Question

Use the MO model to determine which of the following has the smallest ionization energy: \(\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{N}_{2}^{2-}, \mathrm{N}_{2}^{-}, \mathrm{O}_{2}^{+} .\) Explain your answer.

Short answer

The molecule/ion with the smallest ionization energy is \(\mathrm{O}_{2}^{+}\). This is because the HOMO for all species is \(\pi_{2p}\), and the \(\pi_{2p}\) orbitals are higher in energy for \(\mathrm{O}_{2}\) than for \(\mathrm{N}_{2}\). Comparing \(\mathrm{N}_{2}^{-}\) and \(\mathrm{O}_{2}^{+}\), the HOMO in \(\mathrm{N}_{2}^{-}\) is slightly stabilized due to the extra electron, so \(\mathrm{O}_{2}^{+}\) has the smallest ionization energy.

Step-by-step solution

1. Determine the number of valence electrons

For each molecule/ion, we need to find the number of valence electrons involved. - For \(\mathrm{N}_{2}\), there are 10 valence electrons since nitrogen has 5 valence electrons each. - For \(\mathrm{O}_{2}\), there are 12 valence electrons since oxygen has 6 valence electrons each. - For \(\mathrm{N}_{2}^{2-}\), there are 12 valence electrons (10 from the nitrogen atoms and 2 from the negative charges). - For \(\mathrm{N}_{2}^{-}\), there are 11 valence electrons (10 from the nitrogen atoms and 1 from the negative charge). - For \(\mathrm{O}_{2}^{+}\), there are 11 valence electrons (12 from the oxygen atoms and 1 less due to the positive charge).

2. Examine the MO diagrams

Look at the MO diagrams for both Nitrogen and Oxygen diatomic molecules. Note that the MO energy levels for \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are slightly different. For \(\mathrm{N}_{2}\), the \(\sigma_{2p}\) orbitals are lower in energy than the \(\pi_{2p}\) orbitals, while for \(\mathrm{O}_{2}\), the \(\pi_{2p}\) orbitals are lower in energy than the \(\sigma_{2p}\) orbitals.

3. Determine the HOMO

Based on the MO diagrams and the number of valence electrons calculated in step 1, we can determine the HOMO for each molecule/ion. - \(\mathrm{N}_{2}\): 10 electrons, the HOMO is \(\pi_{2p}\) (3 different MOs degenerate in energy). - \(\mathrm{O}_{2}\): 12 electrons, the HOMO is \(\pi_{2p}\) (3 different MOs degenerate in energy). - \(\mathrm{N}_{2}^{2-}\): 12 electrons, the HOMO is \(\pi_{2p}\) (3 different MOs degenerate in energy). - \(\mathrm{N}_{2}^{-}\): 11 electrons, the HOMO is \(\pi_{2p}\) (2 different MOs degenerate in energy). - \(\mathrm{O}_{2}^{+}\): 11 electrons, the HOMO is \(\pi_{2p}\) (2 different MOs degenerate in energy).

4. Compare HOMO energies and determine the smallest ionization energy

Comparing the HOMO energies, we can see that the \(\pi_{2p}\) orbitals are higher in energy for \(\mathrm{O}_{2}\) than for \(\mathrm{N}_{2}\), so \(\mathrm{O}_{2}\) and its ions will have smaller ionization energies than \(\mathrm{N}_{2}\) and its ions. Now compare the two ions with HOMOs in the \(\pi_{2p}\) orbitals: \(\mathrm{N}_{2}^{-}\) and \(\mathrm{O}_{2}^{+}\). Due to the extra electron in \(\mathrm{N}_{2}^{-}\) compared to \(\mathrm{O}_{2}^{+}\), the energy of the HOMO would be slightly stabilized in \(\mathrm{N}_{2}^{-}\). Therefore, \(\mathrm{O}_{2}^{+}\) has the smallest ionization energy out of these molecules and ions.

Key concepts

Ionization Energy

Ionization energy is an essential concept in chemistry which relates to the energy required to remove an electron from a neutral atom or ion in its gaseous state. This property indicates how strongly an atom's nucleus holds onto its electrons.
Generally, an atom or ion with a high ionization energy has a strong hold over its electrons, whereas lower ionization energy signifies weaker attraction between the nucleus and the outermost electrons.
In the context of molecular orbital (MO) theory, ionization energy is closely related to the energy level of the highest occupied molecular orbital (HOMO). It's easier to ionize an electron from a higher energy HOMO, meaning lower ionization energy. Thus, determining which molecule or ion has the smallest ionization energy involves comparing the HOMO energies.

Valence Electrons

Valence electrons play a critical role in defining the chemical properties and reactivity of an atom. These are the electrons found in the outermost shell of an atom. In an atom, valence electrons are involved in forming chemical bonds, transferring during reactions, and giving atoms their characteristic properties.
For molecules or ions, the number of valence electrons helps in constructing molecular orbital diagrams. In the example exercise, each molecule or ion's total valence electron count was calculated. Knowing the count enables us to predict electron distribution in molecular orbitals and identify the HOMO, a key component in determining ionization energies.

• extbf{Nitrogen ( _2):} 10 valence electrons.
• extbf{Oxygen ( _2):} 12 valence electrons.
• extbf{Nitrogen ( _2^{2-}):} 12 valence electrons.
• extbf{Nitrogen ( _2^{-}):} 11 valence electrons.
• extbf{Oxygen ( _2^{+}):} 11 valence electrons.

HOMO (Highest Occupied Molecular Orbital)

The Highest Occupied Molecular Orbital or HOMO is a pivotal concept in understanding chemical reactivity and ionization potential. It signifies the molecular orbital where the highest energy electrons reside.
The position of HOMO in energy levels affects a molecule's ability to donate electrons during reactions or ionization. The closer the HOMO is to the nuclear core, the less reactive and less prone to ionization the molecule is.
In the MO diagrams, identifying the HOMO involves counting the electrons and distributing them according to energy levels. Different molecules might have HOMOs at varying energy levels depending on their electron configuration and the nature of their atoms or ions. In our example, we saw different HOMOs for different molecules, making some more susceptible to ionization due to higher energy HOMOs.

Molecular Orbitals

Molecular orbitals (MOs) result from the combination of atomic orbitals when atoms combine to form molecules. They are spread over the entire molecule, suggesting that electrons belong to the molecule as a whole rather than any individual atom.
MOs come in bonding, antibonding, and non-bonding varieties, each with different energy levels and significance in molecular stability. Bonding orbitals lower the energy of the system and stabilize the molecule, while antibonding orbitals, if filled, increase the molecule's energy.
In constructing molecular orbital diagrams, electrons fill these orbitals based on energy levels, from lowest to highest. The MO theory helps us understand the energy distribution in a molecule and allows us to predict properties such as ionization energy. These diagrams are vital in determining the HOMO, as they visually represent where the highest energy electrons in a molecule reside.