Question

Question: A C-D (carbon–deuterium) bond is electronically much like a C-H bond, and it has a similar stiffness, measured by the spring constant, k. The deuterium atom has twice the mass (m) of a hydrogen atom, however.

(a) The infrared absorption frequency is approximately proportional to$\sqrt{\frac{\mathbf{k}}{\mathbf{m}}}$ , when one of the bonded atoms is much heavier than the other, and m is the lighter of the two atoms (H or D in this case). Use this relationship to calculate the IR absorption frequency of a typical C-D bond. Use as a typical C-H absorption frequency.

(b) A chemist dissolves a sample in deuterochloroform (${\mathbf{CDCl}}_{\mathbf{3}}$) and then decides to take the IR spectrum and simply evaporates most of the${\mathbf{CDCl}}_{\mathbf{3}}$ . What functional group will appear to be present in this IR spectrum as a result of the${\mathbf{CDCl}}_{\mathbf{3}}$ impurity?

Short answer

Answer

Step-by-step solution

Wave number

The number of waves that are present in the unit distance is termed a wave number. The wave number and wavelength are related as:

$\mathbf{wave} \mathbf{number}\mathbf{=}\frac{\mathbf{1}}{\mathbf{wave} \mathbf{length}}$

Subpart (a)

The IR-absorption frequency is proportional to $\sqrt{\frac{k}{m}}$,where k is the force constant and m is the mass of the lighter atom.

Given IR-absorption frequency for C-H bond is$3000 c{m}^{-1}$ .

The mass of D-atom is 2 amu.

The mass of H-atom is 1 amu.

The IR-absorption frequency for C-D bond can be calculated as shown:

$$\begin{gathered} \frac{{\nu }_{C-H}}{{\nu }_{C-D}}=\sqrt{\frac{k}{1 amu}\times \frac{2 amu}{k}} \\ \frac{{\nu }_{C-H}}{{\nu }_{C-D}}=\sqrt{2} \\ {\nu }_{C-D}=\frac{{\nu }_{C-H}}{\sqrt{2}} \\ {\nu }_{C-D}=\frac{3000 c{m}^{-1}}{\sqrt{2}} \end{gathered}$$

On simplification,

${\nu }_{C-D}=2121 c{m}^{-1}$

Hence, the IR-absorption frequency of C-D bond is $2121 c{m}^{-1}$.

Subpart (b)

The C-D bond stretching frequency around$2100 c{m}^{-1}$ matches with the stretching frequency of the$C\equiv C$ . So, if$CDC{l}_3$ is present as an impurity, then it interrupts with the stretching frequencies of the $C\equiv C$if they are present in the given sample