Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are diamagnetic? (a) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (b) \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

(b) \\([\mathrm{Zn(NH_3)_4}]^{2+}\\) and (c) \\([\mathrm{Ni(CN)_4}]^{2-}\\) are diamagnetic.

Step 1: Determine the electronic configuration

For each given complex, determine the electronic configuration of the metal ion. This helps us understand the distribution of electrons in the d-orbitals.- For \([\mathrm{Ni}]^{2+}\): The electronic configuration is \[\mathrm{Ni}^{2+} = [\mathrm{Ar}]\,3d^8\,4s^0\].- For \([\mathrm{Zn}]^{2+}\): The electronic configuration is \[\mathrm{Zn}^{2+} = [\mathrm{Ar}]\,3d^{10}\,4s^0\].- For \([\mathrm{Co}]^{3+}\): The electronic configuration is \[\mathrm{Co}^{3+} = [\mathrm{Ar}]\,3d^6\,4s^0\].

Step 2: Identify ligand field strength

Identify the ligand field strength which helps to determine whether the entering orbitals will form high-spin or low-spin complexes. Ligands like CN^- are strong field ligands leading to low-spin complexes, and H2O or NH3 are weak field ligands which often lead to high-spin configurations.- \(\mathrm{H_2O}\) is a weak field ligand.- \(\mathrm{NH_3}\) is a weak to moderate field ligand.- \(\mathrm{CN}^-\) is a strong field ligand.

Step 3: Determine spin state and magnetic property

Based on the ligand strength, determine whether the complex would be high-spin or low-spin, which allows us to find out whether any unpaired electrons are present.- For \([\mathrm{Ni(H_2O)_6}]^{2+}\): With weak field ligands, the configuration remains high-spin with unpaired electrons.- For \([\mathrm{Zn(NH_3)_4}]^{2+}\): The fully filled d-orbital \(3d^{10}\) makes it diamagnetic.- For \([\mathrm{Ni(CN)_4}]^{2-}\): The presence of a strong field ligand causes pairing of all d-electrons, making it low-spin and diamagnetic.- For \([\mathrm{Co(NH_3)_6}]^{3+}\): The weak to moderate field ligands result in a high-spin complex with unpaired electrons.

Step 4: Conclusion

Compare the determination of unpaired electrons to conclude which complexes are diamagnetic. Diamagnetic complexes have all electrons paired.- \[\mathrm{Zn(NH_3)_4}]^{2+}\] is diamagnetic.- \[\mathrm{Ni(CN)_4}]^{2-}\] is diamagnetic.Therefore, options (b) and (c) are diamagnetic.

Key Concepts

Ligand Field Theory

Ligand Field Theory is a crucial concept in understanding the behavior of transition metal complexes. This theory explains how the electronic structure of metal ions is affected by the surrounding ligands, essentially altering the energy levels of the d-orbitals. When ligands approach a metal ion, they influence the splitting of d-orbitals into different energy levels. This phenomenon, often referred to as "crystal field splitting," is integral to predicting the electronic configurations of complexes.

• Strong field ligands like CN^- cause a large splitting of the d-orbitals. This typically results in low-spin complex formations, where electrons pair up in lower energy orbitals before occupying higher levels.
• Weak field ligands such as H₂O and NH₃ result in smaller splitting. This means more unpaired electrons and often leads to high-spin complexes, where electrons are spread across both low and high energy orbitals to minimize repulsion.

Understanding whether a ligand is a strong or weak field helps predict if the complex will be diamagnetic or paramagnetic, greatly influencing their chemical and physical properties.

Magnetic Properties

Magnetic properties of transition metal complexes stem from the presence or absence of unpaired electrons. Diamagnetism and paramagnetism are the two primary magnetic responses observed:

• Diamagnetic substances have all paired electrons. In these complexes, the magnetic effects cancel out, causing them to be generally repelled by magnetic fields. An example is \(\left[\mathrm{Zn(NH_3)_4}\right]^{2+}\), which is diamagnetic due to its fully paired d-orbital electrons.
• Paramagnetic substances contain unpaired electrons, leading to a net magnetic moment. Such complexes are attracted to magnetic fields. High-spin complexes, where ligands are weak field, are often paramagnetic, much like \(\left[\mathrm{Co(NH_3)_6}\right]^{3+}\).

The effect of ligands on the spin states directly impacts these magnetic properties. Differentiating between high-spin and low-spin states is essential to predicting and explaining the magnetic behavior of transition metal complexes.

Electronic Configuration of Transition Metals

Understanding the electronic configuration of transition metals is fundamental when analyzing their complexes. Transition metals generally have partially filled d-orbitals. Their electronic configurations are typically written as \([ ext{previous noble gas}] (n-1)d^{1-10}ns^{0-2}\). For instance:

• Ni²⁺: Often \([ ext{Ar}] 3d^8 4s^0\). This configuration helps predict whether a nickel complex, such as \(\left[\mathrm{Ni(CN)_4}\right]^{2-}\), will be diamagnetic due to the strong field effect of CN^-.
• Zn²⁺: Configured as \([ ext{Ar}] 3d^{10} 4s^0\), making all electrons paired and leading to a diamagnetic nature in \(\left[\mathrm{Zn(NH_3)_4}\right]^{2+}\).

Electronic configurations reveal not only the distribution of electrons across orbitals but also hint at possible oxidation states, bonding characteristics, and overall stability of the complex. Understanding this helps in deducing the chemical behavior of metal ions in different coordination environments.