Question

Suggest why the molecule \(\mathrm{Be}_{2}\) apparently is so unstable that it has not been observed. Explain why Be with an outer-shell electronic configuration of \((2 s)^{2}\) forms \(\mathrm{BeCl}_{2}\), whereas He with the configuration \((1 s)^{2}\) does not form \(\mathrm{HeCl}_{2}\).

Short answer

Be2 is unstable due to a bond order of 0; BeCl2 forms via hybridization, HeCl2 doesn't because He is inert.

Step-by-step solution

Understanding Be2 Instability

The molecule \( \mathrm{Be}_{2} \) is unstable due to its electronic configuration. Beryllium has an electronic configuration of \((1s)^2 (2s)^2\). When two beryllium atoms come together to form \( \mathrm{Be}_{2} \), the overlap of the \(2s\) orbitals is minimal, leading to weak bonding. Additionally, after accounting for the bonding and antibonding molecular orbitals in the electronic configuration \((\sigma_{1s})^{2}(\sigma^{*}_{1s})^{2}(\sigma_{2s})^{2}(\sigma^{*}_{2s})^{0}\), we find it has a bond order of 0, which indicates no net bonding and thus instability.

Outer-Shell Electron Configuration of Be and He

Beryllium's outer-shell electron configuration is \((2s)^2\). Helium's configuration is \((1s)^2\). Both configurations are closed-shell, but the principles that guide their reactivity differ due to energy levels and electron shielding.

Formation of BeCl2

\(\mathrm{BeCl}_2\) forms because beryllium can use its \(2s\) electrons to form covalent bonds with chlorine atoms. It hybridizes its \(2s\) and \(2p\) orbitals to form bonding orbitals, allowing for the formation of bonds with two chlorine atoms, resulting in \(\mathrm{BeCl}_2\). The molecule is stabilized by the complete filling of bonding orbitals.

Non-Formation of HeCl2

Helium does not form \(\mathrm{HeCl}_2\) because it has a very stable electronic configuration \((1s)^2\), representing the lowest energy state. There is no higher energy level within the first shell for hybridization and bonding. The full outer shell of helium leads to no available orbitals for bonding, resulting in its fundamental inertness.

Key concepts

Beryllium Electronic Configuration

Beryllium, with its atomic number of 4, has the electronic configuration of \(1s^2 2s^2\). This means its first energy shell is fully occupied with two electrons, and its second shell has two electrons in the 2s orbital.
This closed-shell configuration makes beryllium relatively stable on its own. However, it also presents certain challenges for forming stable molecules, such as \(\mathrm{Be}_2\). When beryllium atoms try to bond together, the overlap of the 2s orbitals is weak.
This results in weak bonding interactions. Thus, \(\mathrm{Be}_2\) is highly unstable and has a bond order of 0, indicating no effective bonding.

Molecular Orbital Theory

Molecular Orbital Theory helps us understand the stability of molecules like \(\mathrm{Be}_2\). In this theory, atomic orbitals combine to form molecular orbitals, which can be bonding or antibonding.
For beryllium, the molecular orbitals are represented as \(\sigma_{1s}^2\sigma_{1s}^{*2}\sigma_{2s}^2\sigma_{2s}^{*0}\). The star (*) denotes antibonding orbitals.
The bond order is calculated as \(\frac{1}{2}(\text{number of electrons in bonding orbitals} - \text{number of electrons in antibonding orbitals})\). In \(\mathrm{Be}_2\), this gives a bond order of 0 because the bonding and antibonding interactions cancel each other out.

• No net bonding occurs, leading to the molecule's instability.

Covalent Bonding

Covalent bonding is essential in forming compounds like \(\mathrm{BeCl}_2\). Beryllium can participate in covalent bonding through the hybridization of its orbitals.
Although beryllium's natural electronic configuration is \(2s^2\), it can hybridize its 2s and 2p orbitals to form sp hybrid orbitals.
This hybridization allows it to form two equivalent covalent bonds with chlorine atoms, creating a linear molecule in \(\mathrm{BeCl}_2\).

• The hybridization process stabilizes the molecule by lowering the overall energy through effective overlap of hybrid orbitals with chlorine's orbitals.

Inert Gases

Inert gases, like helium, possess full outer electron shells, leading to their notable lack of reactivity. Helium's electronic configuration of \(1s^2\) is stable and represents a low energy state.
This configuration leaves no available orbitals for bonding. Because of this, helium does not engage in chemical reactions like bonding with chlorine to form \(\mathrm{HeCl}_2\).

• This stability is why helium and other inert gases are often used in applications where non-reactivity is crucial, such as in protecting sensitive materials or environments from oxidation.