Chapter 15, Problem 15.18P

Interpretation Introduction

Interpretation:

Deuterium (D), an isotope of hydrogen, has roughly twice the mass of hydrogen, but the two have nearly identical chemical properties. A $\text{C - H}$ bond, therefore, has essentially the same strength as a $\text{C - D}$ bond. The vibrational mode, a $\text{C - H}$ stretch or a $\text{C - D}$ stretch, absorbs at a higher frequency in the IR region is to be explained.

Concept introduction:

We simplify the picture of molecular vibrations by considering the ball-and-spring model, which treats bonds as simple springs that connect atoms together. According to Hooke’s law, the spring vibrates at a particular frequency (${\text{ν}}_{\text{spring}}$) that depends on the mass (m) of the object connected to the spring (in this case, an atom) and the spring’s force constant (k), which is often thought of as the stiffness of the spring. The stiffer the spring, the more difficult it is to compress and extend it. A decrease in the mass of an atom leads to an increase in vibrational frequency. A stronger and stiffer bond tends to lead to a higher vibrational frequency.