Problem 86 - Chemistry Principles and Practice

Question

Draw the molecular orbital diagram, including the electrons, and write the electron configuration of \(\mathrm{H}_{2}^{-}\). Give the bond order and the number of unpaired electrons, if any. Is this a stable species?

Step-by-Step Solution

Answer

Electron configuration: \( \sigma_{1s}^{2} \sigma_{1s}^{*1} \), Bond order: 0.5, 1 unpaired electron, unstable species.

Step 1: Draw Atomic Orbitals for H

Each hydrogen atom contributes one 1s atomic orbital. In a molecular orbital diagram, start by drawing the atomic orbitals on either side of the diagram. Each hydrogen atom initially has one electron in its 1s orbital.

Step 2: Combine Atomic Orbitals to Form Molecular Orbitals

Combine the two 1s orbitals to form two molecular orbitals: one bonding orbital ( sigma_{1s} ) and one antibonding orbital ( sigma_{1s}^{*} ). Place these in the center of the diagram. sigma_{1s} is lower in energy than the atomic orbitals, and sigma_{1s}^{*} is higher.

Step 3: Add Electrons to Molecular Orbitals

H_{2}^{-} has a total of three electrons: two from the hydrogen atoms and one extra electron for the negative charge. Fill the molecular orbitals starting from the lowest energy level, which is sigma_{1s} , with two electrons and place the remaining electron in sigma_{1s}^{*} .

Step 4: Write the Electron Configuration

The electron configuration of H_{2}^{-} is written by listing the molecular orbitals with their electron occupancy: sigma_{1s}^{2} sigma_{1s}^{*1} .

Step 5: Calculate Bond Order

Bond order is calculated using the formula: \( \text{Bond Order} = \frac{1}{2} (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}) \). For H_{2}^{-}, Bond Order = \( \frac{1}{2} (2 - 1) = \frac{1}{2} \) which is 0.5.

Step 6: Determine Unpaired Electrons and Stability

Since there is one electron in the sigma_{1s}^{*} orbital, H_{2}^{-} has one unpaired electron. The bond order of 0.5 indicates a weak bond, suggesting that H_{2}^{-} is not very stable.

Key Concepts

Bond Order

Bond order is a crucial concept in understanding the nature of a bond within a molecule. It is a measure of the strength and stability of a bond. To calculate the bond order, you can use the formula: \[ \text{Bond Order} = \frac{1}{2} (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}) \]This formula essentially tells you how many net bonding interactions are present in the molecule.

• A higher bond order indicates a stronger, more stable bond.
• A bond order greater than zero suggests that a bond exists.
• If the bond order is zero or negative, it indicates no bond exists.

The bond order of \( \mathrm{H}_2^{-} \) is calculated to be 0.5, which means there is a partial bond. This partial bond represents a weak interaction between the two hydrogen atoms.

Molecular Orbital Diagram

A molecular orbital diagram is a visual representation of the molecular orbitals in a molecule. It shows the relative energy levels of these orbitals and the electrons' distribution between them. In the case of \( \mathrm{H}_2^{-} \):- The molecular orbital diagram consists of: - Two hydrogen 1s atomic orbitals combining to form 1. A lower energy bonding molecular orbital ( \( \sigma_{1s} \) ) 2. A higher energy antibonding molecular orbital ( \( \sigma_{1s}^{*} \) )- Electrons are filled starting from the lowest energy orbitalYou should first fill the bonding molecular orbital ( \( \sigma_{1s} \) ) before placing any electrons in the antibonding ( \( \sigma_{1s}^{*} \) ) orbital. This systematic approach helps to predict the stability and magnetism of the molecule, as illustrated in the steps for \( \mathrm{H}_2^{-} \).

Electron Configuration

Electron configuration is a method of indicating the arrangement of electrons within the orbitals of an atom or molecule. For molecular orbitals, you list the orbitals in the order of filling and note the number of electrons in each.For \( \mathrm{H}_2^{-} \), the electron configuration is \( \sigma_{1s}^{2} \sigma_{1s}^{*1} \). - This means that: - Two electrons occupy the bonding \( \sigma_{1s} \) orbital - One electron resides in the antibonding \( \sigma_{1s}^{*} \) orbitalIt's important to note that adding electrons to higher energy antibonding orbitals can significantly reduce the molecule's stability. This is why \( \mathrm{H}_2^{-} \) is less stable than \( \mathrm{H}_2 \), which has no electrons in antibonding orbitals.

Stability of Molecules

The stability of molecules is influenced by their bond order, electron configuration, and the presence of unpaired electrons. These factors together determine whether a molecule can exist stably or is prone to dissociation.For \( \mathrm{H}_2^{-} \):- The bond order is 0.5. - There is one unpaired electron present in the antibonding orbitals.These characteristics make \( \mathrm{H}_2^{-} \):

• \( \mathrm{H}_2^{-} \) Less stable than a typical diatomic hydrogen molecule (\( \mathrm{H}_2 \)) because any increase in electrons in antibonding orbitals weakens the bond.
• Has a paramagnetic nature due to the presence of unpaired electrons, meaning it is slightly attracted to magnetic fields.

This combination of a low bond order and unpaired electrons indicates \( \mathrm{H}_2^{-} \) is not a strongly stable ion.