Question

In terms of the molecular orbital model, which species in each of the following two pairs will most likely be the one to gain an electron? Explain. $$ \text {a} C N \text { or } N O \qquad \text { b. } O_{2}^{2+} \text { or } N_{2}^{2+} $$

Short answer

a) Neither CN nor NO is more likely to gain an electron, as they both have identical molecular orbital diagrams and available orbitals with the same energy levels. b) \(N_2^{2+}\) is more likely to gain an electron over \(O_2^{2+}\) because the available orbital is lower in energy in \(N_2^{2+}\).

Step-by-step solution

Determine the electron configurations of the species

Use molecular orbital theory to write the electron configurations of each species. We don't need the full configurations, just the last few orbitals. For diatomic molecules, such as the ones in this problem, the ordering of energy levels for molecular orbitals typically follows the pattern: σ1s, σ*_1s, σ2s, σ*_2s, π2p, π*_2p, σ2p. For CN: The total number of valence electrons is 11 (5 from nitrogen and 6 from carbon). Filling the electron configuration, we get σ1s², σ*_1s², σ2s², σ*_2s², π2p^4, σ2p¹. For NO: The total number of valence electrons is 11 (5 from nitrogen and 6 from oxygen). Filling the electron configuration, we get σ1s², σ*_1s², σ2s², σ*_2s², π2p^4, σ2p¹. For \(O_2^{2+}\): The total number of valence electrons is 10 (6 from each oxygen, minus 2 for the 2+ charge). Filling the electron configuration, we get σ1s², σ*_1s², σ2s², σ*_2s², π2p^4, σ2p₀. For \(N_2^{2+}\): The total number of valence electrons is 8 (5 from each nitrogen, minus 2 for the 2+ charge). Filling the electron configuration, we get σ1s², σ*_1s², σ2s², σ*_2s², π2p^2, σ2p₀.

Evaluate which species are more likely to gain an electron

Compare the molecular orbital diagrams of the species to determine which has available orbitals for an additional electron. a) CN or NO: Both CN and NO have an available σ2p orbital with only one electron. So, both species can accommodate an additional electron. b) \(O_2^{2+}\) or \(N_2^{2+}\): For \(O_2^{2+}\), there are two available π*_2p orbitals with two electrons each. An additional electron can enter one of these π*_2p orbitals. For \(N_2^{2+}\), there is an available σ2p orbital with no electrons. An additional electron can enter the σ2p orbital.

Compare the energy levels of the available orbitals

In case of a tie in step 2, compare the energy levels of the available orbitals to determine which species would be more favorable for an electron to enter. a) CN or NO: Both CN and NO have an available σ2p orbital with the same energy level. Since they have identical molecular orbital diagrams and energy levels, neither one is more likely to gain an electron over the other. b) \(O_2^{2+}\) or \(N_2^{2+}\): For \(O_2^{2+}\), an additional electron would enter one of the π*_2p orbitals. For \(N_2^{2+}\), an additional electron would enter the σ2p orbital. Since the σ2p orbital is lower in energy than the π*_2p orbitals, an electron will be more likely to enter \(N_2^{2+}\). #Conclusion# a) Neither CN nor NO is more likely to gain an electron, as they both have identical molecular orbital diagrams and available orbitals with the same energy levels. b) \(N_2^{2+}\) is more likely to gain an electron over \(O_2^{2+}\) because the available orbital is lower in energy in \(N_2^{2+}\).

Key concepts

Electron Configuration

Electrons in a molecule are arranged in a specific order known as electron configuration. This arrangement is vital as it dictates how atoms in a molecule bond and their electronic properties. Let's delve into what electron configuration means within the context of Molecular Orbital Theory (MOT).
In molecular systems, electron configuration refers to the way electrons occupy molecular orbitals. These orbitals are a mixture of atomic orbitals from the atoms making up the molecule.
In diatomic molecules—such as CN and NO—these molecular orbitals follow a specific ordering pattern. Typically, the sequence includes different energy levels: σ1s, σ*_1s, σ2s, σ*_2s, π2p, and so forth. The pattern showcases which molecular orbitals are filled as electrons are added.
Understanding these configurations is crucial because specific orbitals can tell us whether a molecule is stable and if it can gain or lose more electrons.

Molecular Orbitals

Molecular Orbitals (MOs) are a fundamental concept in molecular orbital theory. These are regions in a molecule where electrons are most likely to be found. An essential feature of MOs is that they can extend over multiple atoms, in contrast to atomic orbitals, which are restricted to single atoms.
Molecular orbitals are formed by the combination of atomic orbitals from bonded atoms. This combination can happen constructively (bonding orbitals) or destructively (antibonding orbitals), affecting the molecule's stability. The energy of these molecular orbitals determines the chemical properties of the molecule.
For example, in the case of CN and NO, the molecular orbitals hold a total of 11 electrons. The electrons fill the orbitals from the lowest energy to the higher ones, defining the electron configuration and indicating whether there are vacant spaces for extra electrons.

Valence Electrons

Valence electrons are the electrons that reside in the outermost shell of an atom, or the highest energy level. These electrons are crucial in determining how an atom will bond with others, as they are involved in forming chemical bonds.
In molecular orbital theory, the concept of valence electrons extends to how these electrons distribute across molecular orbitals. For molecules such as CN and NO, the total number of valence electrons is 11, resulting from combining the contributing atoms' valence electrons.
These electrons occupy the molecular orbitals according to the available energy levels, ultimately defining the molecule's stability and reactivity. Understanding the behavior of these valence electrons is key to predicting the likelihood of a molecule to gain or lose electrons.

Energy Levels

Energy levels in molecular orbital theory are like steps in a ladder, where electrons are filled from the bottom up. The energy of a molecular orbital is determined by how the atomic orbitals are combined and whether electrons are likely to be found in bonding or antibonding orbitals.
In the comparison of O₂²⁺ and N₂²⁺, energy levels play a critical role. Electrons will preferentially fill the lowest available energy levels first, stabilizing the molecule. When considering which of these ions is more likely to gain an electron, examining the energy levels of their orbitals becomes crucial.
In O₂²⁺, additional electrons would enter higher energy π* orbitals, while in N₂²⁺, electrons would enter lower energy σ orbitals. As electrons tend to fill lower energy levels to minimize the molecule's energy, N₂²⁺ is more likely to accept an extra electron. This preference for lower energy levels illustrates why certain molecules are more chemically reactive than others.