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 ion \(\left[\mathrm{Fe}( ext{CN})_6\right]^{3-}\) contains \(\mathrm{Fe}^{3+}\) in the strongest ligand field.

Step 1: Identify Metal Ion and Oxidation State

The exercise asks for species containing \(\mathrm{Fe}^{3+}\). Identify which complexes have \(\mathrm{Fe}^{3+}\) as the central metal ion by observing their chemical formulas. All given options have Fe as the central ion. The oxidation state of Fe can be found by considering the charges: In each case, the sum of the ligand charges and the central metal oxidation state should equal the overall charge on the complex.

Step 2: Determine Ligand Field Strength

Examine each option for the ligands surrounding \(\mathrm{Fe}^{3+}\). Ligands are classified by their field strength, which affects the splitting of d-orbitals in the central metal ion. Common ligand field strengths, from weak to strong, are: \[\text{I}^{-} < \text{Br}^{-} < \text{SCN}^{-} < \text{Cl}^{-} < \text{F}^{-} < \text{OH}^{-} < \text{O}^{2-} < \text{C}_2\text{O}_4^{2-} < \text{H}_2\text{O} < \text{NH}_3 < \text{en} < \text{bipy} < \text{phen} < \text{NO}_2^{-} < \text{CN}^{-} < \text{CO}\] \(\text{CN}^{-}\) is considered the strongest among the options given.

Step 3: Match Ligands with Complex

Identify the ligands in each complex and compare them with the list in the previous step. \[\begin{align*} \left[\mathrm{FeF}_{6}\right]^{3-} & : \text{Ligand - }\mathrm{F}^{-} \ \left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} & : \text{Ligand - }\mathrm{NH}_{3} \ \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} & : \text{Ligand - }\mathrm{CN}^{-} \ \left[\mathrm{Fe}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+} & : \text{Ligand - }\mathrm{H}_{2}\mathrm{O} \end{align*}\] \(\text{CN}^{-}\) is the strongest ligand in this list, suggesting the strongest ligand field.

Step 4: Conclusion

Based on the ligand field strengths, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) contains \(\mathrm{Fe}^{3+}\) surrounded by the strongest field ligands (cyanide) compared to the other complexes. Thus, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is the complex with \(\mathrm{Fe}^{3+}\) in the strongest ligand field.

Key Concepts

Ligand Field Theory

Ligand field theory helps us understand how ligands influence the energy levels of the d-orbitals in a metal ion. When ligands approach a metal ion, they cause the d-orbitals to split into two energy levels. This splitting happens because the bonding and non-bonding interactions between the ligands and the orbitals are different.
Different ligands will cause different amounts of splitting, depending on their field strength. When we talk about strong ligands, such as \( ext{CN}^{-}\), they cause a large energy difference between the split d-orbitals. This is known as having a strong ligand field.
By understanding ligand field theory, chemists can predict the properties of complex ions, such as their color, magnetism, and stability. These predictions arise because the electronic configuration of the metal ion changes with the energy difference between the d-orbitals. With strong field ligands like \( ext{CN}^{-}\), the electrons are paired in lower energy orbitals, potentially creating a diamagnetic complex.

Oxidation States

Understanding oxidation states is crucial in coordination chemistry. The oxidation state of a metal ion in a complex tells us how many electrons the metal has gained or lost compared to its elemental state. This number helps in determining the charge on a complex ion and the overall stability of the complex.
In the case of \( ext{Fe}^{3+}\), the iron ion has lost three electrons. This is a common oxidation state for iron, often found in high-spin and low-spin configurations within complexes depending on the ligand strength.
To find the oxidation state of a metal within a complex, it's important to account for the charges of the surrounding ligands and the overall charge of the complex. For the complex \([ ext{Fe(CN)}_6]^{3-}\), the complex charge and ligand charges together indicate the iron is in the +3 oxidation state. This math helps in balancing and understanding the electrochemical behavior of these complexes during reactions.

Ligand Strength

Ligand strength refers to the ability of a ligand to split the d-orbitals of the central metal ion, as per ligand field theory. Different ligands exert different strengths of field, causing varying energy splits within the orbital energies.
The spectrochemical series is a list that ranks ligands from weakest to strongest based on their ability to cause this orbital splitting. For instance, \( ext{F}^{-}\) and \( ext{H}_2 ext{O}\) are weaker ligands, while \( ext{NH}_3\) and \( ext{CN}^{-}\) are much stronger. Strong ligands like \( ext{CN}^{-}\) cause a significant splitting of orbitals, meaning orbitals with strong-field ligands might pair electrons differently.
This understanding is important because it directly influences the properties of a complex ion, such as its color and reactivity. Strong field ligands can change the way electrons are configured, potentially resulting in changes to the compound's magnetic properties, turning a paramagnetic substance into diamagnetic.

Complex Ions

Complex ions are charged entities consisting of a central metal ion surrounded by molecules or ions known as ligands. These ligands can be simple ions like \( ext{F}^{-}\) or more complex molecules such as \( ext{NH}_3\) and \( ext{CN}^{-}\).
The type and arrangement of these ligands determine the characteristics of the complex. The central metal ion, such as \( ext{Fe}^{3+}\), interacts with these ligands to form a stable coordination compound. The specific binding of the ligands impacts the three-dimensional shape of the complex, which further affects its chemical reactivity and interaction with light.
Complex ions are essential in many biological systems and industrial processes. For example, hemoglobin functions due to its complex ion structure with iron in the center.

• ext{Structural diversity is vast, often leading to unique optical and magnetic properties.}
• ext{Application in catalysis, medical treatments, imaging and electronic devices.}
• ext{Color in transition metals generally arises from d-d electronic transitions within these complex ions.}

Understanding how these ions interact and the roles their structures play underpins much of inorganic and bioinorganic chemistry.