Chapter 15, Problem 15.62P

Interpretation Introduction

Interpretation:

The structure of the compound of molecular formula ${\text{C}}_{\text{3}}{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$, whose IR spectrum is shown, is to be proposed. The pK of the compound is to be estimated.

Concept introduction:

Absorption of IR radiation causes excitations of vibrational motion of the atoms in a molecule. The vibrational motion can be of different types. In stretching vibrations, the bond length changes periodically. In bending vibrations, the bond angle or dihedral angle changes periodically. This may be an in-plane vibration or out of plane vibration.

The changes in the vibrational motion of the atoms in a molecule are quantized, i.e., the energy of vibrational motion can only have certain discrete values. In general, the frequency of the quantum of radiation absorbed and the frequency of vibration are the same.

The energy needed to excite molecular vibrations depends on the bond strength as a bond can be considered to behave like a spring. In turn, this also means it depends on the mass of the atoms that form the bond. In effect, this means the absorption peaks in the IR spectrum are characteristic of the bond between a particular pair of atoms. They are characteristic of the functional group to which the atoms belong and do not change much from molecule to molecule.

An IR spectrum records percent transmittance as a function of the wavenumber $\overline{\text{ν}}$, in units of ${\text{cm}}^{-1}$, of absorbed radiation.

The index of hydrogen deficiency (IHD) of a molecule is calculated as the difference between the number of hydrogen atoms in the compound and the number of hydrogen atoms in the corresponding saturated compound divided by two. A double bond and a ring each contribute one to IHD. A triple bond contributes two to IHD.