Problem 104 - General Chemistry: Principles and Modern Applications

Question

Use the valence molecular orbital configuration to determine which of the following species is expected to have the greatest electron affinity: (a) \(\mathrm{C}_{2}^{+} ;\) (b) \(\mathrm{Be}_{2}\) (c) \(\mathrm{F}_{2} ;\) (d) \(\mathrm{B}_{2}^{+}\)

Step-by-Step Solution

Answer

Out of \[\mathrm{C}_{2}^{+}\], \[\mathrm{Be}_{2}\], \[\mathrm{F}_{2}\], and \[\mathrm{B}_{2}^{+}\], \[\mathrm{C}_{2}^{+}\] has the greatest electron affinity.

Step 1: Identify the molecular orbital configuration

The first step is to know the molecular orbital configuration of each species. The molecular orbital configuration can be derived from the periodic table by identifying the total number of valence electrons for each atom in a molecule. \[\mathrm{C}_{2}^{+}\] has 7 valence electrons, \[\mathrm{Be}_{2}\] has 4 valence electrons, \[\mathrm{F}_{2}\] has 14 valence electrons and \[\mathrm{B}_{2}^{+}\] has 5 valence electrons.

Step 2: Determine electron cloud vacancy

Next, identify which of these species have more vacancies for electrons in their valence electron cloud. \[\mathrm{C}_{2}^{+}\] and \[\mathrm{B}_{2}^{+}\] have an odd number of valence electrons, meaning they have one unpaired electron each. \[\mathrm{Be}_{2}\] has its electron cloud full and does not have space for more electrons. \[\mathrm{F}_{2}\] has paired electrons only, meaning its electron cloud is almost full with just a little space for more electrons.

Step 3: Determine electron affinity

Species with more vacancies in their electron cloud are more likely to receive an electron. Species with an unpaired electron have larger electron affinity because the contact of an extra electron with the unpaired electron leads to a stable pairing. Therefore \[\mathrm{C}_{2}^{+}\] and \[\mathrm{B}_{2}^{+}\] have a higher electron affinity compared to \[\mathrm{Be}_{2}\] and \[\mathrm{F}_{2}\] . Among \[\mathrm{C}_{2}^{+}\] and \[\mathrm{B}_{2}^{+}\] , \[\mathrm{C}_{2}^{+}\] has a greater electron affinity because it is on the right side of the Periodic Table where elements are more likely to accept electrons.

Key Concepts

Valence Molecular Orbital Configuration

Understanding the valence molecular orbital configuration is crucial when exploring electron affinity. Valence electrons are the electrons in the outermost shell of an atom, which participate in bonding. For molecules like \( \mathrm{C}_{2}^{+} \), \( \mathrm{Be}_{2} \), \( \mathrm{F}_{2} \), and \( \mathrm{B}_{2}^{+} \), identifying the number of valence electrons helps us understand their bonding and molecular structure.

To find the number of valence electrons, look at each element in the molecule and count its valence electrons from the periodic table:

• \( \mathrm{C}_{2}^{+} \) has 7 valence electrons, 3 from each C atom, minus one for the positive charge.
• \( \mathrm{Be}_{2} \) has 4 valence electrons, 2 from each Be atom.
• \( \mathrm{F}_{2} \) has 14 valence electrons, 7 from each F atom.
• \( \mathrm{B}_{2}^{+} \) has 5 valence electrons, 3 from each B atom, minus one for the positive charge.

By knowing these configurations, you can predict electron pairing and molecular stability.

Unpaired Electron

An unpaired electron is an electron that occupies an atomic orbital on its own rather than being paired with another electron with an opposite spin in the same orbital. These unpaired electrons are important when considering electron affinity because they can influence molecular interactions and reactivity.

For example, in the given species:

• \( \mathrm{C}_{2}^{+} \) has one unpaired electron because it ends with a half-filled orbital.
• \( \mathrm{B}_{2}^{+} \) also has one unpaired electron.
• \( \mathrm{Be}_{2} \) and \( \mathrm{F}_{2} \) have all electrons paired, meaning no unpaired electrons are present.

Species with unpaired electrons like \( \mathrm{C}_{2}^{+} \) and \( \mathrm{B}_{2}^{+} \) tend to have higher electron affinity because they are more likely to accept additional electrons to achieve greater stability through electron pairing.

Molecular Orbital Theory

Molecular Orbital Theory is a fundamental concept that helps explain the behavior of electrons in a molecule. Unlike atomic orbitals that focus on electrons in individual atoms, molecular orbitals cover the entire molecule. They form by the combination of atomic orbitals when atoms bond, providing a more comprehensive view of molecular electron behavior.

In understanding molecular orbitals:

• Molecules like \( \mathrm{C}_2^+ \) and \( \mathrm{B}_2^+ \) have molecular orbitals corresponding to their valence electron configurations.
• Electrons fill these orbitals in order of increasing energy, similar to atomic orbitals.
• The presence of bonding and antibonding molecular orbitals further explains aspects of molecular stability and reactivity.

This theory suggests that molecules seek to minimize energy, often by achieving stable electron configurations, which influences their electron affinity. In the context of the problem, knowing the filling of molecular orbitals helps to predict which molecule is more likely to accept an electron, influenced by the presence of any unpaired electrons or partially filled orbitals.