Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (a) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}\) (b) \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (d) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\)

Step-by-Step Solution

Answer

The complex \([\text{Co}^3+ (CN)_6]^{3-}\) exhibits the lowest paramagnetic behavior.

Step 1: Review Electronic Configurations

The complexes given are cyano complexes, where CN is a strong field ligand. This means it will cause pairing of electrons in the d orbitals. Start by identifying the electron configuration of the central metal ion in its oxidation state. - \(\text{Cr}^{3+}\) has the configuration \([\text{Ar}] 3d^3\).- \(\text{Mn}^{3+}\) has the configuration \([\text{Ar}] 3d^4\).- \(\text{Fe}^{3+}\) has the configuration \([\text{Ar}] 3d^5\).- \(\text{Co}^{3+}\) has the configuration \([\text{Ar}] 3d^6\).

Step 2: Determine Electron Pairing

When the ligands are strong field, such as CN, they cause pairing of electrons. Analyze each configuration.- In \([\text{Cr}^3+ (CN)_6]^{3-}\), all electrons in \(3d\) remain unpaired (3 unpaired electrons).- In \([\text{Mn}^3+ (CN)_6]^{3-}\), CN causes partial pairing (2 unpaired electrons).- In \([\text{Fe}^3+ (CN)_6]^{3-}\), CN causes partial pairing (1 unpaired electron).- In \([\text{Co}^3+ (CN)_6]^{3-}\), CN causes complete pairing (0 unpaired electrons).

Step 3: Assess Paramagnetism

Paramagnetism is due to unpaired electrons. The complex with the least number of unpaired electrons will exhibit the lowest paramagnetic behavior. From the pairing analysis:- \([\text{Cr}^3+ (CN)_6]^{3-}\) has 3 unpaired electrons.- \([\text{Mn}^3+ (CN)_6]^{3-}\) has 2 unpaired electrons.- \([\text{Fe}^3+ (CN)_6]^{3-}\) has 1 unpaired electron.- \([\text{Co}^3+ (CN)_6]^{3-}\) has 0 unpaired electrons.

Step 4: Conclusion

Conclude which compound has the lowest paramagnetic behavior. Since the Co complex \([\text{Co}^3+ (CN)_6]^{3-}\) has 0 unpaired electrons, it does not exhibit paramagnetism, making it the complex with the lowest paramagnetic behavior.

Key Concepts

Paramagnetism

Paramagnetism is a fundamental property observed in substances due to the presence of unpaired electrons in their atomic or molecular orbitals. These unpaired electrons have magnetic moments that align themselves with external magnetic fields, causing the material to be attracted toward the source of the magnetic field. However, when electrons are paired in orbitals, their magnetic moments cancel each other out, making the substance diamagnetic and thus not responsive to magnetic fields.

In coordination chemistry, the paramagnetic behavior of a compound can tell us a great deal about its electronic configuration and electron pairing in the d-orbitals. For example, in coordination complexes, a higher number of unpaired electrons generally leads to stronger paramagnetic behavior. To assess paramagnetism in coordination compounds, it is crucial to determine the correct electronic configuration of the central metal ion and count the number of unpaired electrons. The complex with the lowest number of unpaired electrons, such as \([\text{Co}^3+ (CN)_6]^{3-}\), which has full electron pairing and zero unpaired electrons, exhibits the least or no paramagnetic behavior.

Crystal Field Theory

Crystal Field Theory (CFT) is an essential concept in the study of coordination compounds. It explains how the degenerate d orbitals of a metal ion are affected when they interact with surrounding ligands, which are molecules or ions that donate electron pairs to the metal. The interaction between ligands and the metal ion leads to the splitting of d orbitals into different energy levels. This splitting, known as crystal field splitting, is pivotal in determining the electronic configuration and magnetic properties of the complex.

• In an octahedral field, typical for complexes like \([\text{Co}^3+ (CN)_6]^{3-}\), the five d orbitals split into two higher-energy orbitals (known as e_g) and three lower-energy orbitals (t_2g).
• The extent of this splitting depends on the nature of the ligand. Strong field ligands, like CN^-, lead to larger splittings, often resulting in the pairing of electrons in lower-energy orbitals.

Understanding how d orbitals are arranged and filled helps predict whether a complex will be high-spin or low-spin, which in turn influences its paramagnetic properties. For example, \([\text{Co}^3+ (CN)_6]^{3-}\) demonstrates complete electron pairing due to the significant splitting induced by the strong field CN^- ligand.

Ligand Field Strength

In coordination chemistry, ligand field strength is a crucial factor that influences the electron configuration of complexes. Ligands differ in their ability to split the d orbitals of a central metal ion, which significantly affects the electronic and magnetic properties of the resulting complex.

• Strong field ligands cause a large difference in energy between the split d orbitals. This often results in lower spin complexes, where electrons are paired in the lower energy orbitals before higher energy orbitals are filled.
• Conversely, weak field ligands produce smaller energy differences and are more likely to facilitate the formation of high-spin complexes with unpaired electrons in higher energy orbitals.

The spectrochemical series ranks ligands based on their field strength from weak to strong. CN^- is considered a strong field ligand, inducing significant d orbital splitting, and causing electron pairing in coordination complexes such as \([\text{Co}^3+ (CN)_6]^{3-}\). Understanding ligand field strength allows chemists to predict and tune the properties of coordination compounds, including their color, spin state, and magnetic characteristics.