Problem 51 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For the octahedral complexes of \(\mathrm{Fe}^{3+}\) in \(\mathrm{SCN}^{-}\)(thiocyanato-S) and in \(\mathrm{CN}^{-}\)ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is [Atomic number of \(\mathrm{Fe}=26]\)

Step-by-Step Solution

Answer

4 Bohr Magnetons.

Step 1: Determine Electron Configuration of Fe

Since iron (Fe) has an atomic number of 26, its ground state electron configuration is \([ ext{Ar} ] 3d^6 4s^2\). For \(\mathrm{Fe}^{3+}\), this becomes \([ ext{Ar} ] 3d^5\) due to the loss of three electrons.

Step 2: Identify Ligand Field Strength

\(\mathrm{SCN}^{-}\) is a weak field ligand and \(\mathrm{CN}^{-}\) is a strong field ligand. This affects the splitting of d-orbitals in an octahedral field.

Step 3: Spin State with SCN- (Weak Field)

With a weak field ligand like \(\mathrm{SCN}^{-}\), \(\mathrm{Fe}^{3+}\) remains in a high-spin state, keeping the electrons unpaired as \( t_{2g}^3 e_g^2\). This configuration results in 5 unpaired electrons.

Step 4: Calculate Magnetic Moment with SCN-

The spin-only magnetic moment is given by \(\mu = \sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons. For \(n=5\), \(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92\) Bohr Magnetons.

Step 5: Spin State with CN- (Strong Field)

With a strong field ligand like \(\mathrm{CN}^{-}\), \(\mathrm{Fe}^{3+}\) is in a low-spin state, resulting in the configuration \( t_{2g}^5 e_g^0\). This means there is only 1 unpaired electron.

Step 6: Calculate Magnetic Moment with CN-

For 1 unpaired electron, \(\mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73\) Bohr Magnetons.

Step 7: Calculate Difference in Magnetic Moments

The difference in the spin-only magnetic moments is \(5.92 - 1.73 = 4.19\), approximated to the nearest integer as 4 Bohr Magnetons.

Key Concepts

Spin-Only Magnetic Moment

In coordination chemistry, the spin-only magnetic moment is an important concept to understand how complexes of transition metals behave. It mainly depends on the number of unpaired electrons present in a metal's ion and can be calculated using the formula:

• \( \mu = \sqrt{n(n+2)} \)

where \( n \) is the number of unpaired electrons. Each unpaired electron contributes a magnetic moment, measured in Bohr Magnetons.
For example, in the case of an octahedral complex with \( \mathrm{Fe}^{3+} \) ion, if all d-electrons remain unpaired (as with a weak ligand field), this results in a high-spin state with a higher magnetic moment. Conversely, if electrons are paired due to a strong ligand field, the result is a low-spin state with a lower magnetic moment.
This difference in magnetic moments is critical in determining the nature of the ligands and the resulting electronic configuration of the metal ion.

Electron Configuration

Electron configuration is the arrangement of electrons in atomic or molecular orbitals. For transition metals like \( \mathrm{Fe}\), understanding electron configuration is essential to predicting chemical behavior in different environments.
For example, the element \( \mathrm{Fe} \) typically has a ground state electron configuration of:

• \([ \text{Ar} ] 3d^6 4s^2\)

This changes when forming the \( \mathrm{Fe}^{3+} \) ion. It loses three electrons and its configuration becomes \([ \text{Ar} ] 3d^5 \).In octahedral complexes, the electron configuration of the metal ion changes again due to interactions with surrounding ligands. For example:

• With a weak field ligand, such as \( \mathrm{SCN}^{-} \), the electron configuration remains as high-spin: \( t_{2g}^3 e_g^2 \).
• With a strong field ligand, like \( \mathrm{CN}^{-} \), a low-spin configuration results: \( t_{2g}^5 e_g^0 \).

Understanding these different configurations helps explain the difference in magnetic properties in these complexes.

Ligand Field Strength

Ligand field strength is a measure of the ability of a ligand to split the d-orbitals of a transition metal ion in a coordination complex. A ligand's field strength influences whether a complex will be high-spin or low-spin.Ligands are classified as strong or weak field based on their position in the spectrochemical series. Some key points to remember:- **Weak field ligands**, such as \( \mathrm{SCN}^{-} \), cause only a small splitting in the d-orbitals. Electrons remain unpaired, leading to high-spin configurations.- **Strong field ligands**, like \( \mathrm{CN}^{-} \), result in greater splitting. Here, electrons tend to pair up, causing low-spin configurations.The field strength therefore directly affects the electron arrangement around the metal ion. By understanding ligand field strength, we better grasp the resulting chemical and magnetic properties of the complex. This is crucial for predicting the behavior and reactivity of octahedral complexes involving transition metals.