# 70. Covalent Bonding(16)- Isovalent hybridization.

In the last post, we have seen that the bond angles (θ), hybridization index (i), and the fraction of s and p character in a bond (fs and fp ) values are related to each other.

Determining %s and %p character, bond lengths, and bond angles for symmetric molecules are very easy. However, for asymmetric molecules, the composition of each hybrid orbital varies. Thus, the bond angles and bond lengths change too. We term the hybridization in asymmetric molecules as isovalent /second-order hybridization.

#### Isovalent/second-order hybridization.

When we study hybridized asymmetric molecules, we observe, that the fraction of s and p characters vary in them. The bond angles vary too (from ideal bond angles).
e.g. – Experimentally it is found that the bond angle between two N-H bonds in ammonia molecule is 107.1º.
Now let us find the amount of s and p character in hybridized ammonia orbitals.

FOR BONDING ORBITALS

STEP 1 -Find the hybridization index, i.
i = -1 / cosθ .
∴ iNH3 = – 1/ cos(107.1) = 3.40 – We calcuate this using a scientific calculator.
Thus, in ammonia molecule, the bonding orbitals of N atom are sp3.4 hybridized.

STEP 2 – fs= 1 / (i + 1)
fs= 1 / (3.40 + 1) = 1/4.4 = 0.227.

Thus, there is a 22.7 % s- character in bonding hybrid orbitals of ammonia i.e the orbitals which form the N-H bonds. This percentage is less than the expected value ( 25%).

NOTE – THE ABOVE CALCULATION IS FOR THE BONDING ORBITALS WHICH HAVE INTERHYBRID ORBITAL ANGLE = 107.1 º BETWEEN THEM.

FOR NON-BONDING ORBITALS

For calculating % s- character of the orbital containing non- bonding or lone pair of electrons , we have to use the formula from the previous post –

∴∑ fs = 1 for all orbitals of NH3 molecule.

∴3 × fs bonding)+fs(non bonding) = 1
(0.227) +fs(non bonding) =1
∴fs(non bonding)  = 1 – 0.681

fs(non bonding)= 0.319.

We also know that , fs(non bonding) +fp(non bonding) = 1.

fp(non bonding)= 1-fs(non bonding) = 1- 0.319 = 0.681

So, i(non bonding) = fp(non bonding)/fs(non bonding) .
= 0.681 / 0.319
= 2.13.

∴The hybrid orbital in ammonia which contains non bonding pair of electrons is sp2.13 hybridised.

This kind of hybridization , where fractional number of atomic  orbitals mix to form new hybrid orbitals, is called isovalent or second order hybridization.

In our next post, we shall study the bond angle in much detail. Till then,

Be a perpetual student of life and keep learning..

Good day!

1. Victor Chida says:

Superb entry! I was struggling to understand this concept and your blog helped me a lot!
I´ll just be super picky and tell you I think there is a little confusion in the last sentence about sp2.13 hybridisation. I think you wanted to say “ammonia” but instead you wrote “methane”.

Regards from Brazil!

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1. Gauri Nigudkar says:

Thank you so much for writing to me ! I am glad I could help.
Yes! You are right… I will get that corrected. Thanks again.

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