The Hydrogen Molecule
Skills to develop
- Explain the bonding of two H atoms in the formation of an H2 molecule.
- Describe and differentiate valence bond theory from molecular orbital theory.
- Distinquish bonding and antibonding orbitals and show the distribution of
electron waves for these orbitals.
The Hydrogen Molecule
Atomic hydrogen gas is unstable, unless the gas is at very high temperature.
Diatomic hydrogen molecules, H2, are formed at ordinary
temperature and pressure. Many models and theories have been proposed to
explain the chemical bond, and here are some simplified forms of these
theories, some of which may have been proposed as the society began
to speculate what is happening.
The hydrogen atom has a valency of 1 and it tends to form a chemical bond
with another atom. It forms a covalent bond with another atom of the same
kind to form H-H.
When people realized that the hydrogen atom has one electron, and that
He has two electrons, they thought that a atom has a tendency to share
electrons to achieve a closed shell as those of inert gases. Thus, its
structure should be represented by H:H, the Lewis dot structure.
The invention of quantum mechanics to describe the electron configuration
of atoms led to the electron configuration of 1s1 for hydrogen.
This electron tends to find a partner, and sharing an electron with another
hydrogen atom seems to make it more stable.
Valence bond (VB) theory suggested 1s atomic orbitals of two H atoms
overlap to form a chemical bond.
Molecular orbital (MO) theory suggested atomic orbitals which not
only overlap, but are simultaneously transformed into molecular
orbitals with new energies and new electron distributions.
Some facts are known about the hydrogen due to some careful experimental
measurements. The internuclear distance is 74 pm, and the dissociation of
an H-H bond into two atomic hydrogen atoms requires 7.2x10-19 J,
(usually given as 435.9 kJ/mol).
Molecular Orbitals of H2
molecular orbital approach gives further explanations on chemical bonds.
When the 1s wave functions of the two H atoms are linearly combined,
we get a sigma (s) bonding orbital, denoted as
s1s in the diagram here.
This approach is called linear combination of atomic orbitals (LCAO),
in the MO approach. In this approach, the sum of the two 1s orbitals
(one for each atom) is the bonding orbital. In terms of wave mechanics,
the two waves constructively interact. The difference of the two orbitals
forms the antibonding orbital, s1s*,
due to destructive interference. It is interesting to note that the
anti bonding orbital is at a higher energy than the 1s atomic orbital.
The energy level can be represented below:
Each orbital accommodates two electrons, and the two electrons in H-H
filles the s1s molecular orbital (MO).
The quantum mechanics of the chemical bonding is a little complicated,
but the logic and concept are as simple as describe above.
I have written a program for the DOS version of CAcT to plot electron
densities of the s1s and
s1s* electron densities, but the program
cannot be executed on the web page. The excution of these type of simulations
is sometimes shown during the lecture.
Confidence Building Questions
- What is the bond length (in pm) for the H-H molecule?
No need to memorize this value, but you have a general idea about
bond length. Thus, the covalent radius for H is 37 pm.
- Which one of the following statements is the best description of
valence bond theory?
a. an overlap of atomic orbitals
b. satisfies the octet rule
c. count the number of VSEPR pairs
d. the overlap of atomic orbitals
e. atomic orbitals undergo a transformation
The simple version assumes that atomic orbitals do not change during the
formation of chemical bond. They merely overlap. Modern treatments of
valence bond theory do accept the fact that atomic orbitals do change
- What is a molecular orbital of a molecule?
If your answer is...I'm lost!
When atoms come together to form chemical bonds, new orbitals are formed.
Molecular orbitals play the same role for molecules that atomic orbitals
play for atoms.
- Choose the best Lewis structure for HCN,
The triple bond between C and N is represented by three pairs of electron.