Question

Which of the following species are paramagnetic: (a) \(B_{2}\); (b) \(\mathrm{B}_{2}{ }^{-}\); (c) \(\mathrm{B}_{2}^{+}\)? If the species is paramagnetic, how many unpaired electrons does it possess?

Short answer

Species B2, B2-, and B2+ are all paramagnetic. B2 has two unpaired electrons, while B2- and B2+ each have one unpaired electron.

Step-by-step solution

Understand Paramagnetism

A species is paramagnetic if it has one or more unpaired electrons and is attracted to a magnetic field. This can be determined by examining the molecular orbital (MO) configuration of the electrons.

Determine the MO Configuration for Boron

For diatomic species like B2, B2+, and B2-, the MO configuration follows the order: 1. Sigma (2s); 2. Sigma-star (2s); 3. Pi (2p); 4. Pi-star (2p); 5. Sigma (2p). Since Boron has 3 valence electrons, B2 has 6 total, B2- has 7, and B2+ has 5.

Fill the MO Diagram for B2

In the MO diagram for B2, there are 3 bonding MOs to fill before any anti-bonding MOs. After filling the sigma (2s), and sigma-star (2s) MOs with 4 electrons, 2 electrons will fill the degenerate pi (2p) MOs, resulting in one unpaired electron in each of the pi (2p) orbitals.

Analyze Paramagnetism for B2

With two unpaired electrons in the pi (2p) orbital, B2 is paramagnetic.

Fill the MO Diagram for B2-

B2- has an extra electron compared to B2. This electron will also be placed in a pi (2p) orbital, resulting in one pi (2p) orbital fully occupied and the other with one unpaired electron, making B2- paramagnetic with one unpaired electron.

Fill the MO Diagram for B2+

B2+ has one less electron than B2. Therefore, only one of the pi (2p) orbitals will have an unpaired electron. This makes B2+ paramagnetic with one unpaired electron.

Key concepts

Molecular Orbital Configuration

Understanding the molecular orbital (MO) configuration of an atom or a molecule is essential in predicting its magnetic properties. The MO theory describes how atomic orbitals combine to form molecular orbitals when atoms bond together.

Each molecular orbital can hold a maximum of two electrons with opposite spins. These orbitals are arranged in order of increasing energy levels. The order typically consists of sigma (σ) orbitals formed from s orbitals, followed by pi (π) orbitals formed from p orbitals. In diatomic molecules, these include σ(2s), σ*(2s), π(2p), π*(2p), and σ(2p) orbitals.

The filling of these orbitals is governed by the Aufbau principle, the Pauli exclusion principle, and Hund's rule, much like atomic orbitals in a single atom. For boron, a diagram of its MO configuration reveals how electrons are distributed in these molecular orbitals, providing insight into the magnetic character of the molecule.

Unpaired Electrons

The presence of unpaired electrons in a molecular orbital configuration is a direct indicator of paramagnetism in a molecule. Unpaired electrons have spins that are not compensated by another electron with the opposite spin in the same orbital.

According to Hund's rule, electrons will fill degenerate orbitals (orbitals of the same energy) singularly before pairing up. This behavior maximizes the total spin of the system, leading to more unpaired electrons and therefore, a greater magnetic moment. For instance, in the case of B2 and its ions, B2- and B2+, the number of unpaired electrons can be precisely calculated by filling the molecular orbitals according to these rules. This exercise demonstrated that B2 and its variants have unpaired electrons, which accounts for their paramagnetic characteristics.

Magnetic Field Attraction

The paramagnetic quality of a substance is defined by its attraction to an external magnetic field. This physical property arises due to the magnetic moments of unpaired electrons within the substance's atoms or molecules.

When a paramagnetic substance like B2, B2+, or B2- is exposed to a magnetic field, the unpaired electrons' magnetic moments will align with the field, leading to an attraction. This phenomenon can be used not only to confirm the presence of unpaired electrons but also to measure the magnetic susceptibility of the substance. This susceptibility is directly related to the number of unpaired electrons and is a quantifiable indication of how strongly a substance is attracted to a magnetic field.