Answer to Question #86568 in Organic Chemistry for Chanchal

Question

What is zero point energy? Calculate the number of normal modes of vibration for the following compounds .
i.- pf3, ii.- CINO, iii.- Xef2

Answer 1

Soution: The vibration energy of a molecule is given by E=(v+1/2)hν

where,v= vibrational quantum number, ν=frequency of vibration of the bond,

At 0 K E0=(1/2)hν ,where, E0=zero point energy.

That means even at 0 K temperature bond is vibrating

In order to describe a point in 3d space we need three co-ordinates. So total degree of

freedom =3.So molecules containing N number of atoms =3N,

Among 3N degrees of freedom there are 3 translational degrees of freedom along co-ordinate

axis and 3 rotational degrees of freedom for non-linear molecules,2 for linear molecules.

Since for linear molecules rotation along its bond axis does not change its co-ordinates.

Therefore ,Total number of vibrational degrees of freedom for linear molecules=(3N-5)

And for non-linear molcules=(3N-6)

(i) PF3:Shape-Trigonal pyramidal(Non-linear)

Therefore, Total number of vibrational degrees of freedom=(3×4)-6=6

The number of normal modes of vibration=6

(ii)ClNO:Shape: V shaped(Non-linear)

Therefore ,Total number of vibrational degrees of freedom=(3×3)-6=3

The number of normal modes of vibration=3

(iii) XeF2: Shape: Linear

Therefore ,Total number of vibrational degrees of freedom=(3×3)-5=4

The number of normal modes of vibration=4