12.6 Infrared Spectroscopy

Infrared spectroscopy is a powerful tool for identifying functional groups in organic molecules. By analyzing the absorption of infrared radiation, chemists can determine the structure and composition of compounds based on characteristic vibrations of chemical bonds.

This technique relies on the interaction between infrared light and molecular vibrations. Different functional groups absorb at specific frequencies, creating unique spectral fingerprints. Understanding these patterns allows for rapid and accurate identification of organic compounds.

Infrared Spectroscopy

Functional groups in IR spectra

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• Functional groups absorb infrared radiation at characteristic wavenumbers allows for their identification in organic molecules
  • Alkanes exhibit C-H stretching vibrations in the range of 2850-2960 cm$^{-1}$ (methane, ethane)
  • Alkenes display C=C stretching vibrations between 1620-1680 cm$^{-1}$ (ethene, propene)
  • Alkynes show C$\equiv$C stretching vibrations from 2100-2260 cm$^{-1}$ (acetylene, propyne)
  • Alcohols feature O-H stretching vibrations in the 3200-3600 cm$^{-1}$ range (methanol, ethanol)
  • Carboxylic acids have C=O stretching vibrations between 1700-1725 cm$^{-1}$ (acetic acid, benzoic acid)
  • Amines exhibit N-H stretching vibrations from 3300-3500 cm$^{-1}$ (methylamine, aniline)
• Peak intensity in an IR spectrum indicates the relative abundance of a functional group in the molecule
  • Strong peaks suggest a higher concentration of the corresponding functional group (prominent O-H peak in ethanol)
  • Weak peaks indicate a lower concentration of the corresponding functional group (small C$\equiv$C peak in a complex molecule)
• Peak shape in an IR spectrum provides information about the molecular environment of the functional group
  • Broad peaks suggest hydrogen bonding or a variety of molecular environments (O-H peak in alcohols)
  • Sharp peaks indicate a more uniform molecular environment (C-H peaks in alkanes)

Molecular vibrations and IR radiation

• Infrared radiation causes molecules to vibrate by absorbing energy when the frequency of the radiation matches the natural frequency of the molecular vibration
  • The absorbed energy increases the amplitude of the vibration leading to a peak in the IR spectrum
  • This process is an example of absorption spectroscopy
• Molecular vibrations can be classified as stretching or bending depending on the type of motion
  • Stretching vibrations involve changes in bond length and can be further categorized:
    1. Symmetric stretching: bonds vibrate in phase (CO$_2$ symmetric stretch)
    2. Asymmetric stretching: bonds vibrate out of phase (CO$_2$ asymmetric stretch)
  • Bending vibrations involve changes in bond angle and include:
    1. In-plane bending such as scissoring and rocking (H$_2$O scissoring)
    2. Out-of-plane bending such as wagging and twisting (NH$_3$ wagging)
• The frequency of a molecular vibration depends on the mass of the atoms and the strength of the bond between them
  • Heavier atoms and weaker bonds result in lower vibrational frequencies (C-I stretching)
  • Lighter atoms and stronger bonds result in higher vibrational frequencies (O-H stretching)

Wavenumber calculations in IR spectroscopy

• Wavenumber ($\tilde{\nu}$) is the reciprocal of the wavelength ($\lambda$) and is expressed in units of cm$^{-1}$
  • The relationship between wavenumber and wavelength is given by: $\tilde{\nu} = \frac{1}{\lambda}$
• Wavelength is typically expressed in micrometers ($\mu$m) in infrared spectroscopy and needs to be converted to centimeters (cm) for wavenumber calculations
  • To convert from micrometers to centimeters, divide by 10,000 (1 $\mu$m = 1 $\times$ 10$^{-4}$ cm)
• To calculate wavenumber from wavelength:
  1. Convert wavelength from micrometers to centimeters
  2. Take the reciprocal of the wavelength in centimeters to obtain wavenumber
  • Example calculation for a wavelength of 5 $\mu$m:
    1. Convert 5 $\mu$m to cm: 5 $\mu$m = 5 $\times$ 10$^{-4}$ cm
    2. Calculate wavenumber: $\tilde{\nu} = \frac{1}{5 \times 10^{-4} \text{ cm}} = 2000 \text{ cm}^{-1}$

Advanced IR Spectroscopy Techniques

• Fourier transform infrared spectroscopy (FTIR) is a modern technique that offers improved sensitivity and speed
  • FTIR uses an interferometer to collect data over a wide spectral range simultaneously
  • The resulting interferogram is converted into a spectrum using a mathematical process called Fourier transform
• Attenuated total reflectance (ATR) is a sampling technique used in conjunction with FTIR
  • ATR allows for direct analysis of solid or liquid samples without extensive preparation
  • It utilizes the principle of total internal reflection to generate an evanescent wave that interacts with the sample
• The Beer-Lambert law relates the absorption of light to the properties of the material through which it is traveling
  • This law is fundamental in quantitative analysis using IR spectroscopy
• IR spectroscopy is part of the broader electromagnetic spectrum, which includes other forms of radiation such as visible light and X-rays