Problem 43 - Chemistry and Chemical Reactivity

Question

Which of the homonuclear, diatomic molecules of the second-period elements (from \(\mathrm{Li}_{2}\) to \(\mathrm{Ne}_{2}\) ) are paramagnetic? Which have a bond order of \(1 ?\) Which have a bond order of \(2 ?\) Which diatomic molecule has the highest bond order?

Step-by-Step Solution

Answer

Paramagnetic: \(\text{B}_2\), \(\text{O}_2\); Bond order 1: \(\text{Li}_2\), \(\text{O}_2\); Bond order 2: \(\text{C}_2\), \(\text{B}_2\); Highest bond order: \(\text{N}_2\).

Step 1: Identify Second-Period Elements

The second-period elements are Lithium (Li), Beryllium (Be), Boron (B), Carbon (C), Nitrogen (N), Oxygen (O), Fluorine (F), and Neon (Ne). We are considering homonuclear diatomic molecules like \( \text{Li}_2 \), \( \text{Be}_2 \), ..., \( \text{Ne}_2 \).

Step 2: Construct Molecular Orbital Diagrams

To determine magnetic properties and bond order, construct molecular orbital (MO) diagrams for each diatomic molecule. Fill the orbitals according to increasing energy, starting from \( \sigma_{1s} \) to \( \ \sigma_{2p_z}^* \). Consider magnetic properties—unpaired electrons indicate paramagnetism.

Step 3: Determine Paramagnetic Molecules

Based on the MO diagrams, identify molecules with unpaired electrons. \( \text{B}_2 \) and \( \text{O}_2 \) are paramagnetic due to unpaired electrons in their \( \pi \) orbitals.

Step 4: Calculate Bond Order

Bond order is calculated using the formula:\[ \text{Bond Order} = \frac{\text{(Number of Bonding Electrons)} - \text{(Number of Antibonding Electrons)}}{2} \]Apply this formula to each diatomic molecule's MO diagram.

Step 5: Identify Molecules with Bond Order 1

For \( \text{Li}_2 \), the bond order is:\[ \frac{2 - 0}{2} = 1 \]For \( \text{O}_2 \), the bond order is also 1.

Step 6: Identify Molecules with Bond Order 2

For \( \text{C}_2 \) and \( \text{B}_2 \), the bond order is:\[ \frac{4 - 0}{2} = 2 \]

Step 7: Find Highest Bond Order

\( \text{N}_2 \) has the highest bond order:\[ \frac{6 - 0}{2} = 3 \]

Step 8: Conclusion

Paramagnetic molecules are \( \text{B}_2 \) and \( \text{O}_2 \). \( \text{Li}_2 \) and \( \text{O}_2 \) have a bond order of 1, \( \text{C}_2 \) and \( \text{B}_2 \) have a bond order of 2, and \( \text{N}_2 \) has the highest bond order of 3.

Key Concepts

Diatomic Molecules

Diatomic molecules consist of two atoms, which could be either the same or different elements. When we talk about homonuclear diatomic molecules, we are referring to molecules formed by two identical atoms. In the case of the second-period elements (Li, Be, B, C, N, O, F, Ne), diatomic forms include molecules like \(\text{Li}_2\), \(\text{Be}_2\), and so on up to \(\text{Ne}_2\).
For these elements, molecular orbital theory helps us understand how electrons are distributed within the molecules and predict their properties, such as bond strength and magnetism. The arrangement of electrons in molecular orbitals influences the molecule's stability and reactivity.
Molecular orbitals are formed when atomic orbitals of two atoms overlap, and they are filled based on the principle of increasing energy levels. This forms the basis for predicting various properties of diatomic molecules.

Paramagnetism

Paramagnetism arises in molecules that contain one or more unpaired electrons. These unpaired electrons generate magnetic moments that do not cancel each other out, resulting in a net magnetic moment.
Using molecular orbital theory, we can identify paramagnetic molecules by examining their molecular orbital diagrams. If a molecule has unpaired electrons in its molecular orbitals, it is classified as paramagnetic.

• For second-period diatomic molecules, \( \text{B}_2 \) and \( \text{O}_2 \) are examples of paramagnetic molecules. \( \text{B}_2 \) has unpaired electrons in its \( \pi \) orbitals, whereas \( \text{O}_2 \) retains unpaired electrons in the \( \pi^* \) orbitals.

This means that these molecules will be attracted to magnetic fields, a characteristic property of paramagnetic substances.

Bond Order

Bond order is a concept that helps us determine the strength and stability of a bond between two atoms in a molecule. It is calculated through the formula: \[\text{Bond Order} = \frac{(\text{Number of Bonding Electrons}) - (\text{Number of Antibonding Electrons})}{2}\]Bond order gives us insight into how tightly or loosely bonded two atoms are within a molecule.
In diatomic molecules, a higher bond order indicates a stronger, more stable bond. For example, in the second-period diatomic molecules:

• \( \text{Li}_2 \) and \( \text{O}_2 \) have a bond order of 1, implying a single bond.
• \( \text{C}_2 \) and \( \text{B}_2 \) have a bond order of 2, indicating a double bond.
• \( \text{N}_2 \) has a bond order of 3, which suggests a very strong triple bond.

Thus, \( \text{N}_2 \) is the strongest among the second-period diatomic molecules due to its highest bond order, reflecting its remarkable stability and lesser reactivity.