Problem 38 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Among the following complexes \((\mathbf{K}-\mathbf{P})\) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right](\mathbf{K}),\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}(\mathrm{~L}), \mathrm{Na}_{3}\left[\mathrm{Co}(\text { oxalate })_{3}\right](\mathbf{M})\), the \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{2}(\mathbf{N}), \mathrm{K}_{2}\left[\mathrm{Pt}(\mathrm{CN})_{4}\right](\mathbf{O})\) and \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}(\mathbf{P})\) the diamagnetic complexes are (a) \(\mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N}\) (b) \(\mathrm{K}, \mathrm{M}, \mathrm{O}, \mathrm{P}\) (c) \(\mathrm{L}, \mathrm{M}, \mathrm{O}, \mathrm{P}\) (d) \(\mathrm{L}, \mathrm{M}, \mathrm{N}, \mathrm{O}\)

Step-by-Step Solution

Answer

Answer: (b) K, M, O, P

Step 1: Understanding Diamagnetic Complexes

Diamagnetic complexes are those that have no unpaired electrons. This property causes them to be repelled by a magnetic field.

Step 2: Analyze Each Complex Individually

To determine if a complex is diamagnetic, inspect the electronic configuration of the central metal ion to check for unpaired electrons.

Step 3: Analyzing K Complex

The complex is \( \mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \). Iron in this complex is in the +3 oxidation state, yielding Fe(III) which has d\(^5\) configuration. The \( \mathrm{CN}^- \) ligand causes pairing of electrons. Thus, the complex is diamagnetic.

Step 4: Analyzing L Complex

The complex is \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\mathrm{Cl}_{3} \). Cobalt here is Co(III) which has d\(^6\) configuration, and with \( \mathrm{NH}_{3} \) being a strong field ligand, all electrons pair. Hence, it is diamagnetic.

Step 5: Analyzing M Complex

The complex is \( \mathrm{Na}_{3}\left[\mathrm{Co}( ext{oxalate})_{3}\right] \). Here, cobalt is in the +3 oxidation state (d\(^6\)) and oxalate being a strong field ligand causes pairing, resulting in diamagnetic behavior.

Step 6: Analyzing N Complex

The complex is \( \left[\mathrm{Ni}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\mathrm{Cl}_{2} \). Nickel here is in the +2 oxidation state (d\(^8\)), but the H\(_2\)O ligand does not cause pairing hence it is paramagnetic.

Step 7: Analyzing O Complex

The complex is \( \mathrm{K}_{2}\left[\mathrm{Pt}(\mathrm{CN})_{4}\right] \). Platinum in the +2 state has a d\(^8\) configuration, and with strong field \( \mathrm{CN}^- \) ligands, it is diamagnetic.

Step 8: Analyzing P Complex

The complex is \( \left[\mathrm{Zn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2} \). Zn in the +2 state results in a completely filled d\(^0\) orbital, making it diamagnetic.

Step 9: Conclusion

From the previous evaluations, the diamagnetic complexes are K, L, M, O, and P.

Key Concepts

Diagrams of Complexes

In coordination chemistry, diagrams of complexes serve as visual representations that help us understand their structure and geometry. These diagrams show how ligands bond to a central metal ion. Each ligand donates electrons to the metal, creating what are called coordination bonds.
- Complexes can be depicted in different geometries, such as octahedral, tetrahedral, or square planar, based on the number of ligands and the spatial arrangement around the metal center.

For example, let’s consider the complex \([\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}\). This is an octahedral complex where six ammonia molecules (ligands) are symmetrically positioned around the cobalt ion. The diagram would show these ligands positioned at the corners of an octahedron, with the cobalt ion at the center.

• An octahedral geometry usually involves six ligands.
• Tetrahedral and square planar geometries involve four ligands.

Understanding these diagrams helps predict properties like color, magnetic behavior, and reactivity, which are crucial for identifying and explaining characteristics such as magnetism and stability.

Ligand Field Theory

Ligand Field Theory (LFT) is an essential concept used to explain the electronic structure of coordination compounds, particularly focusing on how ligands affect the energy levels of d-orbitals in transition metals. When ligands approach a central metal ion, they interact with its d-orbitals, causing a split in their energy levels.
- This energy difference, known as the "ligand field splitting energy," is key in determining a complex's color and magnetic properties.

Considering the example of \([\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}\), ammonia is a strong field ligand that creates a significant splitting between the d-orbitals. This strong field leads to electron pairing in lower energy orbitals, making the complex diamagnetic as there are no unpaired electrons.

• Strong field ligands, like cyanide (\(\mathrm{CN^-}\)) and ammonia (\(\mathrm{NH}_3\)), cause large splitting.
• Weak field ligands, such as water (\(\mathrm{H}_2\mathrm{O}\)), result in small splits and affect the magnetic behavior differently.

LFT provides insights into why different complexes have various electronic and magnetic properties, underscoring the importance of the type of ligands present.

Magnetic Properties of Complexes

Magnetic properties of coordination complexes are largely determined by the presence or absence of unpaired electrons in the metal's d-orbitals. Diamagnetism and paramagnetism are the two primary types of magnetic behaviors observed in these complexes.
- Diamagnetic complexes are those with all paired electrons, leading to a slight repulsion from magnetic fields.
- Paramagnetic complexes have at least one unpaired electron and are attracted to magnetic fields.

To identify the magnetic properties, it's crucial to examine the electron configuration of the central metal ion in the context of the ligand field. For instance, in the complex \([\mathrm{Co}(\mathrm{oxalate})_3]^{3-}\), cobalt is in a d\(^6\) configuration, and the oxalate ligands cause enough splitting to pair up all electrons, resulting in a diamagnetic nature.

• Electrons tend to fill lower energy levels first, according to the Aufbau principle.
• High-spin complexes have more unpaired electrons than low-spin complexes.

Understanding the magnetic properties provides insights into the electronic structure and helps predict the reactivity and other characteristics of the complex.