Problem 143 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

(b) \([\text{Co(CN)}_6]^{3-}\) has the lowest paramagnetic behaviour.

Step 1: Determine the Oxidation State

First, determine the oxidation state of the central metal ion in each complex. Cyanide, \(CN^-\), has a charge of \(-1\). (a) \( ext{Fe} ightarrow +3 \) (b) \( ext{Co} ightarrow +3 \) (c) \( ext{Mn} ightarrow +5 \) (d) \( ext{Cr} ightarrow +3 \)

Step 2: Identify Electron Configuration

Find the electron configuration of each metal ion based on its oxidation state. (a) \([ ext{Fe}^{3+}]\) has \(d^5\) configuration. (b) \([ ext{Co}^{3+}]\) has \(d^6\) configuration. (c) \([ ext{Mn}^{5+}]\) has \(d^2\) configuration. (d) \([ ext{Cr}^{3+}]\) has \(d^3\) configuration.

Step 3: Evaluate the Ligand Field Strength

Recognize that CN\(^-\) is a strong field ligand, which tends to cause pairing of electrons in d-orbitals if possible, leading to low-spin configurations.

Step 4: Determine Spin States

Based on the ligand field strength and electron configurations: (a) \([\text{Fe(CN)}_6]^{3-}\): High spin or low spin is possible (depends on pairing energy). Low spin results in \(t_{2g}^5\). (b) \([\text{Co(CN)}_6]^{3-}\): Low spin \(t_{2g}^6\). (c) \([\text{Mn(CN)}_6]^{5-}\): High spin \(t_{2g}^2\) mostly. (d) \([\text{Cr(CN)}_6]^{3-}\): High spin \(t_{2g}^3\).

Step 5: Calculate Unpaired Electrons

Count the number of unpaired electrons for each configuration: (a) \([\text{Fe(CN)}_6]^{3-}\): Typically 1 unpaired electron in low spin. (b) \([\text{Co(CN)}_6]^{3-}\): 0 unpaired electrons (paired \(t_{2g}^6\)). (c) \([\text{Mn(CN)}_6]^{5-}\): 2 unpaired electrons. (d) \([\text{Cr(CN)}_6]^{3-}\): 3 unpaired electrons.

Step 6: Compare Paramagnetic Behaviour

The paramagnetic behaviour is inversely related to the number of unpaired electrons. The fewer unpaired electrons, the lower the paramagnetic behaviour. Here, \([\text{Co(CN)}_6]^{3-}\) has the lowest number of unpaired electrons (0), indicating it has the lowest paramagnetic behaviour.

Key Concepts

Electron Configuration

When we discuss electron configuration in coordination complexes, we're referring to the distribution of electrons among the available d-orbitals of the central metal ion. Each metal ion has a specific electron configuration that depends on its oxidation state. In these cyano complexes, we see metal ions like Fe, Co, Mn, and Cr each in different oxidation states.

• For instance, in \([\text{Fe(CN)}_6]^{3-}\), iron is in the \( +3 \) state and has a \(d^5\) configuration. This means there are 5 electrons spread over the d-orbitals.
• Likewise, cobalt in \( [\text{Co(CN)}_6]^{3-} \) is also in the \( +3 \) state but has a \(d^6\) configuration with 6 electrons to configure.

Understanding electron configuration is crucial as it sets the stage for further interactions within the complex, such as those involving ligands, which can alter electron arrangements through ligand field theory.

Ligand Field Theory

Ligand Field Theory (LFT) is essential for understanding how ligands, specifically the strong field ligand CN\(^-\) in this context, impact the electron distribution in metal d-orbitals.

• CN\(^-\) is known as a strong field ligand, meaning it can significantly influence the energy levels of the d-orbitals, potentially causing electron pairing within lower energy orbitals.
• According to LFT, when CN\(^-\) surrounds a metal ion, it causes a split in the d-orbitals into two sets of different energy levels, often represented as \( t_{2g} \) and \( e_g \).
• The extent of this split, known as the crystal field splitting energy, dictates whether the electrons remain unpaired (high-spin) or pair up (low-spin) if the energy gap is large enough.

This understanding helps predict the spin states and magnetic properties of coordination complexes like those mentioned in the exercise.

Spin States

The concept of spin states in coordination complexes is closely tied to how electrons pair up in the presence of ligand fields. Spin states determine the magnetic properties of the complexes.

• A high-spin state occurs when electrons fill the higher energy orbitals before pairing in the lower energy ones. This typically results in more unpaired electrons.
• A low-spin state, on the other hand, arises when strong field ligands like CN\(^-\) cause electrons to pair in the lower energy \( t_{2g} \) orbitals first, reducing the number of unpaired electrons.

In the given complexes, we observe different behaviors:

• ewcommand{\llergod} For example, \( [\text{Co(CN)}_6]^{3-} \) exhibits a low-spin \(d^6\) configuration.
• Conversely, \( [\text{Mn(CN)}_6]^{5-} \) maintains a high-spin \(d^2\) configuration.

Understanding these concepts helps predict which complex will have more or fewer unpaired electrons, directly affecting their paramagnetic behavior.

Unpaired Electrons

The number of unpaired electrons in a coordination complex is a major determinant of its paramagnetic properties. Paramagnetism arises from unpaired electrons, which generate a magnetic field when exposed to an external magnetic field.

• A complex with unpaired electrons, such as \( [\text{Mn(CN)}_6]^{5-} \), will exhibit paramagnetic behavior due to the presence of these unpaired spins.
• In contrast, a complex like \( [\text{Co(CN)}_6]^{3-} \), with all electrons paired, shows no unpaired electrons, thereby exhibiting no paramagnetism or being diamagnetic.

Investigating the number of unpaired electrons provides insight into the magnetic nature of a complex, which is crucial for applications in magnetic materials and understanding bioinorganic chemistry.