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

Pairs (b) and (d) have different EANs.

Step 1: Understand EAN

The effective atomic number (EAN) is calculated by the formula: \( \text{EAN} = \text{atomic number of the metal} - \text{oxidation state} + 2 \times \text{number of ligands} \). This measures the apparent full electron shell configuration attained by the central metal atom.

Step 2: Calculate EAN for \([\mathrm{FeF}_{6}]^{3+}\)

Iron has an atomic number of 26. In the complex, \([\mathrm{FeF}_{6}]^{3+}\), if we assume oxidation state \(+3\), the EAN calculation is:\[\text{EAN} = 26 - 3 + 6 \times 2 = 35\]

Step 3: Calculate EAN for \([\mathrm{Fe}( ext{CN})_{6}]^{3-}\)

For iron in this complex, the assumed oxidation state is also \(+3\). The EAN is:\[\text{EAN} = 26 - 3 + 6 \times 2 = 35\]

Step 4: Compare Pair (a)

\([\mathrm{FeF}_{6}]^{3+}\) and \([\mathrm{Fe}( ext{CN})_{6}]^{3-}\) both give an EAN of 35. Hence, the EAN is the same for pair (a).

Step 5: Calculate EAN for \([\mathrm{Fe}( ext{CN})_{6}]^{3-}\) and \([\mathrm{Fe}( ext{CN})_{6}]^{4-}\)

Since each case involves \([\mathrm{Fe}( ext{CN})_{6}]\), reevaluate only the charge influence:1. For \([\mathrm{Fe}( ext{CN})_{6}]^{3-}\): Same calculation as Step 3, EAN = 35.2. For \([\mathrm{Fe}( ext{CN})_{6}]^{4-}\): Oxidation state possibly reduced by one, EAN = 36.

Step 6: Compare Pair (b)

\([\mathrm{Fe}( ext{CN})_{6}]^{3-}\) and \([\mathrm{Fe}( ext{CN})_{6}]^{4-}\), differ by a unit in EAN, thus, pair (b) does not have the same EAN.

Step 7: Calculate EAN for \([\mathrm{Cr}( ext{NH}_{3})_{6}]^{3+}\)

Chromium has an atomic number of 24. With an assumed +3 oxidation state, the EAN is:\[\text{EAN} = 24 - 3 + 6 \times 2 = 33\]

Step 8: Calculate EAN for \([\mathrm{Cr}( ext{CN})_{6}]^{3-}\)

With chromium in an assumed oxidation state of +3, the EAN is:\[\text{EAN} = 24 - 3 + 6 \times 2 = 33\]

Step 9: Compare Pair (c)

Both result in an EAN of 33, therefore pair (c) has the same EAN.

Step 10: Calculate EAN for \([\mathrm{Ni}( ext{CO})_{4}]\)

Nickel has an atomic number of 28 and, with CO being a neutral ligand, assumed oxidation state 0:\[\text{EAN} = 28 - 0 + 4 \times 2 = 36\]

Step 11: Calculate EAN for \([\mathrm{Ni}( ext{CN})_{4}]^{2-}\)

The oxidation state for nickel may be assumed as +2:\[\text{EAN} = 28 - 2 + 4 \times 2 = 34\]

Step 12: Compare Pair (d)

\([\mathrm{Ni}( ext{CO})_{4}]\) and \([\mathrm{Ni}( ext{CN})_{4}]^{2-}\) yield EAN differences. Hence, they do not have the same EAN.

Key Concepts

Coordination Chemistry

Coordination chemistry is all about understanding the unique arrangements where central metal atoms bind with molecules or ions known as ligands. This forms coordination complexes, a prevalent concept in chemistry.
Coordination complexes have a distinct formula, where the number of bonds (ligands to metal atom) is referred to as the coordination number.
- Central Metal Atom: This is the metal that forms the core of the complex. Often these are transition metals, renowned for their ability to bind with ligands. - Ligands: These species donate electron pairs to the metal atom, forming coordination bonds.
This collective forms a stable structure crucial for many biological and industrial processes. The study of these complexes provides insights into metal ion reactivity, symmetry, and structure.

Oxidation State

The oxidation state of a metal within a complex is pivotal for calculating its effective atomic number (EAN) and understanding its reactivity.
The oxidation state is essentially the charge of the central metal ion if we assume complete transfer of electrons from ligands.
- Determining the Oxidation State: Consider the known charges of all components. For instance, in \([\mathrm{FeF}_{6}]^{3+}\), if "Fe" accounts for a charge of \(+3\), \([\mathrm{F}^{-}]\) being \(-1\), hence the oxidation state for "Fe" is \(+3\).- Effect on EAN: More positive oxidation states mean fewer electrons around central metal, reducing potential to attain a filled shell.
Identifying oxidation states permit us to delve deeper into complex stability and reactivity.

Ligands in Coordination Compounds

Ligands are crucial participants in the formation of coordination compounds. Their role transcends being just an electron pair donor, impacting the properties of the metal center profoundly.
Ligands can be categorized based on their charge and number of electrons they donate to a central metal atom:

• Neutral Ligands: Such as CO, H₂O, and NH₃, donate electron pairs without contributing a charge.
• Charged Ligands: Like CN^- or F^-, possess a charge, influencing the overall charge and oxidation state of the complex.

Understanding the nature of ligands assists in predicting the behavior and establishing equilibrium in the resulting coordination complex.

Transition Metals Chemistry

Transition metals are a special group in the periodic table known for their variable oxidation states and ability to form complex ions with ligands, making them central to coordination chemistry.
Key characteristics of transition metals include:

• Multiple Oxidation States: Their d orbits allow for the exchange of varied electrons states.
• Catalytic Properties: Transition metals often serve as catalysts in both industrial and biological reactions.
• Colored Compounds: Due to d-d transitions, many transition metal compounds exhibit vibrant colors.

In coordination compounds like \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), these characteristics come into play, as transition metals define the properties of complex ions through their unique electron donation and acceptance capabilities.