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) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (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

\(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) has the lowest degree of paramagnetism.

Step 1: Identify Paramagnetic Ions

Paramagnetism arises in compounds due to unpaired electrons in their constituent ions. We will first identify the metal ions present in the given compounds: - \(\text{MnSO}_4 \cdot 4 \text{H}_2\text{O}\) contains \(\text{Mn}^{2+}\).- \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) contains \(\text{Cu}^{2+}\).- \(\text{FeSO}_4 \cdot 6 \text{H}_2\text{O}\) contains \(\text{Fe}^{2+}\).- \(\text{NiSO}_4 \cdot 6 \text{H}_2\text{O}\) contains \(\text{Ni}^{2+}\).

Step 2: Determine Number of Unpaired Electrons

We check the electronic configurations and count the unpaired electrons for each ion.- \(\text{Mn}^{2+}\): \([\text{Ar}] \, 3d^5\), has 5 unpaired electrons.- \(\text{Cu}^{2+}\): \([\text{Ar}] \, 3d^9\), has 1 unpaired electron.- \(\text{Fe}^{2+}\): \([\text{Ar}] \, 3d^6\), has 4 unpaired electrons.- \(\text{Ni}^{2+}\): \([\text{Ar}] \, 3d^8\), has 2 unpaired electrons.

Step 3: Compare Paramagnetism

Paramagnetism is directly related to the number of unpaired electrons in a compound. Lower unpaired electrons mean lower paramagnetism. From Step 2, we find:- \(\text{Mn}^{2+}\) has 5 unpaired electrons (most paramagnetic).- \(\text{Cu}^{2+}\) has 1 unpaired electron (least paramagnetic).- \(\text{Fe}^{2+}\) has 4 unpaired electrons.- \(\text{Ni}^{2+}\) has 2 unpaired electrons.

Step 4: Conclusion

Since \(\text{Cu}^{2+}\) has the least unpaired electrons (1), \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) will have the lowest degree of paramagnetism amongst the considered compounds.

Key Concepts

Unpaired Electrons

Unpaired electrons are electrons that do not have a partner occupying the opposite spin in an atomic or molecular orbital. These unpaired electrons are crucial in determining the magnetic properties of a substance. They are like solo dancers on the floor, free to engage in magnetic activities.

In the context of paramagnetism, the presence of unpaired electrons in a material allows it to interact with external magnetic fields. When a magnetic field is applied, these unpaired electrons will align with the field, causing the material to become magnetized. This alignment is temporary and disappears once the magnetic field is removed. The more unpaired electrons there are, the stronger the paramagnetism.

It's akin to having more dancers dance in sync with a piece of music; the more there are, the more visually striking the scene is. Therefore, knowing the number of unpaired electrons in metal ions gives you insight into how magnetic a compound might be.

Transition Metal Ions

Transition metal ions are ions derived from transition metals, which are elements found in the d-block of the periodic table. These elements are known for their ability to form compounds with a variety of oxidation states and coordination numbers. Transition metals are distinct because their unpaired d-electrons lead to unique electronic configurations and magnetic properties.

In transition metal ions, the availability of d-electrons allows various interactions with magnetic fields. For instance, \\(\text{Mn}^{2+}\) has a 3d ext{5} configuration, offering five unpaired d-electrons that contribute to its strong paramagnetism. This diversity in electron configurations is typical for many transition metal ions, and it explains why these metals are often studied for their magnetic properties.

Transition metal ions, like those in the compounds \\(\text{MnSO}_4\), \\(\text{CuSO}_4\), \\(\text{FeSO}_4\), and \\(\text{NiSO}_4\), display a wide range of paramagnetic behavior due to their unique electronic configurations.

Electronic Configuration

The electronic configuration of an ion reveals how electrons are distributed across various orbitals. It provides insight into the chemical behavior, reactivity, and magnetic characteristics of the ion. For transition metals, d-orbitals play a crucial role.

Let's consider some configurations. The \\(\text{Mn}^{2+}\) ion has an electronic configuration of \\([\text{Ar}]\, 3d^5\), indicating five unpaired electrons, making it quite paramagnetic. Similarly, \\(\text{Fe}^{2+}\) with four unpaired electrons in its \\(3d^6\) configuration also exhibits paramagnetism but to a lesser degree. On the flip side, \\(\text{Cu}^{2+}\) possesses a configuration of \\([\text{Ar}]\, 3d^9\), with only one unpaired electron, making it the least paramagnetic of the group.

Understanding the electronic configuration helps us predict the magnetic properties of metal ions. By determining these configurations, one can estimate how these ions will behave under a magnetic field.

Magnetic Properties

The magnetic properties of a substance are directly linked to its electronic structure. In particular, the presence of unpaired electrons in the d-orbitals of transition metals gives rise to magnetic phenomena like paramagnetism.

Paramagnetic substances have positive magnetic susceptibility, meaning they get magnetized in the same direction as the applied magnetic field. The more unpaired electrons there are, the stronger the paramagnetic effect. For instance, we have established that \\(\text{Mn}^{2+}\) ions, with five unpaired electrons, show significant paramagnetic properties compared to other ions such as \\(\text{Cu}^{2+}\), which has only one unpaired electron.

Magnetic properties do not only help us understand materials better but also have practical implications. Let's take paramagnetic materials: they are used in MRI technology for medical imaging and in other applications requiring sensitivity to magnetic fields. Recognizing these properties accurately is crucial not only for academic purposes but also for their practical applications in technology and healthcare.