Problem 106 - Chemistry The Central Science In Si Units

Question

Place the following molecules and ions in order from smallest to largest bond order: \(\mathrm{N}_{2}{\underline{\phantom{xx}}}^{2+}, \mathrm{He}_{2}^{+}, \mathrm{Cl}_{2} \mathrm{H}_{2}^{-}, \mathrm{O}_{2}{\underline{\phantom{xx}}}^{2-}\).

Step-by-Step Solution

Answer

\( \mathrm{He}_{2}^{+}, \mathrm{H}_{2}^{-}, \mathrm{O}_{2}^{2-}, \mathrm{N}_{2}^{2+}, \mathrm{Cl}_{2} \)

Step 1: Understanding Bond Order

Bond order is the number of chemical bonds between a pair of atoms. It can be calculated from molecular orbital theory as half the difference between the number of bonding electrons and antibonding electrons.

Step 2: Calculating Bond Order for Each Molecule/Ion

- For \( \mathrm{N}_{2}^{2+} \), remove 2 electrons from \( \mathrm{N}_2 \). Bond order = \( (8 - 4)/2 = 2 \).- For \( \mathrm{He}_{2}^{+} \), bond order = \( (2 - 1)/2 = 0.5 \).- For \( \mathrm{Cl}_{2} \), bond order = \( (14 - 8)/2 = 3 \).- For \( \mathrm{H}_{2}^{-} \), bond order = \( (2 - 0)/2 = 1 \).- For \( \mathrm{O}_{2}^{2-} \), bond order = \( (8 - 6)/2 = 1 \).

Step 3: Ordering the Bond Orders

Identify the bond orders calculated: \( \mathrm{He}_{2}^{+} = 0.5 \), \( \mathrm{H}_{2}^{-} = 1 \), \( \mathrm{O}_{2}^{2-} = 1 \), \( \mathrm{N}_{2}^{2+} = 2 \), \( \mathrm{Cl}_{2} = 3 \).

Step 4: Arranging in Sequence

Arrange the molecules/ions in the sequence of increasing bond order: \( \mathrm{He}_{2}^{+} \), \( \mathrm{H}_{2}^{-} \), \( \mathrm{O}_{2}^{2-} \), \( \mathrm{N}_{2}^{2+} \), \( \mathrm{Cl}_{2} \).

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MO Theory) offers a comprehensive way to understand how electrons are distributed in molecules. This theory suggests that atomic orbitals combine to form molecular orbitals when atoms bond together. These molecular orbitals can hold electrons, similar to atomic orbitals, but they are spread out over the entire molecule rather than being localized around individual atoms. This approach helps explain the bonding and properties of molecules that might not be easily understood through other models, such as Valence Bond Theory. MO theory divides molecular orbitals into bonding and antibonding types:

• Bonding Molecular Orbitals: These are lower in energy and tend to hold atoms together. Electrons in these orbitals increase stability.
• Antibonding Molecular Orbitals: These are higher in energy and can destabilize a molecule. Electrons here can pull atoms apart.

The bond order, a major concept in MO Theory, is calculated as half the difference between the number of electrons in bonding orbitals and antibonding orbitals, reflecting the overall bond strength.

Chemical Bonds

Chemical bonds are the connections between atoms that result from the attraction of electrons. Understanding these bonds is crucial, as they determine the structure and stability of molecules. Chemical bonds can be represented and analyzed in various ways. In the context of Molecular Orbital Theory, we can easily visualize how electrons shared between atoms result in bonding or antibonding interactions.

• Ionic Bonds: Formed when electrons are transferred from one atom to another, typically between metals and nonmetals.
• Covalent Bonds: Occur when electrons are shared between atoms, commonly observed between nonmetals.
• Metallic Bonds: Characterized by a 'sea' of shared free electrons moving through a lattice of metal ions, giving metals their unique properties.

Molecular orbital theory predominantly focuses on covalent bonding, where overlapping atomic orbitals create shared molecular orbitals that maintain the molecule's structural integrity.

Electrons in Molecules

Electrons play a vital role in the formation, structure, and stability of molecules. Within MO Theory, electrons can occupy various molecular orbitals, impacting the molecule's energy and stability. These electrons can be distributed in two main types of orbitals:

• Bonding Orbitals: Occupied by electrons that enhance the stability of a molecule, leading to the formation of chemical bonds.
• Antibonding Orbitals: Higher in energy, these can reduce stability if occupied by electrons.

The arrangement of electrons in these orbitals directly influences molecular properties such as bond length, bond angle, and bond energy. Calculating bond order involves determining how many electrons are in bonding vs. antibonding orbitals, giving us a window into the strength and type of bond present in the molecule. Understanding these concepts is crucial to predicting molecular behavior and reactivity in chemical reactions.