Molecular Orbital Theory & Bonding Order of O2 [+ MCQs & FAQs]

Overview
The molecular orbital theory considers the whole molecule as a single unit.
It presumes that the atomic orbitals of the combining atoms overlap to form new orbitals called molecular orbitals which are characteristic of the whole molecule.

Table of Contents Hide

1) Molecular Orbital Theory
2) Molecular Orbital Theory – MCQs
3) FAQs on Molecular Orbital Theory Tutorial
4) 10 Problems/Solutions for Molecular Orbital Theory
5) Summary of Molecular Orbital Theory Tutorial
6) You may also like to learn:

Molecular Orbital Theory

The molecular orbital surrounds two or more nuclei of the bonded atoms. 2 atomic orbitals, after overlapping, form 2 molecular orbitals that differ in energy.

Among them, having lower energy is called bonding molecular orbital while the other having higher energy is called an anti-bonding molecular orbital.

The bonding molecular orbital is symmetrical about the axis joining the nuclei of the bonded atoms (molecular axis).

It is designated as the sigma (σ) bonding molecular orbital while the antibonding molecular orbital, is called σ *.

The filling of electrons into the molecular orbitals occurs according to the Aufbau principle, Pauli’s exclusion concept, and Hund’s rule.

The two electrons (one from each hydrogen atom), therefore fill the low energy σ1s-orbital and have combined spin (↿⇂), while the high energy σ * 1sorbital stays empty.

Up until now, we have considered s and s orbital overlap for the formation of molecular orbitals of the hydrogen molecule.

Other kinds of overlaps happening in between p and p atomic orbitals to form molecular orbitals are described below.

There are three 2p atomic orbitals directed along with the three-perpendicular x, y, and z coordinates.

For the formation of molecular orbitals from p- orbitals, two cases arise:

(a) Head-on Approach

Here, the p-orbitals of the two atoms approach along the very same axis (i.e. p_x axis). This combination of the atomic orbitals generates σ(2p_x) bonding andσ* (2p_x) antibonding molecular orbitals. Both are in proportion to the nuclear axis.

(b) Sideways Approach

When the axes of two p-orbitals (i.e.p _y or p_z orbitals) are parallel to each other, they connect to form molecular orbitals.

The bonding molecular orbitals π(2p_y) or p (2p_z) have absolutely zero electron density on the nuclear axis (called the nodal plane). The electron density is consistently distributed above and listed below the nodal plane.

On the other hand, anti-bonding molecular orbitalsπ* (2p_y) andπ* (2p_z) have the least electron density in the π inter-nuclear area. Considering that the 2p_y and 2p_z atomic orbitals are degenerate (having the very same energy), the π – molecular orbitals i.e. π (2p_y) and π (2p_z) are likewise degenerate. So, are likewise theπ*(2p_y) andπ*(2p_z) molecular orbitals.

Total six molecular orbitals (3 bonding and three anti-bonding) are formed from two sets of 2p atomic orbitals. The bond formed as a result of direct overlap is σ bond, while that formed as a result of sideways overlap is called a π (pi) bond. As there are 3 bonding molecular orbitals, the p-orbitals overlap can result in the formation of at the most three bonds: one sigma and 2 π-bonds.

Relative Energies of the Molecular Orbitals

The relative energies of the molecular orbitals formed from 2s and 2p atomic orbitals in the case of homonuclear di-atomic molecules. The energies of the molecular orbitals are determined by spectroscopic measurements. The molecular orbitals of diatomic molecules such as O₂, F₂ and their negative and positive ions can be arranged in the following-increasing order of energy

σ (1s) <σ*(1s) <σ(2s) <σ*(2s) <σ (2p_x) <π (2p_y) =π(2p_z) <π*(2p_y) =π*(2p_z) <σ*(2p_x)

The diatomic molecules, such as N₂ and other -lighter molecules like B₂, C₂show slightly different energy order.

σ (1s) < σ*(1s) < σ(2s) < σ*(2s) <π (2p_y)= π(2p_z)< σ (2p_x)< π*(2p_y)= π*(2p_z)< σ*(2p_x)

Reason

It has been observed that in case of B₂, C₂ and N₂, σ2p_x is higher in energy than π2p_y= π2p_z. MOs. This reversal is because of mixing of 2s and 2p_x atomic orbitals.

Actually, the energy difference of 2s and 2p atomic orbitals is small. There is a possibility of mixing of these orbitals (i.e. hybridization of A.O.) as a result of which σ2s and σ * 2s MOs do not keep pure s-character. Similarly, σ2p_x and σ * 2p_x MOs do not have pure p-character. All the 4 MOs get sp-character.

Due to this mixing, their energies change in such a manner in which MOs σ2s and σ * 2s become more stable and are reduced in energy MOs as σ2p_x and σ* 2p_x become less stable and are raised in energy. Since πp-orbitals are not associated with mixing, so the energy of π2p_y= π2p_z stays unchanged.σ 2p_xis raised to such an extent that it ends up being greater in energy than π bondings.

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Anyways, O₂ and F₂ do not do so. The reason is the high energy difference of their 2s and 2p i.e. 1595 and 2078 kJmol^-1, for O₂ and F₂, respectively. These values are 554kJmol^-1 for boron, 846kJmol^-1 for carbon, and 1195kJmol^-1 for nitrogen. These energy differences have actually been calculated by spectroscopic techniques.

Bond Order

The variety of bonds formed between 2 atoms after the atomic orbitals overlap, is called the bond order and is taken as half of the difference between the number of bonding electrons and anti-bonding electrons. The number of bonds formed between H-atoms in hydrogen molecule may be calculated as follows:

Number of electrons in the bonding orbitals = 2

Number of electrons in the anti-bonding orbitals = 0

Bond order = 2 − 0/2 =1.

It is a typical practice that only MOs formed from valence orbital are thought about in bond order computations.

Molecular Orbital Structures of Some Diatomic Molecules

(i)Helium, He₂

The electronic configuration of He is 1s². The 1s orbitals of He-atoms combine to form one bonding σ (1s) and one anti-bonding σ * (1s) orbitals. Each He-atom contributes 2 electrons. Two electrons go into bonding molecular orbital σ (1s) and the remaining 2 go to antibondingσ* (1s) molecular orbital. The bond order for He₂ is absolutely zero i.e. 2 − 2/2= 0 and thus He₂molecule is not formed.

(ii) Nitrogen, N₂

Electronic configuration of N₂molecule is

From the electronic configuration of N₂, it is clear that six electrons enter into 3 outer bonding orbitals while no electrons participate in anti-bonding orbitals.

Hence, the bond order in N₂ molecule is 6-0/2= 6/2 = 3, which corresponds to the triple bond including one sigma and 2 π bonds. The bond dissociation energy of N₂ is very high, i.e. 941kJmol^-1.

(iii) Oxygen, 0₂

The bond order in O₂, is 6-2/2= 2, which corresponds to a double bond.

This is consistent with the big bond energy of 496kJ mol^-1 of oxygen molecule. The filling of molecular orbitals leaves 2 unpaired electrons in each of the π *(2p_y) and π *(2p_z) orbitals. Hence, the electronic configuration of the molecular orbitals accounts admirably for the paramagnetic properties of oxygen. This is among the greatest successes of the molecular orbital theory. Liquid O₂ is attracted towards the magnet.

Anyhow, when 2 more electrons are provided to O₂, it ends up being O₂^2-. The pragmatism disappears. Likewise, in O₂²⁺ the unpaired electrons are gotten rid of and paramagnetic property disappears there. The bond order of O₂^2-are likewise different from O₂ and are one and three, respectively. Similarly, M.O.T justifies that F₂ has a bond order of one and Ne does not make a bond with Ne.

Molecular Orbital Theory – MCQs

What is the central premise of the Molecular Orbital Theory?
- a) The nucleus is the central unit.
- b) Electrons move in fixed orbits.
- c) The whole molecule is considered as a single unit.
- d) Electrons are shared between atoms.
Answer: c) The whole molecule is considered as a single unit.
How are molecular orbitals designated in Molecular Orbital Theory?
- a) Alpha and Beta
- b) Bonding and Anti-bonding
- c) p and s orbitals
- d) Up and Down
Answer: b) Bonding and Anti-bonding
Which molecular orbital is symmetrical about the molecular axis?
- a) Sigma (σ)
- b) Pi (π)
- c) Delta (δ)
- d) Alpha (α)
Answer: a) Sigma (σ)
How are anti-bonding molecular orbitals designated in Molecular Orbital Theory?
- a) Pi (π)
- b) Delta (δ)
- c) Sigma (σ)*
- d) Alpha (α)*
Answer: c) Sigma (σ)*
How is the filling of electrons into molecular orbitals determined?
- a) Aufbau principle, Pauli’s exclusion principle, and Hund’s rule.
- b) Newton’s laws of motion.
- c) Boyle’s law.
- d) Avogadro’s principle.
Answer: a) Aufbau principle, Pauli’s exclusion principle, and Hund’s rule.
In the Head on Approach of p-orbitals, what molecular orbitals are formed?
- a) Sigma (σ) and Pi (π)
- b) Sigma (σ) and Sigma (σ)*
- c) Pi (π) and Pi (π)*
- d) Delta (δ) and Delta (δ)*
Answer: a) Sigma (σ) and Sigma (σ)*
Which approach results in the formation of a π (pi) bond?
- a) Head on Approach
- b) Sideways Approach
- c) Diagonal Approach
- d) Inverted Approach
Answer: b) Sideways Approach
What determines the relative energies of the molecular orbitals?
- a) The number of electrons.
- b) Spectroscopic measurements.
- c) Atomic radius.
- d) Molecular weight.
Answer: b) Spectroscopic measurements.
What is the bond order formula in Molecular Orbital Theory?
- a) (Number of bonding electrons + Number of anti-bonding electrons)/2
- b) (Number of bonding electrons – Number of anti-bonding electrons)/2
- c) (Number of bonding electrons x Number of anti-bonding electrons)/2
- d) (Number of bonding electrons / Number of anti-bonding electrons)/2
Answer: b) (Number of bonding electrons – Number of anti-bonding electrons)/2
What is the bond order of He2 according to Molecular Orbital Theory?
- a) 0
- b) 1
- c) 2
- d) 3
Answer: a) 0
How many electrons participate in the bonding orbitals of N2 according to Molecular Orbital Theory?
- a) 2
- b) 4
- c) 6
- d) 8
Answer: c) 6
What is the bond order of O2 according to Molecular Orbital Theory?
- a) 1
- b) 2
- c) 3
- d) 4
Answer: b) 2
Which property of oxygen is successfully explained by the Molecular Orbital Theory?
- a) Density
- b) Boiling point
- c) Paramagnetic behavior
- d) Color
Answer: c) Paramagnetic behavior
What is the bond order of O2^2- according to Molecular Orbital Theory?
- a) 0
- b) 1
- c) 2
- d) 3
Answer: b) 1
What is the bond order of O2^2+ according to Molecular Orbital Theory?
- a) 0
- b) 1
- c) 2
- d) 3
Answer: d) 3
What does the Molecular Orbital Theory predict for the bond between Ne and Ne?
- a) Single bond
- b) Double bond
- c) Triple bond
- d) No bond
Answer: d) No bond
Which of the following is NOT a designation for molecular orbitals in Molecular Orbital Theory?
- a) Sigma (σ)
- b) Delta (δ)
- c) Omega (ω)
- d) Pi (π)
Answer: c) Omega (ω)
How is the energy difference of 2s and 2p atomic orbitals minimized in certain molecules?
- a) By increasing atomic radius.
- b) By decreasing molecular weight.
- c) By hybridization of atomic orbitals.
- d) By changing the molecular shape.
Answer: c) By hybridization of atomic orbitals.
What is the energy order of σ2px and π2py=π2pz in certain diatomic molecules?
- a) σ2px < π2py = π2pz
- b) σ2px > π2py = π2pz
- c) σ2px = π2py = π2pz
- d) σ2px ≈ π2py ≈ π2pz
Answer: b) σ2px > π2py = π2pz
Why does the energy order change in certain diatomic molecules like B2, C2, and N2?
- a) Due to changes in molecular weight.
- b) Due to the mixing of 2s and 2px atomic orbitals.
- c) Due to changes in atomic radius.
- d) Due to changes in molecular shape.
Answer: b) Due to the mixing of 2s and 2px atomic orbitals.
What is the bond order of the hydrogen molecule (H2) in the Molecular Orbital Theory?
- a) 0
- b) 1
- c) 2
- d) 3
Answer: b) 1
How many molecular orbitals are formed from two sets of 2p atomic orbitals in Molecular Orbital Theory?
- a) 2
- b) 3
- c) 4
- d) 6
Answer: c) 4
What kind of bond results from the direct overlap of atomic orbitals?
- a) Sigma (σ) bond
- b) Pi (π) bond
- c) Delta (δ) bond
- d) Alpha (α) bond
Answer: a) Sigma (σ) bond
In the Sideways Approach, which molecular orbitals are formed?
- a) Sigma (σ) and Pi (π)
- b) Sigma (σ) and Sigma (σ)*
- c) Pi (π) and Pi (π)*
- d) Delta (δ) and Delta (δ)*
Answer: c) Pi (π) and Pi (π)*
What does the bond order represent in Molecular Orbital Theory?
- a) The strength of the bond.
- b) The length of the bond.
- c) The number of bonds formed between two atoms.
- d) The stability of the molecule.
Answer: c) The number of bonds formed between two atoms.

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FAQs on Molecular Orbital Theory Tutorial

1. What is Molecular Orbital Theory?Molecular Orbital Theory considers a molecule as a single unit, presuming that atomic orbitals overlap to form molecular orbitals characteristic of the whole molecule. These molecular orbitals surround the nuclei of bonded atoms.

2. How are molecular orbitals classified based on energy?

Molecular orbitals are classified as bonding (lower energy) and anti-bonding (higher energy). The bonding orbital is symmetrical about the molecular axis, designated as sigma (σ), while the anti-bonding orbital is denoted as σ*.

3. How are electrons filled into molecular orbitals?

Electron filling follows the Aufbau principle, Pauli’s exclusion concept, and Hund’s rule. Electrons fill low-energy orbitals first, considering spin and avoiding pairing until necessary.

4. Explain the Head on Approach in molecular orbital formation.

In the Head on Approach, p-orbitals of two atoms approach along the same axis (px axis), generating σ(2px) bonding and σ*(2px) antibonding molecular orbitals.

5. Describe the Sideways Approach in molecular orbital formation.

In the Sideways Approach, two p-orbitals’ axes (py or pz) are parallel, forming bonding molecular orbitals π(2py) or π(2pz) and anti-bonding orbitals π*(2py) or π*(2pz).

6. What determines the relative energies of molecular orbitals?

The relative energies of molecular orbitals are determined by spectroscopic measurements. For homonuclear diatomic molecules, the order of energies may vary, and mixing of atomic orbitals can influence their relative stability.

7. How is bond order calculated in Molecular Orbital Theory?

Bond order, representing the number of bonds between two atoms, is calculated as half of the difference between the number of bonding electrons and anti-bonding electrons.

8. Explain the Molecular Orbital Structures of some Diatomic Molecules.

He2: Bond order is zero; the molecule is not formed.
N2: Triple bond with one sigma and two π bonds; high bond dissociation energy.
O2: Double bond with paramagnetic properties; unpaired electrons in π* orbitals.

9. How does Molecular Orbital Theory justify the paramagnetic properties of oxygen?

10 Problems/Solutions for Molecular Orbital Theory

Problem 1: Describe the basic principles of Molecular Orbital Theory and how it differs from Valence Bond Theory.
Solution 1: Molecular Orbital Theory (MOT) considers the entire molecule as a single unit, assuming atomic orbitals overlap to form molecular orbitals. In contrast, Valence Bond Theory describes bonds as overlapping atomic orbitals, emphasizing localized electron pairs.

Problem 2: Explain the formation of σ and π bonds using the Head on Approach and Sideways Approach in Molecular Orbital Theory.

Solution 2: In the Head on Approach, p-orbitals of two atoms along the same axis generate σ(2px) bonding and σ*(2px) antibonding molecular orbitals. The Sideways Approach, with parallel p-orbitals, forms bonding molecular orbitals, π(2py) or π(2pz), and anti-bonding orbitals, π*(2py) or π*(2pz).

Problem 3: Calculate the bond order for a molecule with the following electron configuration: σ(1s)² σ(1s)² σ(2s)² σ*(2s)² π(2py)² π*(2pz)¹.*

Solution 3: Bond Order = (Number of bonding electrons – Number of anti-bonding electrons) / 2

Bond Order = [(2 + 2 + 2 + 1) – (0)] / 2 = 7 / 2 = 3.5

Problem 4: Discuss the relative energies of molecular orbitals for the diatomic molecule N₂ and explain any deviations from the typical energy order.

Solution 4: For N₂, the energy order is σ(1s) < σ*(1s) < σ(2s) < σ*(2s) < π(2py) = π(2pz) < σ(2px) < π*(2py) = π*(2pz) < σ*(2px). Deviations occur due to the mixing of 2s and 2px atomic orbitals.

Problem 5: Explore the electronic configuration and bond order of the diatomic molecule He₂.

Solution 5: Electronic Configuration of He₂: 1s²

Bond Order = (Number of bonding electrons – Number of anti-bonding electrons) / 2

Bond Order = [(2 – 0) / 2] = 1

Problem 6: Investigate the paramagnetic properties of the diatomic molecule O₂ using Molecular Orbital Theory.

Solution 6: O₂ has unpaired electrons in π*(2py) and π*(2pz) orbitals, making it paramagnetic according to Molecular Orbital Theory.

Problem 7: Examine the bond order changes in O₂²⁻ compared to O₂ and explain the differences.

Solution 7: The bond order of O₂ is 2. O₂²⁻ has one more electron, resulting in a bond order of 1. This decrease in bond order indicates a weaker bond in the anion.

Problem 8: Discuss the molecular orbital structures of Nitrogen (N₂) and explain the high bond dissociation energy.

Solution 8: N₂ has a bond order of 3, corresponding to a triple bond with one sigma and two π bonds. The high bond dissociation energy (941 kJ/mol) reflects the strength of the triple bond.

Problem 9: Explain the concept of hybridization in Molecular Orbital Theory and its impact on energy levels.

Solution 9: Hybridization involves the mixing of atomic orbitals. In Molecular Orbital Theory, the mixing of orbitals alters energy levels, leading to stabilized and destabilized molecular orbitals.

Problem 10: Discuss the limitations of Molecular Orbital Theory in explaining the properties of certain molecules.

Solution 10: Molecular Orbital Theory faces challenges in accurately predicting properties for highly complex molecules due to simplifications in its model. It may not fully account for certain electronic behaviors and is often complemented by other theories.

Summary of Molecular Orbital Theory Tutorial

The Molecular Orbital Theory explores the nature of molecular orbitals formed by the overlap of atomic orbitals in a molecule. It treats the entire molecule as a single unit, emphasizing bonding and anti-bonding molecular orbitals. Two main approaches, the Head on Approach and Sideways Approach, explain the formation of σ and π bonds, respectively.

The tutorial explains the relative energies of molecular orbitals, particularly in homonuclear diatomic molecules, and discusses the impact of hybridization on energy levels. The calculation of bond order, representing the number of bonds between atoms, is explained, and the tutorial provides examples of molecular orbital structures for diatomic molecules like Helium (He₂), Nitrogen (N₂), and Oxygen (O₂).

Significantly, the Molecular Orbital Theory successfully justifies the paramagnetic properties of oxygen and discusses variations in bond order for ions such as O₂²⁻. The tutorial concludes with insights into the bond order of various diatomic molecules, demonstrating the comprehensive application of the Molecular Orbital Theory in understanding molecular structures and properties.