Problem 141 - A Complete Resource Book in Chemistry for JEE Main

Question

Amongst the following, the total number of species which are diamagnetic is ______ . \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})], \mathrm{K}_{3}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right], \mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right],\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, \mathrm{K}_{2} \mathrm{TiF}_{6}\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\)

Step-by-Step Solution

Answer

There are 6 diamagnetic species.

Step 1: Understanding Diamagnetism

Diamagnetic substances have all their electrons paired. In coordination complexes, we need to determine the electron configuration and the presence of unpaired electrons in the central metal.

Step 2: Analyzing \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})]\)

\(\mathrm{Fe}^{2+}\) in \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\) has an electron configuration of \([\mathrm{Ar}]\ 3d^6\). The strong field ligand \(\mathrm{CN}^-\) pairs up all electrons, making it diamagnetic.

Step 3: Analyzing \(\mathrm{K}_{3}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]\)

\(\mathrm{Cr}^{3+}\) in \(\mathrm{K}_{3}[\mathrm{Cr}(\mathrm{CN})_{6}]\) has the electron configuration \([\mathrm{Ar}]\ 3d^3\). With \(\mathrm{CN}^-\) as a ligand, this complex still has unpaired electrons, making it paramagnetic.

Step 4: Analyzing \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\)

\(\mathrm{Co}^{3+}\) in \(\mathrm{K}_{3}[\mathrm{Co}(\mathrm{CN})_{6}]\) with electron configuration \([\mathrm{Ar}]\ 3d^6\) paired by \(\mathrm{CN}^-\) is diamagnetic.

Step 5: Analyzing \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]\)

\(\mathrm{Ni}^{2+}\) in \(\mathrm{K}_{2}[\mathrm{Ni}(\mathrm{CN})_{4}]\) has electron configuration \([\mathrm{Ar}]\ 3d^8\) with a strong field ligand \(\mathrm{CN}^-\), resulting in all paired electrons, thus it is diamagnetic.

Step 6: Analyzing \([\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

\(\mathrm{Co}^{3+}\) in \([[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}]^{3+}\) has electron configuration \([\mathrm{Ar}]\ 3d^6\), considering that \(\mathrm{NH}_3\) is a strong field ligand, allowing electron pairing, so it is diamagnetic.

Step 7: Analyzing \(\mathrm{K}_{2}\mathrm{TiF}_{6}\)

\(\mathrm{Ti}^{4+}\) in \(\mathrm{K}_{2}\mathrm{TiF}_{6}\) has electron configuration \([\mathrm{Ar}]\) with no unpaired electrons, making it diamagnetic.

Step 8: Analyzing \([\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\)

\(\mathrm{Pt}^{2+}\) in \([[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}]^{2+}\) has electron configuration \([\mathrm{Xe}]\ 4f^{14}\ 5d^8\) with all paired electrons due to the strong field ligand \(\mathrm{NH}_3\), making it diamagnetic.

Step 9: Counting Diamagnetic Species

Based on the analysis: \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\), \(\mathrm{K}_{3}[\mathrm{Co}(\mathrm{CN})_{6}]\), \(\mathrm{K}_{2}[\mathrm{Ni}(\mathrm{CN})_{4}]\), \([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{3+}\), \(\mathrm{K}_{2}\mathrm{TiF}_{6}\), \([\mathrm{Pt}(\mathrm{NH}_{3})_{4}]^{2+}\) are diamagnetic. That makes a total of 6 diamagnetic species.

Key Concepts

Coordination Complexes

Coordination complexes are compounds consisting of a central metal atom or ion bonded to surrounding molecules or ions known as ligands. These structures play a crucial role in understanding properties such as magnetism and color in chemistry. The metal atom or ion acts as the center to which the ligands are attached, forming coordinate covalent bonds.

One important factor in coordination complexes is the coordination number, which refers to the number of ligand bonds to the central metal. This number dictates the geometry of the complex, such as octahedral or tetrahedral shapes. Coordination complexes are important in the study of electron configurations and ligand impacts on metal properties.

• Central Metal: A transition metal that holds the complex together and provides potential sites for chemical reactions.
• Ligands: Molecules or ions that are surrounded by the central metal, which donate electron pairs to form bonds.
• Coordination Number: The number of ligand atoms bonded to the central metal, influencing complex geometry.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom or molecule, typically represented by a notation that details the occupancy of an atom's energy levels by electrons. In coordination complexes, the electron configuration of the central metal can greatly influence the complex's magnetic and optical properties.

Transition metals, often found in coordination complexes, have partially filled d orbitals. For example, \([\text{Fe}^{2+}]\) in \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\) has an electron configuration of \(\left[\text{Ar}\right]\ 3d^6\). Strong field ligands like cyanide (\(\text{CN}^-\)) can pair up electrons, filling the d orbitals and leading to a lack of unpaired electrons. This full pairing results in diamagnetic properties. Conversely, when there are unpaired electrons, the complex is paramagnetic.

• Electron Distribution: Arrangement in atomic orbitals influences chemical reactivity and bonding.
• Strong Field Ligands: Lead to the pairing of electrons, affecting the magnetic properties of the complex.
• Unpaired Electrons: Presence results in paramagnetism.

Ligand Field Theory

Ligand field theory (LFT) is a method that explains how the arrangement of ligands around a central metal ion influences the energies of its d orbitals. This theory helps understand how ligands impact the splitting of d orbitals, leading to distinctive magnetic and optical properties of coordination compounds.

In ligand field theory, ligands are considered to create an electric field around the central metal atom. This field affects the energy of the d orbitals, leading to a phenomenon known as crystal field splitting. Strong field ligands, like \(\text{CN}^-\) or \(\text{NH}_3\), cause a significant energy gap, or splitting, which forces { the pairing of d electrons, making complexes frequently diamagnetic.

• Crystal Field Splitting: The separation of d orbital energies due to ligand fields.
• Strong vs. Weak Field: Strong field ligands cause wider orbital splitting, promoting electron pairing.
• Magnetic Properties: Influenced by electron pairing, complexes can be diamagnetic or paramagnetic.