Problem 45 - 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

\(\mathrm{B}_{2}\) is paramagnetic. Bond order 1: \(\mathrm{Li}_2\), \(\mathrm{B}_2\), \(\mathrm{F}_2\). Bond order 2: \(\mathrm{C}_2\), \(\mathrm{O}_2\). Highest bond order: \(\mathrm{N}_2\).

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). The homonuclear diatomic molecules of these elements range from \(\mathrm{Li}_2\) to \(\mathrm{Ne}_2\).

Step 2: Determine Paramagnetic Molecules

A molecule is paramagnetic if it has unpaired electrons. By assessing molecular orbital configurations, \(\mathrm{B}_{2}\) is paramagnetic as it has two unpaired electrons.

Step 3: Calculate Bond Orders

Calculate bond order using the formula: \( \text{Bond order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons}) \).

Step 4: Apply Bond Order Calculations

- \(\mathrm{Li}_2\) has a bond order of 1.- \(\mathrm{Be}_2\) has a bond order of 0.- \(\mathrm{B}_2\) has a bond order of 1.- \(\mathrm{C}_2\) has a bond order of 2.- \(\mathrm{N}_2\) has a bond order of 3.- \(\mathrm{O}_2\) has a bond order of 2.- \(\mathrm{F}_2\) has a bond order of 1.- \(\mathrm{Ne}_2\) has a bond order of 0.

Step 5: Identify Molecules with Specific Bond Orders

- Bond order of 1: \(\mathrm{Li}_2\), \(\mathrm{B}_2\), \(\mathrm{F}_2\).- Bond order of 2: \(\mathrm{C}_2\), \(\mathrm{O}_2\).- Highest bond order: \(\mathrm{N}_2\) with a bond order of 3.

Key Concepts

Paramagnetism and Molecular Orbitals

In the realm of chemistry, **paramagnetism** is a lot more engaging than it sounds. It occurs in molecules that have unpaired electrons, which can make them attracted to magnetic fields. Essentially, unpaired electrons give these molecules their magnetic vibe. To figure out if a molecule is paramagnetic, you can look at its molecular orbital (MO) configuration.
A prime example among second-period elements is \( \text{B}_2 \). By sketching its MO diagram, you'd observe it has two unpaired electrons. Here's why this happens: Although it's counterintuitive, the energy levels for the pi orbitals are lower than the sigma orbital when we move from \( \text{Li}_2 \) to \( \text{N}_2 \). Hence, in \( \text{B}_2 \), electrons tend to occupy the pi orbitals first, resulting in unpaired electrons.
Key takeaways for identifying paramagnetic molecules:

• Check for unpaired electrons in the MO configuration.
• Compare to determine spin states – unpaired means paramagnetic.
• MO diagrams provide crucial insights.

Understanding Bond Order

Bond order is like a relationship score for atoms within a molecule. It tells us about the stability and strength of a bond. The higher the bond order, the stronger the bond. Calculation of bond order involves counting bonding and antibonding electrons in the MO diagram and applying a simple formula: \[\text{Bond order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons})\]This formula is straightforward, but so powerful! For example, a bond order of 1 means one bond, akin to a single covalent bond, while a bond order of 2 represents a double bond.
Relating to second-period elements:

• For \( \text{Li}_2 \), \( \text{B}_2 \), and \( \text{F}_2 \), the bond order is 1, signifying weaker, but existing bonds.
• \( \text{C}_2 \) and \( \text{O}_2 \) have a bond order of 2, hence more stable and strong bonds.
• \( \text{N}_2 \) stands out with a bond order of 3, indicating a notably robust triple bond.

Understanding bond order helps explain why some molecules are more resilient than others, providing a predictive tool for chemical behavior.

Second-Period Elements and Diatomic Molecules

The **second-period elements** occupy the second row of the periodic table, ranging from lithium (Li) to neon (Ne). These elements form various homonuclear diatomic molecules, such as \( \text{Li}_2 \) and \( \text{Ne}_2 \). These diatomic molecules help us understand fundamental chemical bonding concepts.
In terms of molecular bonding, this row unveils a fascinating transition in properties:

• Moving from left to right, you'll observe a shift from metallic to non-metallic character in elements.
• Bonding tendencies also transition from ionic (Li, Be) to covalent (B, C, N, O, F).
• Neon is an inert gas, typically not forming bonds, hence \( \text{Ne}_2 \) has a bond order of zero as it doesn't exist naturally.

This progression is pivotal in understanding molecular structure and behavior. It particularly shines in explaining how electron configuration plays a central role in bond formation and stability. The second-period elements also demonstrate the unique features and nuances that come with filling the \(2p\) orbitals.