Question

Sulfur dioxide is a nonlinear molecule. How many vibrational modes will this compound have? How many IR absorption bands would sulfur dioxide be expected to have?

Short answer

Three absorption peaks and three absorption bands are expected.

Step-by-step solution

Step 1. Given information

Sulfur dioxide is given as a non-linear molecule.

Step 2. Number of vibration mode

For non-linear molecule the formula for vibrational frequency is $3N-6$

N is the number of atoms.

For sulfur dioxide $N=3$,

$$\begin{gathered} 3N-6=3\times 3-6 \\ =9-6 \\ =3 \end{gathered}$$

Step 3. Number of bands

Sulfur dioxide has three vibrational frequency and as we know that absorption bands occur due to stretching of bonds in the molecule.

Therefore, expected number of IR absorption bands is three.