Question

In which of the following diatomic molecules would the bond strength be expected to weaken as an electron is removed? a. \(\mathrm{H}_{2}\) c. \(\mathrm{C}_{2}^{2-}\) b. \(\mathrm{B}_{2}\) d. \(\mathrm{OF}\)

Short answer

The bond strength is expected to weaken as an electron is removed for the diatomic molecule \(\mathrm{H}_{2}\).

Step-by-step solution

Let's first review the molecular orbital diagrams for each of the molecules. We need to know the electronic configuration and identify the highest occupied molecular orbital (HOMO) since this is where an electron would be removed: - For \(\mathrm{H}_{2}\), the electronic configuration is σ1s^2. The HOMO is σ1s. - For \(\mathrm{B}_{2}\), the electronic configuration is σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2p_x^1 π2p_y^1. The HOMO is π2p_y (before π2p_x based on filling rules). - For \(\mathrm{C}_{2}^{2-}\), the electronic configuration is σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2p_x^2 π2p_y^2 σ2p_z^1. The HOMO is σ2p_z. - For \(\mathrm{OF}\), the electronic configuration is σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 σ2p^2 π2p_x^2 π2p_y^2 σ*2p_z^2 π*2p_x^1 π*2p_y^1. The HOMO is π*2p_y (before π*2p_x based on filling rules). #step 2#: Calculate the initial bond orders

Now, let's calculate the bond order (BO) for each molecule: - For \(\mathrm{H}_{2}\): BO = (2 - 0) /2 = 1 - For \(\mathrm{B}_{2}\): BO = (4 - 4) /2 = 0 - For \(\mathrm{C}_{2}^{2-}\): BO = (6 - 4) /2 = 1 - For \(\mathrm{OF}\): BO = (8 - 6) /2 = 1 #step 3#: Determine bond order after electron removal

Next, let's calculate the bond order of each molecule after removing an electron: - For \(\mathrm{H}_{2}\): The electronic configuration becomes σ1s^1. The new BO = (1 - 0) /2 = 0.50. - For \(\mathrm{B}_{2}\): The electronic configuration becomes σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2p_x^1. The new BO = (3 - 4) /2 = -0.50. - For \(\mathrm{C}_{2}^{2-}\): The electronic configuration becomes σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 π2p_x^2 π2p_y^2. The new BO = (6 - 4) /2 = 1. - For \(\mathrm{OF}\): The electronic configuration becomes σ1s^2 σ*1s^2 σ2s^2 σ*2s^2 σ2p^2 π2p_x^2 π2p_y^2 σ*2p_z^2 π*2p_x^1. The new BO = (8 - 5) /2 = 1.50. #step 4#: Identify which bond weakens

Now, we need to find which bond will weaken (i.e. the bond order decreases) when an electron is removed: - For \(\mathrm{H}_{2}\): The bond order decreases from 1 to 0.50. - For \(\mathrm{B}_{2}\): The bond order increases from 0 to -0.50 (bond formation, not weakening). - For \(\mathrm{C}_{2}^{2-}\): The bond order remains the same, at 1. - For \(\mathrm{OF}\): The bond order increases from 1 to 1.50 (bond strengthening, not weakening). #answer#: The bond strength is expected to weaken as an electron is removed for the diatomic molecule \(\mathrm{H}_{2}\).

Key concepts

Bond Order Calculation

Bond order is a useful concept when it comes to understanding the strength and stability of bonds between atoms. In molecular orbital theory, the bond order is half the difference between the number of bonding electrons and the number of antibonding electrons. Mathematically, bond order (BO) is given by the formula:

\[\begin{equation} BO = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \end{equation}\]
To calculate the bond order in diatomic molecules, we first need to establish the electronic configuration and identify which orbitals are occupied by the bonding and antibonding electrons. The bonding electrons strengthen the bond between atoms, while the antibonding electrons weaken it.

• The higher the bond order, the stronger and more stable the bond.
• A bond order of zero suggests that the molecule is unstable under normal conditions.
• Removing electrons from antibonding orbitals can increase the bond order and therefore increase bond strength.

In the exercise provided, calculations showed how bond orders change when an electron is removed, leading to an understanding of the effects on bond strength.

Diatomic Molecules

Diatomic molecules are molecules composed of only two atoms, which can be either the same element or different elements. Understanding these molecules is critical in chemistry because they serve as simple models for studying chemical bonding.

In the context of molecular orbital theory, each diatomic molecule has a specific electronic configuration that describes the distribution of electrons in bonding and antibonding molecular orbitals. The electronic configurations are determined by applying principles such as Hund's rule and the Pauli exclusion principle.

For example:

• \textbf{Homonuclear diatomic molecules} like \( \mathrm{H}_{2} \) and \( \mathrm{B}_{2} \) consist of atoms from the same element. These molecules' molecular orbitals are symmetrical.
• \textbf{Heteronuclear diatomic molecules}, like \( \mathrm{OF} \), consist of different atoms and have molecular orbitals that are not symmetrical due to differences in electronegativity.

Given how changes in electronic configurations influence properties like bond strength, diatomic molecules are also key in exploring concepts like ionization energy and bond lengths.

Electron Removal Effect on Bond Strength

The removal of an electron from a diatomic molecule can significantly affect its bond strength. If an electron is removed from a bonding molecular orbital, the bond is expected to weaken because there are fewer electrons contributing to the bond. Alternatively, if an electron is taken out from an antibonding orbital, the bond may actually become stronger since antibonding electrons act to destabilize the bond.

In the exercise given, we observe this by comparing the bond order before and after an electron is removed. A decrease in bond order indicates a weakening of the bond, which is precisely the case with \( \mathrm{H}_{2} \). The bond order calculation is a predictor of the overall bond strength and whether the molecular bond will be weakened or strengthened by such electron changes.

It's important to remember that the location of the electron removed plays a critical role. Electrons in the highest occupied molecular orbital (HOMO) are typically removed first, and based on molecular orbital theory, the impact on bond strength is immediate and quantifiable through bond order calculations.