Problem 195 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following species is diamagnetic in nature? 2 (a) \(\mathrm{H}_{2}^{-}\) (b) \(\mathrm{H}_{2}\) (c) \(\mathrm{H}_{2}^{+}\) (d) \(\mathrm{He}_{2}^{+}\)

Step-by-Step Solution

Answer

The species \\(\mathrm{H}_{2}\\) is diamagnetic.

Step 1: Define Diamagnetic

A diamagnetic species is one that does not have any unpaired electrons. It is repelled by a magnetic field due to the absence of unpaired electrons.

Step 2: Determine Molecular Orbital Configuration

Using molecular orbital theory, determine the electron configuration for each option. Diamagnetic species will have fully paired electrons in molecular orbitals.

Step 3: Evaluate \\(\mathrm{H}_{2}^{-}\\)

For \(\mathrm{H}_{2}^{-}\), construct the molecular orbitals: - It has 3 electrons. - The configuration is \(\sigma_{1s}^2\, \sigma^*_{1s}^1\).- It has one unpaired electron, so it is paramagnetic.

Step 4: Evaluate \\(\mathrm{H}_{2}\\)

For \(\mathrm{H}_{2}\), construct the molecular orbitals: - It has 2 electrons.- The configuration is \(\sigma_{1s}^2\).- All electrons are paired, so it is diamagnetic.

Step 5: Evaluate \\(\mathrm{H}_{2}^{+}\\)

For \(\mathrm{H}_{2}^{+}\), construct the molecular orbitals:- It has 1 electron.- The configuration is \(\sigma_{1s}^1\).- It has one unpaired electron, so it is paramagnetic.

Step 6: Evaluate \\(\mathrm{He}_{2}^{+}\\)

For \(\mathrm{He}_{2}^{+}\), construct the molecular orbitals:- It has 3 electrons.- The configuration is \(\sigma_{1s}^2\, \sigma^*_{1s}^1\).- It has one unpaired electron, so it is paramagnetic.

Step 7: Conclusion

Out of the options, only \(\mathrm{H}_{2}\) has all electrons paired and is thus diamagnetic.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory is an essential concept in chemistry that helps understand the behavior of electrons in molecules. Unlike the valence bond theory that considers electrons localized between two atoms, molecular orbital theory suggests that electrons in a molecule are delocalized and exist in orbitals that belong to the entire molecule.

In this theory, atomic orbitals from each atom combine to form molecular orbitals. These molecular orbitals can be classified as bonding, anti-bonding, or non-bonding.

• Bonding molecular orbitals have lower energy and more stability compared to the original atomic orbitals. Electrons here contribute to the bond between two atoms.
• Anti-bonding molecular orbitals are higher in energy and can destabilize a molecule if occupied by electrons. They are typically indicated with an asterisk, for example, \(\sigma^*\).
• Non-bonding molecular orbitals are those that do not help in holding the two atoms together.

The arrangement of electrons in these molecular orbitals determines the chemical properties, such as the magnetic nature, of molecules.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom or molecule's orbitals. In molecular orbital theory, electron configuration is crucial in determining the properties of a species.

For example, when evaluating the electron configuration of the molecular species \(\mathrm{H}_2\), \(\mathrm{H}_{2}^{-}\), and \(\mathrm{H}_{2}^{+}\), you need to know the number of electrons and then fill in the orbitals in order of increasing energy:

• \(\mathrm{H}_2\) has two electrons filling the \(\sigma_{1s}\) bonding orbital with a configuration of \(\sigma_{1s}^2\).
• \(\mathrm{H}_{2}^{-}\) has three electrons, filling \(\sigma_{1s}^2\) and one electron in \(\sigma^*_{1s}\), making it \(\sigma_{1s}^2\ \sigma^*_{1s}^1\).
• \(\mathrm{H}_{2}^{+}\) contains only one electron in the \(\sigma_{1s}\) orbital, \(\sigma_{1s}^1\).

Understanding electron configuration within molecular orbitals allows chemists to describe important characteristics like electronic structure and chemical bonding.

Paramagnetic

A paramagnetic species is identified by the presence of one or more unpaired electrons in its atomic or molecular orbital configuration. These unpaired electrons have a magnetic moment, allowing the species to be attracted to magnetic fields.

In the context of the original exercise:

• \(\mathrm{H}_{2}^{-}\) is paramagnetic because its electron configuration \(\sigma_{1s}^2\ \sigma^*_{1s}^1\) includes an unpaired electron in the anti-bonding orbital.
• \(\mathrm{H}_{2}\) is diamagnetic as all electrons are paired.
• \(\mathrm{H}_{2}^{+}\) is paramagnetic with its single unpaired electron in the \(\sigma_{1s}\) orbital.

Paramagnetism is an important property in understanding the behavior of substances around magnetic fields and has practical implications in various fields like material science and medicine.