Question

A).N₂O is a greenhouse gas. Draw the IR active vibrations of N₂O. The frequency of the bending vibration is 596 cm^-1, calculate the wavelength of light that N₂O can absorb due to this vibration (show your working).

Answer 1

Answer 1) IR active vibrations of NO2

NO2 is an angular molecule, hence no. of modes of vibration =3N-6……(N is the number of atoms in molecule)

No. of modes of vibration in NO2 = 3x3-6 = 3.

3 modes of vibrations in NO2 are IR active. They are as follows

1. Symmetric stretch of N-O bond
2. Asymmetric stretch of N-O bond and,
3. Bending vibrations of O=N-O as we can see in picture.

Now, Frequency of bending vibration given as 596 cm^-1. Its not the frequency actually but the wavenumber nu bar, so nu bar = 596 cm^-1.

Formula to calculate wavelength at which NO2 absorbs the light is Wavelength = 1/wavenumber

Wavelength= 1/596 = 1.6778x10(to the power -3) cm

                                     = 1677.8x10(to the power -6) cm

                                     = 1677.8 x 10(to the power -8) m………………(1 cm = 10(to the power -2)

=16778 x 10(to the power -9)

= 16778 ………………………….( 1 nm = 10(to the power -9) (nm: nanometer)