Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following complex ions, the species containing \(\mathrm{Fe}^{3+}\) in strong ligand field is (a) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) (b) \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (d) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

The species is \( \left[\mathrm{Fe}( 9mathrm{CN})_6\right]^{3-} \).

Step 1: Identify the Central Metal Ion

The central metal ion in each of the given complex ions is iron in the +3 oxidation state, denoted as \( \mathrm{Fe}^{3+} \).

Step 2: Recognize Ligand Strengths

Evaluate the ligands in each complex ion based on their position in the spectrochemical series. Ligands can be strong field or weak field. The order of ligand strength (from weakest to strongest) in the given options is \( \mathrm{F}^- < \mathrm{H_2O} < \mathrm{NH_3} < \mathrm{CN}^- \). Here, \( \mathrm{CN}^- \) is known as a strong field ligand.

Step 3: Determine the Strong Field Ligand Complex

Among the listed complex ions, \( \left[\mathrm{Fe}( 9mathrm{CN})_6\right]^{3-} \) contains \( \mathrm{CN}^- \), which is a strong field ligand. This means it will cause a large splitting of the d-orbitals in \( \mathrm{Fe}^{3+} \).

Step 4: Conclusion

The species that includes \( \mathrm{Fe}^{3+} \) in a strong ligand field is \( \left[\mathrm{Fe}( 9mathrm{CN})_6\right]^{3-} \). This is because \( \mathrm{CN}^- \) is a known strong field ligand that results in significant crystal field splitting.

Key Concepts

Complex Ions

Complex ions are formed when a central metal atom or ion is surrounded by molecules or ions called ligands. These ligands are bound to the metal core via coordinate covalent bonds. This structure is referred to as a coordination complex. The primary metal ion, like the \( \mathrm{Fe}^{3+} \) ion in our exercise, typically takes a specific charge based on its oxidation state.
Other components of complex ions, the ligands, are responsible for lending unique properties to the ion. They influence both physical and chemical characteristics, including color and magnetic properties. There are various types of ligands, such as:

• Monodentate ligands: These ligands bind through a single donor atom, e.g., \( \mathrm{F}^- \).
• Bidentate ligands: They use two donor atoms, allowing them to bind more strongly.
• Polydentate ligands: Multiple bonding sites allow for these ligands to form more stable complexes, e.g., \( \mathrm{EDTA}^{4-} \).

Spectrochemical Series

The spectrochemical series is a sequence of ligands ordered by the strength of the electric field they produce when binding to a metal ion. This series plays an important role in coordination chemistry as it helps to predict the magnitude of splitting in the d-orbitals known as crystal field splitting.
In the sequence from weakest to strongest field, we have:

• \( \mathrm{I}^- \) (weak field)
• \( \mathrm{Br}^- \)
• \( \mathrm{S}^{2-} \)
• \( \mathrm{Cl}^- \)
• \( \mathrm{F}^- \)
• \( \mathrm{H_2O} \)
• \( \mathrm{NH_3} \)
• \( \ldots \)
• \( \mathrm{CN}^- \) (strong field)

This list helps determine not only the extent of splitting but also the spectroscopic parameters of the complex ions. The placement of ligands in this series is crucial for predicting the geometry and reactivity of the complexes.

Ligand Field Strength

Ligand field strength refers to the ability of ligands to split the d-orbitals of a central metal ion. In our example, the \( \mathrm{CN}^- \) ligand is a strong field ligand that causes significant splitting of the d-orbitals in \( \mathrm{Fe}^{3+} \).
When ligands are termed as "strong field," they indicate significant d-orbital splitting that can convert high-spin complexes into low-spin ones. Conversely, weak field ligands, such as \( \mathrm{H_2O} \), generally cause smaller splitting, allowing electrons to occupy higher energy levels, resulting in high-spin complexes. This splitting profoundly influences magnetic properties:

• Low-spin complexes: fewer unpaired electrons, less paramagnetic.
• High-spin complexes: more unpaired electrons, more paramagnetic.

Crystal Field Splitting

Crystal field splitting is a quantifiable property that measures how lligand loading influences the energy levels of a metal ion's d-orbitals. When ligands approach a metal ion, the repulsion causes the d-orbitals' energy to increase.
In the context of our exercise, \( \left[ \mathrm{Fe}(\mathrm{CN})_6 \right]^{3-} \) exhibits a substantial crystal field splitting, indicating that the \( \mathrm{CN}^- \) ligand splits the d-orbitals into two energy levels. The d-orbitals become manipulated such that specific orientations—like the \( e_g \) and \( t_{2g} \) of the orbitals—see a disparity in energy levels.
The degree of crystal field splitting is given by \( \Delta \). Strong field ligands show large \( \Delta \) values, while weak field ligands have smaller ones. This splitting impacts properties such as:

• Color: dictated by absorption of certain wavelengths as electrons transition between split levels.
• Reactivity: influenced by how electrons reside in split d-orbitals.

This understanding is fundamental when designing complexes for specific functions, such as in catalysis or materials science.