Understanding the Concept:
The intensity of an absorption band in Infrared (IR) spectroscopy is fundamentally dictated by the magnitude of the dynamic dipole moment change that occurs when the specific chemical bond undergoes a stretching or bending vibrational mode.
According to classical electrodynamics, the intensity of IR absorption is directly proportional to the square of the derivative of the dipole moment with respect to the vibrational coordinate:
\[
I \propto \left(\frac{d\mu}{dx}\right)^2
\]
The internal dipole moment (\(\mu\)) of a covalent bond depends heavily on the electronegativity difference (\(\Delta \chi\)) between the two bonded atoms. A larger electronegativity gap creates a more highly polarized bond, resulting in a larger dipole moment shift during stretching vibrations, which translates to a much more intense (stronger) spectral absorption peak.
Step 1: Compare the electronegativity differences
Let us review the standard Pauling electronegativity values for the elements involved:
• Hydrogen (\(\text{H}\)) = 2.2
• Carbon (\(\text{C}\)) = 2.5 \(\quad \Rightarrow \Delta\chi_{\text{C-H}} = 2.5 - 2.2 = 0.3\)
• Sulfur (\(\text{S}\)) = 2.5 \(\quad \Rightarrow \Delta\chi_{\text{S-H}} = 2.5 - 2.2 = 0.3\)
• Nitrogen (\(\text{N}\)) = 3.0 \(\quad \Rightarrow \Delta\chi_{\text{N-H}} = 3.0 - 2.2 = 0.8\)
• Oxygen (\(\text{O}\)) = 3.5 \(\quad \Rightarrow \Delta\chi_{\text{O-H}} = 3.5 - 2.2 = 1.3\)
Step 2: Match electronegativity with peak intensity
The Oxygen–Hydrogen (\(\text{O-H}\)) bond possesses the highest electronegativity difference (\(1.3\)), making it the most highly polarized bond among the choices. Consequently, its stretching vibration induces an exceptionally large change in the local dipole moment, producing a characteristic, intensely strong, broad absorption band in the \(3200-3600\text{ cm}^{-1}\) region of an IR spectrum.