Problem 112 - Chemistry The Molecular Science

Question

Suppose in building up molecular orbitals, the \(\pi_{2 p}\) were placed above the \(\sigma_{2 p} .\) Prepare a diagram similar to Figure 6.11 based on these changes. For which species in Table 6.4 would this change in relative energies of the MOs affect the prediction of number of bonds and number of unpaired electrons?

Step-by-Step Solution

Answer

Species like B\(_2\), C\(_2\), and N\(_2\) might be affected by the change in MO order.

Step 1: Understanding Molecular Orbitals

In molecular orbital (MO) theory, atomic orbitals combine to form molecular orbitals that are classified as bonding, non-bonding, or anti-bonding. The typical order for the 2p orbitals is \(\sigma_{2p} < \pi_{2p} < \pi_{2p}^* < \sigma_{2p}^*\). In this exercise, we must reverse the order of the \(\pi_{2p}\) and \(\sigma_{2p}\) orbitals.

Step 2: Rearrange MO Energy Levels

Reorder the molecular orbitals such that \(\pi_{2p}\) is above \(\sigma_{2p}\) instead of the other way around. The modified sequence becomes \(\sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^* < \pi_{2p}\). Draw this configuration.

Step 3: Compare to Original Molecular Orbital Diagram

Compare the modified diagram to the original orbitals in Figure 6.11. Identify any changes in the filling order for molecular species due to the shift in energy levels of \(\pi_{2p}\) and \(\sigma_{2p}\) orbitals.

Step 4: Analyze Bond Orders

Determine the bond order by calculating \(\text{Bond Order} = \frac{1}{2}(\text{Number of Electrons in Bonding MOs} - \text{Number of Electrons in Antibonding MOs})\) for each species in Table 6.4 using both the original and modified MO configurations.

Step 5: Assess Unpaired Electrons

Examine each species in Table 6.4 to see how electrons fill the modified MOs. Determine the number of unpaired electrons by checking the electron spin in both the original and modified orbital diagram.

Step 6: Identify Affected Species

List all the species where the modified arrangement affects the predicted number of bonds or unpaired electrons by comparing the new calculations to the original predictions.

Key Concepts

MOs energy levels

Molecular Orbital (MO) theory investigates how atomic orbitals combine to create molecular orbitals, having distinct energy levels. These orbitals can be classified as bonding, non-bonding, or anti-bonding. In typical cases, for 2p orbitals, the order is

• \(\sigma_{2p}\)
• \(\pi_{2p}\)
• \(\pi_{2p}^*\)
• \(\sigma_{2p}^*\)

In this exercise, however, you reverse the positions of \(\pi_{2p}\) and \(\sigma_{2p}\). This means that \(\pi_{2p}\) orbitals become higher in energy than \(\sigma_{2p}\) orbitals. Such a reordering influences how electrons fill these orbitals, ultimately affecting molecular properties like bond order and magnetic characteristics.

bond order

Bond order is an important aspect in the stability and number of bonds between atoms. It is calculated using the formula: \[\text{Bond Order} = \frac{1}{2} (\text{Number of Electrons in Bonding MOs} - \text{Number of Electrons in Antibonding MOs})\]When the energy levels of molecular orbitals are adjusted, the number of electrons in bonding or anti-bonding orbitals might change, potentially altering bond order. A higher bond order often indicates a stronger bond. For instance, a bond order of 1 represents a single bond, while a bond order of 2 signifies a double bond. By comparing the bond orders in both the original and modified orbital configurations, you can predict which molecular species undergo changes in bonding.

unpaired electrons analysis

Determining the number of unpaired electrons is crucial for predicting magnetic properties. In MO theory, this involves examining how electrons populate the orbitals. A molecule with unpaired electrons typically exhibits paramagnetism, which is an attraction to magnetic fields.
When you rearrange the MO energy levels, the order in which electrons fill these levels may result in different numbers of unpaired electrons than initially expected. By examining both the original and modified MO diagrams, you can identify changes in electron pairing, impacting whether a molecule will be magnetic or not.

atomic orbitals combination

The foundation of MO theory is the combination of atomic orbitals from each atom to form molecular orbitals. This creates new energy levels for electrons in a molecule. Each type of atomic orbital (s, p, d, etc.) from different atoms overlaps to form bonding and anti-bonding molecular orbitals.
The position and energy of these molecular orbitals determine how electrons are distributed in a molecule. When

• \(\sigma\)
• and \(\pi\)

orbitals change order, it affects the overlap and energy differences of these orbitals. Understanding how atomic orbitals combine allows you to predict the molecular structure and behavior, such as bond lengths and angles.