Problem 91 - Chemistry Principles and Practice

Question

Which species, \(\mathrm{N}_{2}\) or \(\mathrm{N}_{2}^{-}\), has the higher bond order? Explain your answer.

Step-by-Step Solution

Answer

\(\mathrm{N}_2\) has a higher bond order (3) than \(\mathrm{N}_{2}^{-}\) (2.5), indicating a stronger bond.

Step 1: Define Bond Order

Bond order is a measure of the number of chemical bonds between a pair of atoms. It can be calculated using the formula: \[ \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \] A higher bond order indicates a stronger, more stable bond.

Step 2: Determine Electrons for \(\mathrm{N}_2\)

The nitrogen molecule, \(\mathrm{N}_2\), has a total of 14 electrons. We will distribute these electrons into molecular orbitals, starting with the lowest energy level to the highest: \[ \sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \pi_{2p}^4, \sigma_{2p}^2 \] For \(\mathrm{N}_2\), there are 10 bonding electrons and 4 antibonding electrons.

Step 3: Calculate Bond Order for \(\mathrm{N}_2\)

Using the bond order formula, calculate the bond order for \(\mathrm{N}_2\): \[ \text{Bond Order} = \frac{10 - 4}{2} = 3 \] This means \(\mathrm{N}_2\) has a bond order of 3, indicating a strong triple bond between the nitrogen atoms.

Step 4: Determine Electrons for \(\mathrm{N}_{2}^{-}\)

The species \(\mathrm{N}_{2}^{-}\) involves one extra electron compared to \(\mathrm{N}_2\), making the total electron count 15. With this additional electron, it enters the next available molecular orbital, which is an antibonding orbital: \(\pi^*_{2p}^1\). The electrons are now: \[ \sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \pi_{2p}^4, \sigma_{2p}^2, \pi^*_{2p}^1 \] Thus, there are 10 bonding electrons and 5 antibonding electrons.

Step 5: Calculate Bond Order for \(\mathrm{N}_{2}^{-}\)

Using the bond order formula, calculate the bond order for \(\mathrm{N}_{2}^{-}\): \[ \text{Bond Order} = \frac{10 - 5}{2} = 2.5 \] This means \(\mathrm{N}_{2}^{-}\) has a bond order of 2.5, indicating a slightly weaker bond compared to \(\mathrm{N}_2\).

Step 6: Compare Bond Orders

Comparing the bond orders, we find \(\mathrm{N}_2\) has a bond order of 3, while \(\mathrm{N}_{2}^{-}\) has a bond order of 2.5. Since a higher bond order means a stronger bond, \(\mathrm{N}_2\) has the higher bond order compared to \(\mathrm{N}_{2}^{-}\).

Key Concepts

Molecular Orbitals

Molecular orbitals are crucial in understanding how atoms bond together in molecules. In a simple sense, they are regions in a molecule where electrons have a high probability of being found. When atoms, like those in nitrogen molecules ( {N}_2 ) , come together, their atomic orbitals overlap to form molecular orbitals. This process helps explain how electrons are shared in a molecule. These orbitals can be bonding, which help hold the atoms together, or antibonding, which can weaken the bond. In nitrogen molecules, electrons fill these molecular orbitals following set rules, similar to the way they fill atomic orbitals. Understanding the distribution of electrons across these molecular orbitals is essential to determine a molecule's bond order.

Chemical Bonds

Chemical bonds are the attractive forces that hold atoms together in molecules. In the context of molecular orbitals, these bonds form as a result of electron sharing between atoms. The strength and number of these bonds can be described by the bond order, which is calculated from the number of electrons in bonding and antibonding molecular orbitals. In a nitrogen molecule ( {N}_2 ) , the triple bond results in a bond order of 3. This indicates strong, stable, and multiple overlapping bonds between the atoms. In contrast, an additional electron in ( {N}_2^{-} ) creates an antibonding effect, slightly reducing the overall bond order to 2.5, reflecting a weakened but still significant bonding interaction.

Bond Strength

Bond strength refers to how strongly atoms are held together in a molecule. It directly relates to the bond order: the higher the bond order, the stronger the bond. A triple bond, as seen in ( {N}_2 ) , results in significant bond strength due to a high bond order of 3. This makes the molecule extremely stable and difficult to break apart. On the other hand, ( {N}_2^{-} ) has a bond order of 2.5, meaning its bond strength is slightly reduced compared to ( {N}_2 ) . This reduction is due to the presence of an additional antibonding electron weakening the connection between the atoms. Nevertheless, the bond remains relatively strong, just not as strong as the parent ( {N}_2 ) molecule.

Stability of Molecules

The stability of molecules is often linked to their bond order and the arrangement of their electrons in molecular orbitals. A higher bond order typically implies a more stable molecule. For ( {N}_2 ) , the bond order of 3 signifies outstanding stability, making it one of the most stable diatomic molecules known. This stability is due to the high number of bonding electrons relative to antibonding electrons, resulting in low reactivity. For ( {N}_2^{-} ) , the addition of an electron decreases the bond order to 2.5, indicating slightly reduced stability. Although still relatively stable, this slight reduction in bond order makes ( {N}_2^{-} ) more prone to engaging in chemical reactions compared to ( {N}_2 ). Understanding bond stability helps in predicting how molecules react under various conditions.