Using VB theory and the Lewis structure model, determine the bond order in (a) H2, (b) Na2, (c) S2, (d) N2 and (e) Cl2. Is there any ambiguity with finding the bond orders by this method?
- Does VB theory indicate that the diatomic molecule He2 is a viable species? Rationalize your answer.
(a) Use MO theory to determine the bond order in each of [He2] 2 and [He2] 2. (b) Does the MO picture of the bonding in these ions suggest that they are viable species?
The Correct Answer and Explanation is:
1. Bond Order Using Valence Bond (VB) Theory and Lewis Structures
Using VB theory and Lewis structures, bond order is the number of bonds shared between atoms in a molecule. It’s calculated as:
Bond Order = (Number of bonding electron pairs between atoms)
(a) H₂
- Each H atom has 1 valence electron.
- H₂ shares a pair of electrons → 1 single bond.
- Bond Order = 1
(b) Na₂
- Each Na has 1 valence electron (3s¹).
- Like H₂, they share a pair of electrons → 1 bond.
- Bond Order = 1
(c) S₂
- Sulfur has 6 valence electrons (Group 16).
- S₂ forms a double bond (like O₂): S=S.
- Bond Order = 2
(d) N₂
- Nitrogen has 5 valence electrons.
- Triple bond in N₂: N≡N.
- Bond Order = 3
(e) Cl₂
- Chlorine has 7 valence electrons.
- Shares one pair → single bond.
- Bond Order = 1
Ambiguity in VB/Lewis Bond Orders:
Yes. VB theory and Lewis structures can be ambiguous, especially:
- When dealing with resonance structures, delocalized bonding (e.g., O₃).
- Transition metals or molecules with unpaired electrons.
- Fails to explain bonding in excited states, magnetism, or bonding energies accurately.
2. He₂ and VB Theory
According to Valence Bond theory, He₂ is not a viable species:
- Each He atom has a full 1s² shell.
- No need to share electrons; forming a bond would increase repulsion.
- No unpaired electrons to overlap; so no covalent bond can form.
- Hence, He₂ is unstable and does not exist under normal conditions.
3. Bond Order of [He₂]²⁺ and [He₂]²⁻ Using MO Theory
In Molecular Orbital (MO) Theory, we calculate bond order as:
Bond Order = (Bonding electrons – Antibonding electrons) / 2
(a) [He₂]²⁺
- He₂ has 4 electrons (2 per He).
- [He₂]²⁺ loses 2 electrons → 2 electrons total.
- Fill σ(1s): 2 electrons.
- No electrons in σ*(1s).
- Bond Order = (2 – 0) / 2 = 1
- Viable species: Yes, stable in high-energy environments.
(b) [He₂]²⁻
- He₂ has 4 electrons + 2 = 6 electrons.
- σ(1s): 2, σ*(1s): 2, then next 2 go into σ*(1s) → total of 4 in antibonding.
- Bond Order = (2 – 4) / 2 = –1
- Viable species: No, negative bond order → repulsion > attraction.
Explanation
The stability and bonding of diatomic species like H₂, N₂, or He₂ can be understood using both Valence Bond (VB) theory and Molecular Orbital (MO) theory, though each has its strengths and limitations. VB theory, based on Lewis structures, predicts bond order by counting shared electron pairs. For instance, H₂ has one shared pair and thus a bond order of 1, while N₂ has a triple bond (bond order 3). However, this model oversimplifies bonding in molecules with delocalized electrons or resonance, such as O₂ or benzene, and cannot explain magnetic or energetic behavior accurately.
He₂ provides a good example of the limitations of VB theory. Helium atoms have full 1s orbitals, and thus no tendency to form bonds; VB theory correctly predicts He₂ as non-viable. MO theory, however, gives a quantitative basis: He₂ has two electrons in bonding and two in antibonding orbitals, yielding a bond order of 0, confirming its instability.
Charged helium species give more insight. [He₂]²⁺, which has two electrons, fills only the bonding σ(1s) orbital, with no electrons in the antibonding σ*(1s) orbital. This gives a bond order of 1, indicating a stable bond. On the other hand, [He₂]²⁻ has six electrons: two in bonding and four in antibonding orbitals, resulting in a bond order of –1. This negative bond order suggests that the molecule is inherently unstable and will not exist under normal conditions.
Thus, MO theory extends VB theory by explaining why certain molecules exist or not based on energy considerations and orbital overlap. It offers a more complete picture, especially for ions, excited states, and molecules with unusual electron configurations.
