Question

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

Short answer

The bond strength weakens for the \(\mathrm{H}_{2}\) molecule as we remove an electron. Thus, the answer is option a. \(\mathrm{H}_{2}\).

Step-by-step solution

Finding the initial bond orders of the molecules

First, we need to find the bond orders of the given diatomic molecules using the Molecular Orbital Theory. Remember that the bond order can be calculated with the formula: Bond Order = (Number of electrons in bonding orbitals - Number of electrons in anti-bonding orbitals) / 2 a. \(\mathrm{H}_{2}\) has 2 electrons, both in the bonding orbital (1s). Bond order = (2 - 0) / 2 = 1 b. \(B_{2}\) has 10 electrons: 4 in the 1s orbitals (2 bonding, 2 anti-bonding), 2 in the 2s orbitals (2 bonding), and 4 in the 2p orbitals (2 bonding, 2 anti-bonding). Bond order = (6 - 4) / 2 = 1 c. \(C_{2}^{2-}\) has 12 electrons: 4 in the 1s orbitals (2 bonding, 2 anti-bonding), 2 in the 2s orbitals (2 bonding), and 6 in the 2p orbitals (4 bonding, 2 anti-bonding). Bond order = (8 - 4) / 2 = 2 d. OF has 14 electrons: 4 in the 1s orbitals (2 bonding, 2 anti-bonding), 2 in the 2s orbitals (2 bonding), and 8 in the 2p orbitals (4 bonding, 4 anti-bonding). Bond order = (8 - 6) / 2 = 1

Finding the new bond orders after removing an electron

Next, we need to find the new bond order for each molecule after removing one electron. We will remove the electron from the highest occupied molecular orbital (HOMO) of each molecule. a. \(\mathrm{H}_{2}\): After removing an electron from the bonding orbital (1s) Bond order = (1 - 0) / 2 = 0.5 b. \(B_{2}\): After removing an electron from the anti-bonding orbital (2p) Bond order = (6 - 3) / 2 = 1.5 c. \(C_{2}^{2-}\): After removing an electron from the anti-bonding orbital (2p) Bond order = (8 - 3) / 2 = 2.5 d. OF: After removing an electron from the anti-bonding orbital (2p) Bond order = (8 - 5) / 2 = 1.5

Comparing the bond orders before and after electron removal

Now we need to compare each molecule's bond order before and after one electron is removed. a. \(\mathrm{H}_{2}\): Bond order changed from 1 to 0.5 (weakened). b. \(B_{2}\): Bond order changed from 1 to 1.5 (strengthened). c. \(C_{2}^{2-}\): Bond order changed from 2 to 2.5 (strengthened). d. OF: Bond order changed from 1 to 1.5 (strengthened). Finally, we can answer the question: In which of these diatomic molecules would the bond strength be expected to weaken as an electron is removed? The bond strength weakens for the \(\mathrm{H}_{2}\) molecule as we remove an electron. Thus, the answer is option a. \(\mathrm{H}_{2}\).

Key concepts

Molecular Orbital Theory

When exploring the nature of chemical bonds in diatomic molecules, the Molecular Orbital Theory (MOT) is an indispensable framework. It postulates that atomic orbitals combine to form molecular orbitals which extend over the entire molecule.

These molecular orbitals are classed into two categories: bonding and anti-bonding orbitals. Electrons in bonding orbitals stabilize the molecule, contributing to bond formation, while electrons in anti-bonding orbitals can destabilize it, potentially leading to bond breakage.

Visualizing Molecular Orbitals

Imagine two atoms getting closer; their atomic orbitals overlap to form molecular orbitals. If the overlap is constructive, a bonding orbital is formed; if it's destructive, it results in an anti-bonding orbital. The electron placement in these orbitals is governed by the same principles as atomic orbitals, including Aufbau's principle, Hund's rule, and the Pauli exclusion principle.

Bond Order Calculation

The concept of bond order is a pivotal part of understanding molecular structure and stability. In MOT, the bond order essentially provides a count of the number of chemical bonds between a pair of atoms. It is calculated using a simple formula:
Bond Order = (Number of electrons in bonding orbitals - Number of electrons in anti-bonding orbitals) / 2

This quantity can predict the strength and length of the bond: a higher bond order implies a stronger, shorter bond. Vice versa, a lower bond order suggests a weaker, longer bond. For instance, a single bond has a bond order of 1, a double bond has a bond order of 2, and so on.

Applying Bond Order

Bond order serves as an excellent tool for predicting molecular stability. When applied to diatomic molecules, it helps us visualize which molecules are more likely to exist and persist in nature.

Diatomic Molecules Electron Removal

Investigating how the bond strength in diatomic molecules changes with electron removal is a thought-provoking topic. When an electron is removed, it is typically taken from the highest occupied molecular orbital (HOMO), which can be either a bonding or an anti-bonding orbital.

Electron removal from a bonding orbital decreases the bond order, thereby weakening the bond. In contrast, removing an electron from an anti-bonding orbital increases the bond order, strengthening the bond. This variance can be critically analyzed through MOT, providing insights into the resulting molecular stability after such electron shifts.

Real-World Implications

The behavior observed with electron removal has practical implications, such as in the field of spectroscopy or when predicting the behavior of reactive intermediates in chemical reactions. Understanding this process is also crucial for grasp in topics like ionization energy and redox reactions.