70.CHEMICAL BONDING (17)- 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 (f_s  and f_p ) values are related to each other.

Determining %s and %p character ,bond lengths and bond angles for symmetric molecules is 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  hybridised asymmetric molecules , we observe, that the fraction of s and p character varies 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 hybridised ammonia orbitals.

FOR BONDING ORBITALS

STEP 1 -Find the hybridization index, i.
              i = -1 / cosθ .
             ∴ i_NH3 = – 1/ cos(107.1) = 3.40 – We calcuate this using a scientific calculator.
             Thus, in ammonia molecule , the bonding orbitals of N atom is sp^3.4 hybridised.

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

Thus, there is 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 – 

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

∴3 × f_{s bonding)}+f_{s(non bonding)} = 1
3 (0.227) +f_{s(non bonding)} =1
∴f_{s(non bonding)}  = 1 – 0.681

f_{s(non bonding)}= 0.319.

We also know that , f_{s(non bonding)} +f_{p(non bonding)} = 1.

∴f_{p(non bonding)}= 1-f_{s(non bonding)} = 1- 0.319 = 0.681

So, i_{(non bonding)} = f_{p(non bonding)}/f_{s(non bonding)} .
= 0.681 / 0.319
= 2.13.

∴The hybrid orbital in methane which contains non bonding pair of electrons is sp^2.13 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 !