Question

Both polyatomic ions and uncharged molecules can be detected using spectroscopic measurements. Two examples of polyatomic ions are \(\mathrm{He}_{2}^{2+}\) and \(\mathrm{HHe}^{+}\). Predict the arrangement of electrons in MOs and the bond order for each ion.

Short answer

\(\mathrm{He}_{2}^{2+}\) has no bond order; \(\mathrm{HHe}^{+}\) has a bond order of 0.5.

Step-by-step solution

Understand the concepts

To predict the arrangement of electrons in molecular orbitals (MOs) and the bond order for the given polyatomic ions, we need to recall that MOs are formed by the linear combination of atomic orbitals. The bond order is determined by the difference between the number of bonding and antibonding electrons, divided by two.

Analyze \\(\mathrm{He}_{2}^{2+}\\)

The ion \(\mathrm{He}_{2}^{2+}\) consists of two helium nuclei and no electrons left after removing two electrons. Normally, \(\mathrm{He}_2\) would have 4 electrons, but \(\mathrm{He}_{2}^{2+}\) has zero electrons. Since there are no electrons to fill any molecular orbitals, the concept of bond order does not apply to this ion.

Analyze \\(\mathrm{HHe}^{+}\\)

The ion \(\mathrm{HHe}^{+}\) consists of hydrogen (1 electron) and helium (2 electrons), forming a total of 3 electrons. Hydrogen's 1s orbital overlaps with helium's 1s orbital, forming bonding \(\sigma_{1s}\) and antibonding \(\sigma_{1s}^*\) molecular orbitals. Placing 2 electrons in \(\sigma_{1s}\) and 1 electron in \(\sigma_{1s}^*\), the bond order is calculated as \((2 - 1)/2 = 0.5\).

Conclusion

For \(\mathrm{He}_{2}^{2+}\), there are no electrons, so no MOs to consider, and bond order does not apply. For \(\mathrm{HHe}^{+}\), a bond order of 0.5 suggests a weak bond due to only partial filling of antibonding orbitals.

Key concepts

Polyatomic Ions

Polyatomic ions are ions that consist of two or more atoms. These atoms can be of the same or different elements, and they bond together, sharing or transferring electrons to create an ion with a charge. Consider a simple example such as hydroxide ion (OH⁻), where oxygen and hydrogen combine, giving an overall negative charge.

In the given exercise,

• \(\mathrm{He}_{2}^{2+}\) is an interesting polyatomic ion without electrons. Normally, a neutral \(\mathrm{He}_2\) molecule would have 4 electrons (2 from each helium atom), but after losing two electrons, the \(\mathrm{He}_{2}^{2+}\) doesn’t have any electrons left to occupy molecular orbitals (MOs).
• \(\mathrm{HHe}^{+}\) consists of one hydrogen atom and one helium atom. This ion has a total of 3 electrons, with one carrying a positive charge, indicating it is missing an electron.

Polyatomic ions with a full understanding of bonding and electrons can explain unique structures and behaviors of ions like \(\mathrm{HHe}^{+}\).

Bond Order

Bond order is a concept that helps us understand the strength and stability of a bond between two atoms. It is calculated by considering the number of electrons in bonding versus antibonding molecular orbitals. The formula for bond order \[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]gives insight into the bonding framework.

In

• \(\mathrm{He}_{2}^{2+}\), since there are no electrons left, no molecular orbitals are formed, meaning the bond order is undefined. Essentially, there is no bond to describe due to the absence of electrons.
• \(\mathrm{HHe}^{+}\), the molecular orbitals are occupied with 2 electrons in the \(\sigma_{1s}\) (bonding orbital) and 1 electron in the \(\sigma_{1s}^*\) (antibonding orbital). Therefore, the bond order is \(0.5\), suggesting a rather weak bond, due to the partially filled antibonding orbital.

Understanding the bond order provides clarity on how electrons are shared or transferred and dictates how strongly atoms are bonded.

Spectroscopic Measurements

Spectroscopy is a technique used to identify substances, including polyatomic ions, based on how they interact with electromagnetic radiation. This interaction can tell us a lot about the arrangement of electrons and the structure of the ions.

In spectroscopic measurements,

• Polyatomic ions can absorb or emit light at certain wavelengths, depending on their electronic structure.
• By analyzing these wavelengths, scientists can determine the distribution and arrangement of electrons within an ion, which helps in predicting molecular structure and bond characteristics.
• For ions like \(\mathrm{HHe}^{+}\), spectroscopy could reveal insights into its weak bonding, as seen in the bond order calculation.

Thus, spectroscopic measurements are essential in providing evidence of the electronic and structural properties of ions, making it a crucial tool in modern chemical analysis.