Problem 95 - A Complete Resource Book in Chemistry for JEE Main

Question

Amongst the following, the lowest degree of paramagnetism per mole of the compound at \(298 \mathrm{~K}\) will be shown by (a) \(\mathrm{MnSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2}^{2} \mathrm{O}\) (c) \(\mathrm{FeSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NiSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

\(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) shows the lowest degree of paramagnetism due to having the least unpaired electrons (1).

Step 1: Understand the Definition of Paramagnetism

Paramagnetism is a form of magnetism that occurs in materials that have unpaired electrons. It depends on the number of unpaired electrons in the atom or compound.

Step 2: Identify Unpaired Electrons in Each Compound

Examine the oxidation state of the metal ions in each compound to determine the number of unpaired electrons:- Mn in \(\mathrm{MnSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) is \(\text{Mn}^{2+}\), with 5 unpaired electrons.- Cu in \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2}^{2} \mathrm{O}\) is \(\text{Cu}^{2+}\), with 1 unpaired electron.- Fe in \(\mathrm{FeSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is \(\text{Fe}^{2+}\), with 4 unpaired electrons.- Ni in \(\mathrm{NiSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is \(\text{Ni}^{2+}\), with 2 unpaired electrons.

Step 3: Compare the Number of Unpaired Electrons

Paramagnetism is stronger with more unpaired electrons. Compare:- \(\text{Mn}^{2+}\) has 5 unpaired, highest.- \(\text{Fe}^{2+}\) has 4 unpaired.- \(\text{Ni}^{2+}\) has 2 unpaired.- \(\text{Cu}^{2+}\) has 1 unpaired, lowest.

Step 4: Identify the Compound with Lowest Paramagnetism

The compound with the fewest unpaired electrons will exhibit the lowest degree of paramagnetism per mole. \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2}^{2} \mathrm{O}\) has only 1 unpaired electron.

Key Concepts

Unpaired Electrons

In chemistry, the idea of unpaired electrons is crucial when discussing paramagnetic properties. Electrons in atoms occupy orbitals, and these orbitals can hold up to two electrons each, normally with opposite spins. When an orbital is filled with two electrons, it is known as paired. However, if it contains only one electron, it's called unpaired. Paramagnetism arises from these unpaired electrons. The more unpaired electrons present in a substance, the stronger the material's paramagnetism. In metals or metal compounds, like the transition metal ions, unpaired electrons can interact more freely because orbitals such as d and f are involved. This interaction with applied magnetic fields describes why such materials are paramagnetic.

• Mn²⁺ has 5 unpaired electrons contributing to its strong paramagnetic nature.
• Fe²⁺ comes next with 4 unpaired electrons.
• Ni²⁺ has 2, indicating weaker paramagnetism.
• Cu²⁺ with 1 unpaired electron exhibits the least paramagnetism.

Oxidation States

Understanding oxidation states is vital when exploring the paramagnetism of different compounds. The oxidation state of an element in a compound indicates the number of electrons that have been lost, gained, or shared when forming compounds. This can affect the number of unpaired electrons in transition metal ions. Transition metals, due to their complex electron configurations, can exhibit various oxidation states. By identifying the oxidation state, we can predict the number of unpaired electrons. For instance:

• Manganese (Mn) in MnSO₄·4H₂O with oxidation state +2 has 5 unpaired electrons.
• Copper (Cu) in CuSO₄·5H₂O with oxidation state +2 has only 1.
• Iron (Fe) in FeSO₄·6H₂O at +2 has 4 unpaired electrons.
• Nickel (Ni) in NiSO₄·6H₂O, also at +2, has 2 unpaired electrons.

This difference in oxidation states and, consequently, their electronic arrangements influences their magnetic properties.

Transition Metal Ions

Transition metal ions play a special role in chemistry due to their d electron subshells and variable oxidation states. These ions, found in the center of the periodic table, can give rise to interesting properties such as magnetism, color, and complex formation. The transitional nature of these metals is due to the incomplete filling of their d orbitals. As the oxidation state increases, some of these d orbitals become unpaired, contributing directly to magnetism. For example:

• Mn²⁺ has partially filled 3d orbitals contributing to high magnetic susceptibility.
• Cu²⁺ has higher occupation in its d orbitals, leading to only one unpaired electron.
• Fe²⁺ and Ni²⁺ show an intermediate range of unpaired electrons based on their unique d configurations.

The behavior and properties of transition elements, including magnetism, result from their electronic structures and varying oxidation states, making them key players in both inorganic chemistry and materials science.