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In: Chemistry

9.5 Explain the concepts of the molecular orbital model and apply to diatomic molecules Define diamagnetism...

9.5 Explain the concepts of the molecular orbital model and apply to diatomic molecules

Define diamagnetism and paramagnetism
Determine if specific ions are paramagnetic or diamagnetic
Explain what a molecular orbital is and how it is different from a hybrid orbital
Explain the difference between an anti-bonding and a bonding as well as a sigma and pi

molecular orbitals.
Populate a molecular orbital diagram with the valence electrons of an atom or ion
Determine the bond order and magnetic properties of a substance based on its

molecular orbital filling diagram.

Expert Solution

Molecular Orbital Theory

Molecular orbital (MO) theory is used to describe the electronic structure of molecules by the help of quantum mechanics.
This theory uses a linear combination of atomic orbitals (LCAO) to represent molecular orbitals.
Atomic orbitals of same energy and proper symmetry combine to form molecular orbitals. As a result, the atomic orbitals loose their identity. For ex: 1s can only combine with 1s and not with 2s as they have different energies. Similarly, s-orbital can combine with p_z but not with p_x or p_y.
Molecular orbital is polycentric in nature.
The number of molecular orbitals formed is equal to the number of combining atomic orbitals.
When two atomic orbitals combine, two molecular orbitals are formed.
One molecular orbital possess higher energy than corresponding atomic orbitals and is known as anti bonding molecular orbital (ABMO).
Another molecular orbital possesses lower energy and is called bonding molecular orbitals (BMO).
Filling of electrons in molecular orbitals is according Pauli's exclusion principle, Aufbau principle and Hund's rule.

Let us have an example of O_² (diatomic molecule)-

In O₂ molecule, total number of electrons in valence shell = 12 (6 in each oxygen). These electrons are filled in the order as follow-

2s² *2s²2p_z²2p_x²2p_y²2p_x¹2p_y¹

Diamagnetism and Paramagnetism

When a molecule or ion has only paired electrons in its molecular orbitals, then it is said to possess diamagnetism. For example N₂ molecule as it has no unpaired electron in any of the molecular orbital.

When a molecule or ion has unpaired electrons in its molecular orbitals, then it is said to possess paramagnetism. For example O₂ because it has two unpaired electrons in 2p_x and 2p_y molecular orbitals.

Specific ions are paramagnetic or diamagnetic

Ions which possess unpaired electrons are known as paramagnetic ions. For example - Superoxide ion (O₂^-). On the opposite end, ions which possess paired electrons are known as diamagnetic ions. For example - Peroxide ion (O₂^2-).

Difference between Molecular orbital and Hybrid orbital

A molecular orbital is a wave-function of a molecule's electron and is used to calculate its chemical and physical properties. A molecular orbital is used to find the potential regions of a molecule where an electron can occupy the orbital. It is formed by the linear combination of atomic orbitals of appropriate energy and symmetry.

Molecular orbitals are different from the hybrid orbitals in the manner that they are formed by the interactions of atomic orbitals of two different atoms while hybrid orbitals are formed by the interactions of atomic orbitals in the same atom while molecular orbitals.

Difference between Bonding and Antibonding Molecular orbital

Bonding Molecular orbital

It is formed by the addition overlap of atomic orbitals.
It may or may not have a node.
In this orbital electron density is more in between the nuclei. Electrons in this orbital lead to attraction between atoms.
Its energy is less than the energy of the atomic orbitals.

Antibonding Molecular orbital

It is formed by subtraction overlap of atomic orbital.
It always has a node in between the nuclei of bonded atoms.
In this orbital electron density is less in between the nuclei. Electrons in this orbital lead to repulsion between atoms.
Its energy is more than the energy of the atomic orbitals.

Difference between sigma and pi Molecular orbital

Sigma Molecular orbital

It is formed by the overlap of atomic orbitals along the internuclear axis.
Overlapping is maximum due to head-on overlap.
it consists of one electron cloud that is symmetrical about the internuclear axis.

Pi Molecular orbital

It is formed by the lateral or side-wise overlap of atomic orbitals.
Overlapping is minimum due to side-wise overlap.
it consists of two electron clouds in which one lying above and another lying below the plane passing through the nuclei. Its electron cloud is not symmetrical about the internuclear axis.

Molecular orbital diagram with the valence electrons

Molecular orbital diagram of Lithium atom to form Li₂ with filling of electrons has been shown as follows-

Bond order from molecular orbital diagram

Bond order can be defined as the difference of bonding and antibonding electrons divided by two Bond order is also an index of bond strength, and it is used extensively in valence bond theory.

Bond order = (Total electrons in bonding molecular orbitals - Total electrons in bonding molecular orbitals) / 2

Magnetic properties from molecular orbital diagram

The magnetic properties of a compound can be determined by examining its electron configuration from molecular orbital diagram. If it has unpaired electrons, then the substance is paramagnetic and if all electrons are paired, the substance is diamagnetic. Whole process can be divided into three steps:

Write down the electron configuration of the compound from molecular orbital diagram
Draw the valence orbitals
Identify if unpaired electrons exist
Determine whether the substance is paramagnetic or diamagnetic

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