}]]}]}]}] 30:T2664,

### Instrumentation Techniques #### FTIR (Fourier Transform Infrared Spectroscopy) - Uses a Michelson Interferometer instead of dispersive elements. - Light passes through the sample, collected as an interferogram (energy vs. time). - A Fourier Transform (FT) converts this raw data into an interpretable spectrum (Intensity vs. Wavenumber). #### ATR-IR (Attenuated Total Reflection) - Based on internal reflection. - IR beam passes through a crystal; reflection creates an evanescent wave extending into the sample. - Sample absorbs energy from the evanescent wave, attenuating the reflected beam, which is then measured. #### Transmission vs. Absorption - Historically, measuring transmission ($T = I/I_0$) was easier than absorption. - While absorbance ($A = -\log T$) is directly proportional to concentration (Beer-Lambert Law), transmission spectra remain standard in organic chemistry. ### The Physics of Vibration: Hooke's Law Chemical bonds behave like springs connecting two masses (atoms). The frequency of vibration is given by Hooke's Law: $$\nu = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}$$ Where: - $\nu$ = Frequency (wavenumber in cm$^{-1}$) - $c$ = Speed of light - $k$ = Force constant (bond stiffness). Stronger bonds $\implies$ Higher $k \implies$ Higher frequency. - $\mu$ = Reduced mass, calculated as: $$\mu = \frac{m_1 m_2}{m_1 + m_2}$$ **Key Takeaway:** Frequency is directly proportional to bond strength and inversely proportional to the mass of the vibrating atoms. ### Factors Affecting Frequency #### A. Mass Effect (Isotope Effect) Heavier atoms vibrate slower (lower wavenumber). - C–H: 3000 cm$^{-1}$ (Lightest) - C–D (Deuterium): 2200 cm$^{-1}$ (Heavier) - C–O: 1100 cm$^{-1}$ - C–Cl: 700 cm$^{-1}$ (Heaviest) #### B. Bond Strength Stronger bonds vibrate faster (higher wavenumber). - C$\equiv$C (Triple bond): 2200 cm$^{-1}$ - C$=$C (Double bond): 1650 cm$^{-1}$ - C–C (Single bond): 1200 cm$^{-1}$ ### Vibration Modes & Regions #### Vibration Modes Molecules exhibit various vibrational modes: - **Stretching:** - Symmetric: Atoms move in the same direction. - Asymmetric: Atoms move in opposite directions. - **Bending modes:** Rocking, wagging, twisting, scissoring. #### The Four Regions of the IR Spectrum The IR spectrum is categorized from high to low frequency (left to right): 1. **X–H Region:** 4000-2500 cm$^{-1}$ (Bonds to H: O-H, N-H, C-H). 2. **Triple Bond Region:** 2500-2000 cm$^{-1}$ (C$\equiv$C, C$\equiv$N). 3. **Double Bond Region:** 2000-1500 cm$^{-1}$ (C$=$O, C$=$C, C$=$N). 4. **Single Bond Region (Fingerprint):** 1500-400 cm$^{-1}$ (C-C, C-O, C-N, C-X). ### The X–H Region Details (4000-2500 cm$^{-1}$) Although O, N, and C have similar masses, their bond strengths to hydrogen differ, leading to distinct peak positions: | Bond | Approximate Range (cm$^{-1}$) | Strength Logic | |---|---|---| | O–H | 3650-3200 | Strongest bond, highest frequency. | | N–H | 3500-3300 | Weaker than O-H. | | C–H | 3300-2800 | Weakest of the three group. | #### The Amine (N-H) "Hump" - **Observation:** Primary amine ($\text{NH}_2$) groups typically show a doublet (two peaks/humps). - **Reason:** This arises from the two fundamental N-H stretching modes: - **Asymmetric stretch:** Both N-H bonds move in opposite directions. Requires more energy (higher wavenumber). - **Symmetric stretch:** Both N-H bonds move in the same direction. Requires less energy (lower