74.Covalent Bonding(20)- Bent’s rule(3).

Example 3 – PCl₃F₂ molecule .

This molecule has TBP geometry, with two F atoms and three Cl atoms as substituents. According to Bent’s rule, the F atoms are more electronegative and so they will prefer the axial position, where there is no s-character (less electronegative). The three Cl atoms will occupy the equatorial positions. Thus, the correct structure of this molecule is as shown below –

Relationship between bond length and bond angle.

The angle between the central and terminal atoms of a molecule is called a bond angle. The distance between the centers of two nuclei of atoms connected by a chemical bond is ‘bond length’.

In general, there is an inverse relationship between the bond angle and bond length. However, some very strained molecules show different behavior too. Let us first study the normal behavior of simple molecules, where bond length decreases as bond angle increases and vice versa.

We have studied the above example before in post 73, and learned that the value of the H-C – F bond angle is less than expected. Naturally, the value of the bond length is more.

Consider the fluoromethane molecule. According to Bent’s rule,

F is more electronegative than H → so less %s character in C- F bond → θ decreases → Bond length increases.

Here, all four bonds are NOT equal. In the C-F bond, fluorine being more electronegative will pull the electron density more towards itself. So, the electron density near the C atom is reduced. To make up for this loss, the s- character in hybrid orbitals is shifted towards the other three C-H bonds. This increases the electron density on carbon, thus making C-H bonds more stable.

In difluoromethane(CH₂F₂),the bond length increases slightly due to the presence of two fluorine atoms. Here, the s- character is shifted towards only two C-H bonds (instead of three in fluoromethane). So, in total, less s-character is directed away from F- atoms.(There’s a limit to how much s- character can be directed at a substituent). This slightly decreases the bond length.

This trend continues as we go on adding more F- atoms in the structure –

Name	Average C-F bond length
Fluromethane	1.388 Å
Difluoromethane	1.358 Å
Trifluoromethane	1.329 Å
Tetrafluoromethane	1.323 Å

FYI – We know that most halogenated hydrocarbons, which were used as refrigerants, are known to deplete the ozone layer. Difluoromethane is an exception to that! This compound is widely used as a refrigerant as it has ZERO OZONE DEPLETION POTENTIAL.

Bent Rule Energetics.

Any system in the universe always tries to lower its energy as lower energy corresponds to more stability. How does Bent’s rule explain the lowering of energy?

According to Bent’s rule, in isovalent hybridization (hybridization in asymmetric molecules),

%s character is directed more towards electropositive elements &
%s character is directed less towards electronegative elements.

An electronegative substituent draws electron density away from the central atom. This results in the central atom being less stable. So, automatically, the molecule adjusts the s- character in such a way, as to render stability to the central atom. So, what happens? The s- character (which has more electron density) is directed towards the less electronegative atoms. In the bond between the less electronegative atoms(e.g.- H atoms) and carbon, carbon is more electronegative. So, now the electron density in C-less electronegative bonds gets concentrated near carbon. What happens in the overall molecule?

1)The electronegative element wants more electron density (as it has a tendency to accept electrons). So, the electrons from the C-electronegative substituent bond get closer to the electronegative element(e.g. – F). So, the electronegative element is happy! However, the energy of the bonding electrons slightly increases in this case. Let us assume that,

the increase in energy of bonding electrons = E_increase .

2)The transfer of s character towards electropositive elements,leads to maximum bonding between C- electropositive substituent bonds. Thus, there is a decrease in the energy of the electrons in these orbitals. Let us assume that,

the decrease in energy of bonding electrons = E_decrease .

The decrease in the energy due to shifting the s-character towards the electropositive substituents is more than the increase in energy due to the shifting of electrons( in C- electronegative element) towards the more electronegative element i.e

E_decrease> E_increase .

E_increase – E_decrease = – ΔE

– ΔE = Net decrease in the overall energy of the system.

Thus, the overall energy of the molecule becomes less( the negative sign on ΔE indicates there is a decrease in energy ) and the molecule tends to be more stable.

We can use this rule to predict the bond angles and bond lengths in various molecules and to easily solve problems related to these concepts. In our next post, we will have a sneak preview of how hybrid molecules exists in solid-state. Till then,

Be a perpetual student of life and keep learning…

Good day!

References and Further Reading –

1.https://www.researchgate.net/post/What_is_the_correlation_between_bond_angle_and_bond_length2

2.https://en.wikipedia.org/wiki/Bent%27s_rule

3.https://pubs.acs.org/doi/abs/10.1021/ic50225a098