Problem 85 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following pairs, the EAN of the central metal atom is not the same? (a) \(\left[\mathrm{FeF}_{6}\right]^{3^{+}}\)and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (b) \(\left[\mathrm{Fe}\left(\mathrm{CN}_{6}\right)\right]^{3-}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4^{-}}\) (c) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}\) (d) \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) and \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\)

Step-by-Step Solution

Answer

In pairs (b) and (d), the EAN of the central metal atom is not the same.

Step 1: Understand the EAN Formula

The Effective Atomic Number (EAN) can be calculated using the formula: \( \text{EAN} = Z - \text{Oxidation state} + 2 \times \text{number of ligands} \), where \(Z\) is the atomic number of the metal.

Step 2: Calculate EAN of [FeF6]3+

For \([\text{FeF}_6]^{3+}\), the metal is Fe with \(Z = 26\). Oxidation state = +3. Number of ligands = 6. \[ \text{EAN} = 26 - 3 + 2 \times 6 = 35 \]

Step 3: Calculate EAN of [Fe(CN)6]3-

For \([\text{Fe(CN)}_6]^{3-}\), Fe again with \(Z = 26\), oxidation state = +3, and number of ligands = 6. \[ \text{EAN} = 26 - 3 + 2 \times 6 = 35 \]

Step 4: Compare Pair (a) Results

Both \([\text{FeF}_6]^{3+}\) and \([\text{Fe(CN)}_6]^{3-}\) have EAN = 35, so they are the same.

Step 5: Calculate EAN of [Fe(CN)6]4-

For \([\text{Fe(CN)}_6]^{4-}\), Fe with \(Z = 26\), oxidation state = +2, and number of ligands = 6.\[ \text{EAN} = 26 - 2 + 2 \times 6 = 36 \]

Step 6: Compare Pair (b) Results

\([\text{Fe(CN)}_6]^{3-}\) has EAN = 35 and \([\text{Fe(CN)}_6]^{4-}\) has EAN = 36, so they are not the same.

Step 7: Calculate EAN of [Cr(NH3)6]3+

For \([\text{Cr(NH}_3)_6]^{3+}\), Cr with \(Z = 24\), oxidation state = +3, number of ligands = 6.\[ \text{EAN} = 24 - 3 + 2 \times 6 = 33 \]

Step 8: Calculate EAN of [Cr(CN)6]3-

For \([\text{Cr(CN)}_6]^{3-}\), Cr with \(Z = 24\), oxidation state = +3, and number of ligands = 6.\[ \text{EAN} = 24 - 3 + 2 \times 6 = 33 \]

Step 9: Compare Pair (c) Results

Both \([\text{Cr(NH}_3)_6]^{3+}\) and \([\text{Cr(CN)}_6]^{3-}\) have EAN = 33, so they are the same.

Step 10: Calculate EAN of [Ni(CO)4]

For \([\text{Ni(CO)}_4]\), Ni with \(Z = 28\), oxidation state = 0, number of ligands = 4.\[ \text{EAN} = 28 - 0 + 2 \times 4 = 36 \]

Step 11: Calculate EAN of [Ni(CN)4]2-

For \([\text{Ni(CN)}_4]^{2-}\), Ni with \(Z = 28\), oxidation state = +2, and number of ligands = 4.\[ \text{EAN} = 28 - 2 + 2 \times 4 = 34 \]

Step 12: Compare Pair (d) Results

\([\text{Ni(CO)}_4]\) has EAN = 36 and \([\text{Ni(CN)}_4]^{2-}\) has EAN = 34, so they are not the same.

Key Concepts

Coordination Compounds

Coordination compounds are fascinating structures composed of a central metal atom bonded to surrounding molecules or ions called ligands. These ligands can be anything from simple ions like chloride to complex organic molecules. The bonds formed in coordination compounds are coordinate bonds, where the ligand donates a pair of electrons to the metal center.
These compounds are represented by a formula that typically looks like \[ \left[ M(L)_n \right]^z \] where \( M \) is the central metal,\( L \) denotes the ligands, \( n \) is the number of ligands, and \( z \) represents the charge on the complex.
Coordination compounds exhibit various properties based on the nature of ligands, oxidation state of the metal, and the overall arrangement of the bonds. They are widely studied for their applications in chemistry, biology, and material science. For example, they play a crucial role in catalysis and medical imaging.

Oxidation State

The oxidation state of a metal in a coordination compound describes the total number of electrons the metal has lost or gained. It's an essential concept because it helps in predicting the properties and reactivity of the compound.
In coordination chemistry, the oxidation state of the central metal can be determined by assigning -1 for monodentate ligands such as CN\(^-\) or Cl\(^-\), 0 for neutral ligands like CO, and then balancing the total charge of the compound against the charge of the ligands.
For example, in \([FeF_6]^{3+}\),fluoride is a ligand with a -1 charge, and with six such ligands and an overall +3 charge, the oxidation state of Fe can be calculated as +3. Knowing the oxidation state is crucial, as it is directly used to calculate the Effective Atomic Number (EAN), which predicts stability and electronic arrangement in these compounds.

Ligand Field Theory

Ligand Field Theory (LFT) is a theoretical framework that explains the way electronic structures of metals are affected by the ligands surrounding them. It builds upon crystal field theory, which considers the electrostatic interactions between the ligands and metal's d-orbitals.
LFT explains how the energy levels of these d-orbitals split when ligands approach the metal. This splitting is a result of the different spatial arrangements of the ligands, and varying qualities of ligand-metal interaction.
For instance, weak field ligands, like halides, cause a small splitting, whereas strong field ligands like CN\(^-\) result in greater splitting, significantly altering the properties of the metal. This theory is crucial because it helps predict important characteristics of coordination compounds, such as their color, magnetism, and stability. The Effective Atomic Number (EAN) concept also intertwines with LFT, as higher EANs can suggest a more filled, and thus, stable electronic configuration.