Problem 45 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one has the highest paramagnetism among the following ions? (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (b) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2+}\) (c) \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (d) \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)

Step-by-Step Solution

Answer

\([\mathrm{Fe(\mathrm{H}_2\mathrm{O})_6}]^{2+}\) has the highest paramagnetism with 4 unpaired electrons.

Step 1: Determine the Electronic Configuration

Begin by determining the electronic configurations for the central metal ions in each complex. (a) Cr in \([\mathrm{Cr(\mathrm{H}_2\mathrm{O})_6}]^{3+}\): Chromium initially has the electronic configuration [Ar]3d⁵4s¹. Since it loses 3 electrons, the configuration becomes [Ar]3d³.(b) Fe in \([\mathrm{Fe(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): Iron has the electronic configuration [Ar]3d⁶4s². Losing 2 electrons makes it [Ar]3d⁶.(c) Cu in \([\mathrm{Cu(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): Copper's initial configuration is [Ar]3d¹⁰4s¹. It forms [Ar]3d⁹ upon losing 2 electrons.(d) Zn in \([\mathrm{Zn(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): Zinc starts as [Ar]3d¹⁰4s², which becomes [Ar]3d¹⁰ after losing 2 electrons.

Step 2: Count the Unpaired Electrons

Evaluate each ion to determine the number of unpaired electrons. Paramagnetism is due to unpaired electrons in the d-orbitals.(a) In \([\mathrm{Cr(\mathrm{H}_2\mathrm{O})_6}]^{3+}\), the electronic configuration is [Ar]3d³. There are 3 unpaired electrons.(b) In \([\mathrm{Fe(\mathrm{H}_2\mathrm{O})_6}]^{2+}\), the configuration [Ar]3d⁶ results in 4 unpaired electrons.(c) In \([\mathrm{Cu(\mathrm{H}_2\mathrm{O})_6}]^{2+}\), [Ar]3d⁹ leaves 1 unpaired electron.(d) In \([\mathrm{Zn(\mathrm{H}_2\mathrm{O})_6}]^{2+}\), [Ar]3d¹⁰ has 0 unpaired electrons.

Step 3: Compare Paramagnetic Behavior

Using the number of unpaired electrons count:- \([\mathrm{Cr(\mathrm{H}_2\mathrm{O})_6}]^{3+}\): 3 unpaired electrons.- \([\mathrm{Fe(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): 4 unpaired electrons.- \([\mathrm{Cu(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): 1 unpaired electron.- \([\mathrm{Zn(\mathrm{H}_2\mathrm{O})_6}]^{2+}\): 0 unpaired electrons.Ion with the highest number of unpaired electrons will have the highest paramagnetism. In this case, \([\mathrm{Fe(\mathrm{H}_2\mathrm{O})_6}]^{2+}\) has 4 unpaired electrons.

Key Concepts

Electronic Configuration

Understanding electronic configuration is crucial for grasping the basics of chemistry, particularly in the study of atomically diverse substances like transition metal complexes. Electron configuration explains how electrons are distributed among atomic and molecular orbitals. These configurations can affect properties like magnetism, bonding, and conductivity.

For example, a neutral Chromium (Cr) atom has an electronic configuration of [Ar]3d⁵4s¹. When it forms a cation by losing electrons, its configuration changes based on the number of electrons lost. In the case of the chromium ion in \([\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]^{3+}\), three electrons are lost, leading to the configuration [Ar]3d³. Understanding these changes is key to predicting the chemical behavior of ions.

• Chromium: [Ar]3d³ after losing 3 electrons
• Iron: [Ar]3d⁶ after losing 2 electrons
• Copper: [Ar]3d⁹ after losing 2 electrons
• Zinc: [Ar]3d¹⁰ after losing 2 electrons

Unpaired Electrons

Unpaired electrons play a pivotal role in the magnetic properties of an atom or a molecule. Paramagnetism, a form of magnetism, arises due to the presence of unpaired electrons in atomic orbitals. These unpaired electrons generate a magnetic field when exposed to an external magnetic source.

In transition metal complexes, the number of unpaired electrons determines the extent of paramagnetism. This is because each unpaired electron contributes to the magnetic field. Consider the electronic configurations after ion formation:

• \([\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]^{3+}\) with [Ar]3d³ has 3 unpaired electrons
• \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) with [Ar]3d⁶ has 4 unpaired electrons
• \([\mathrm{Cu}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) with [Ar]3d⁹ has 1 unpaired electron
• \([\mathrm{Zn}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) with [Ar]3d¹⁰ has no unpaired electrons

Iron complex \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) has the most unpaired electrons, making it the most paramagnetic.

Transition Metal Complexes

Transition metal complexes are fascinating chemical species formed by transition metals bound to other molecules or ions, typically referred to as ligands. They are renowned for their rich chemistry and the dynamic properties they exhibit, such as varied oxidation states, colorful compounds, and complex formations.

In these complexes, the d-orbitals of transition metals play a crucial role. For example, when Cr, Fe, Cu, and Zn form complexes with water, ligands surround the metal ions, and the electronic configuration of these transition metal ions changes, thereby altering their chemical properties. The geometry and number of ligands can further affect their stability and magnetic properties.

Key examples discussed include:

• Chromium in \([\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]^{3+}\)
• Iron in \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\)
• Copper in \([\mathrm{Cu}(\mathrm{H}_2\mathrm{O})_6]^{2+}\)
• Zinc in \([\mathrm{Zn}(\mathrm{H}_2\mathrm{O})_6]^{2+}\)

These complexes highlight different forms of coordination chemistry where ligands and metal ions interact perfectly, demonstrating why transition metal compounds are indispensable in both industrial and biological contexts.