ is [Ar] 3d⁶. In the presence of CN⁻, a strong field ligand, all electrons pair up, resulting in a diamagnetic complex.

Step 3: Analyze Compound (2)

For K₃[Cr(CN)₆], Cr is in the +3 oxidation state, giving Cr³⁺ with an electronic configuration of [Ar] 3d³. With CN⁻ as a strong field ligand, the electrons in Cr³⁺ pair up. However, since there are only three electrons initially, not all d orbitals can be fully paired, leading to a paramagnetic nature.

Step 4: Analyze Compound (3)

For K₃[Co(CN)₆], Co is in the +3 oxidation state. The electronic configuration of Co³⁺ is [Ar] 3d⁶. CN⁻, being a strong field ligand, causes all electrons to pair up, making the compound diamagnetic.

Step 5: Analyze Compound (4)

For K₂[Ni(CN)₄], Ni is in the +2 oxidation state, and the electronic configuration of Ni²⁺ is [Ar] 3d⁸. With CN⁻, a strong ligand, all electrons pair up, resulting in a diamagnetic complex.

Step 6: Identify Diamagnetic Compounds

From our analysis, K₄[Fe(CN)₆], K₃[Co(CN)₆], and K₂[Ni(CN)₄] are diamagnetic due to the pairing of all their electrons.

Step 7: Compare with Options

The compounds identified as diamagnetic are (1), (3), and (4). Comparing with given options, the correct selection is (c): 1, 3, and 4.

Key Concepts

Coordination Complexes

Coordination complexes are fascinating structures formed when metal atoms bind with groups of molecules or ions, called ligands. In essence, a coordination complex consists of a central metal ion surrounded by these ligands. These ligands are usually electron-rich species and form coordination bonds with the metal ion. The complex formation is driven by the metal ion's ability to accept electron pairs, which ligands donate.

The number of ligands attached to the central metal ion typically defines its coordination number. For instance, in a complex such as \( ext{K}_4[ ext{Fe(CN)}_6]\), the central iron atom is surrounded by six cyanide (CN⁻) ligands. This forms an octahedral geometry:

• The geometry of coordination complexes can vary.
• Common geometries include octahedral, tetrahedral, and square planar.
• The geometry largely depends on the number and arrangement of ligands around the metal ion.

Coordination complexes are crucial in many chemical processes and have applications in fields such as catalysis, medicine, and materials science.

Electronic Configuration of Transition Metals

The electronic configuration of transition metals is key to determining their chemical behavior, particularly in coordination complexes. Transition metals possess partially filled d orbitals, which are critical in forming chemical bonds. The unpaired electrons in these orbitals significantly influence the metal's properties such as magnetism and color.

Let's discuss some basics:

• Transition metals are typically found in the d-block of the periodic table.
• Their general electron configuration is [noble gas] \(ns^{2} (n-1)d^{1-10}\).
• When these metals form ions, they usually lose the s orbital electrons first.
• The filling of d orbitals follows Hund's rule, where electrons remain unpaired if possible, to minimize electron-electron repulsions.

The electronic configurations change when transition metals form complexes, especially when influenced by ligands, as seen in our examples: \( ext{Fe}^{2+} ext{ is [Ar] 3d}^6\), and the presence of a strong field ligand like CN⁻ can cause it to fully pair up its electrons, leading to a possible shift to diamagnetism.

Strong Field Ligands

Strong field ligands are notorious for their ability to influence the electronic configuration of transition metal ions in coordination complexes. These ligands cause a significant splitting of the d orbitals in the metal ion, which affects the magnetic and optical properties of the complex.

Understanding Ligand Field Theory:

• Ligands approach the metal ions, interacting with the d orbitals.
• This interaction causes the d orbitals to split into higher and lower energy levels.
• A strong field ligand results in a substantial energy difference between these split d orbitals.

Cyanide (CN⁻) is a classic example of a strong field ligand. Its presence in coordination complexes often leads to the pairing of electrons in the lower energy d orbitals. This results in:

• Reduced number of unpaired electrons.
• Possible shift to diamagnetism as seen in \( ext{Fe(CN)}_6^{4-}\), \( ext{Co(CN)}_6^{3-}\), and \( ext{Ni(CN)}_4^{2-}\).

By causing electrons to pair up, strong field ligands directly influence the complex's magnetic properties, switching them from what might have been paramagnetic behavior to diamagnetic.