Chapter 14 Study Guide: Infrared Spectroscopy and Mass Spectrometry

Introduction to Spectroscopy

• Electromagnetic Spectrum and Chemical Identification: Different regions of the electromagnetic spectrum provide distinct types of information about organic compounds.

  • Nuclear Magnetic Resonance (NMR) Spectroscopy: Utilizes radio waves to determine the specific arrangement of all carbon and hydrogen atoms in a compound.

  • Infrared (IR) Spectroscopy: Utilizes infrared radiation to identify the functional groups present in a compound.

  • Ultraviolet-Visible (UV-VIS) Spectroscopy: Utilizes visible and ultraviolet light to detect the presence of conjugated $\pi$ systems.

• Radiation Properties: Wavelength ($\lambda$) and frequency ($\nu$) are inversely related. Energy ($E$) is directly proportional to frequency and inversely proportional to wavelength.

  • $E = h \times \nu = h \times \frac{c}{\lambda}$

  • $h = 6.626 \times 10^{-34}\,J\cdot s$ (Planck’s constant)

Infrared (IR) Spectroscopy Fundamentals

• Molecular Vibrations: Molecular bonds are not static; they vibrate by stretching or bending in various ways.

  • Stretching: A change in bond length.

  • Bending: A change in bond angle.

• Energy and Vibration: The energy required to cause a vibration depends on the specific type of bond. Higher energy radiation corresponds to higher frequency (wavenumber) and lower wavelength.

• The IR Absorption Spectrum: A plot representing the percentage of transmittance as a function of frequency.

  • Absorption Bands: The ‘peaks’ in the spectrum, which actually point downward as transmittance decreases when energy is absorbed by the sample.

  • Wavenumbers: The unit of frequency in IR spectroscopy, expressed as inverse centimeters ($cm^{-1}$). The standard range is $400\,cm^{-1}$ to $4000\,cm^{-1}$.

• Energy Gap and Bond Type: The energy gap ($\Delta E$) between vibrational energy levels is progressive:

  • Single bonds ($C-C$): Lowest energy gap (e.g., $\approx 1400\,cm^{-1}$).

  • Double bonds ($C=C$): Intermediate energy gap (e.g., $\approx 1700\,cm^{-1}$).

  • Triple bonds ($C \equiv C$): Highest energy gap (e.g., $\approx 2200\,cm^{-1}$).

IR Signal Characteristics: Wavenumber

• Influencing Factors: The frequency/wavenumber for a stretching vibration depends on two primary factors:

  1. Bond Strength: Stronger bonds vibrate at higher frequencies.

  2. Atomic Mass: Bonds between atoms with a larger mass difference (lighter atoms) vibrate at higher frequencies.

• Standard Absorption Regions:

  • Bonds to Hydrogen ($X-H$): High frequency range ($2700\,cm^{-1}$ to $4000\,cm^{-1}$). Includes $O-H$, $N-H$, and $C-H$.

  • Triple Bonds ($C \equiv C$, $C \equiv N$): Range of $2100\,cm^{-1}$ to $2300\,cm^{-1}$.

  • Double Bonds ($C=O$, $C=C$, $C=N$): Range of $1600\,cm^{-1}$ to $1850\,cm^{-1}$.

  • Single Bonds ($C-O$, $C-N$, $C-C$): Range of $400\,cm^{-1}$ to $1600\,cm^{-1}$. This area is often referred to as the fingerprint region.

• Hybridization and C-H Bonds: The hybridization of carbon affects the strength of the $C-H$ bond and its stretching frequency:

  • $sp$ hybridized C-H: $\approx 3300\,cm^{-1}$ (strongest bond, highest $s$-character).

  • $sp^2$ hybridized C-H: $\approx 3100\,cm^{-1}$.

  • $sp^3$ hybridized C-H: $\approx 2900\,cm^{-1}$.

• Conjugation and Wavenumber: Conjugation (resonance) decreases the double-bond character of carbonyls, resulting in a lower stretching frequency. For example, a conjugated ketone will appear at a lower wavenumber than a non-conjugated ketone.

IR Signal Characteristics: Intensity and Shape

• Signal Intensity: This is determined by the dipole moment of the bond.

  • Dipole Moment: Larger changes in dipole moment during vibration lead to stronger (more intense) signals.

  • Carbonyls ($C=O$): Typically produce very strong signals due to the high polarity of the bond.

  • Symmetrical Bonds: If a bond is completely symmetrical (e.g., tetramethylethylene), it has no dipole moment change and produces no IR signal (IR inactive).

  • Abundance: Multiple bonds of the same type (like many $C-H$ bonds in an alkane) will result in a stronger signal due to the additive effect of many vibrations.

• Signal Shape: Signals are categorized by their width.

  • Broad Signals: Characteristically seen in $O-H$ stretching. This breadth is caused by hydrogen bonding, which weakens the $O-H$ bond to varying degrees across a sample, creating a range of frequencies.

  • Narrow/Sharp Signals: Typically seen when hydrogen bonding is absent (free $O-H$).

• Amine Signals ($N-H$):

  • Primary Amines ($R-NH_2$): Exhibit two signals in the $3300\,cm^{-1}$ to $3500\,cm^{-1}$ range (symmetric and asymmetric stretching).

  • Secondary Amines ($R_2N-H$): Exhibit only one signal.

Analyzing an IR Spectrum

• Systematic Approach:

  1. Diagnostic Region: Focus on signals above $1500\,cm^{-1}$.

     • Analyze $1600\text{--}1850\,cm^{-1}$ for double bonds.

     • Analyze $2100\text{--}2300\,cm^{-1}$ for triple bonds.

     • Analyze $2700\text{--}4000\,cm^{-1}$ for $X-H$ bonds.

  2. The 3000 Line: Draw a vertical line at $3000\,cm^{-1}$.

     • Signals just above $3000\,cm^{-1}$ indicate $sp^2$ hybridized carbon ($C=C-H$).

     • Signals just below $3000\,cm^{-1}$ indicate $sp^3$ hybridized carbon ($CH_3, CH_2, CH$).

Introduction to Mass Spectrometry (MS)

• Primary Utility: Mass spectrometry is used to determine the molar mass and the molecular formula of a compound.

• The Process:

  1. Vaporization and Ionization: The compound is vaporized into a gas and then struck with a high-energy electron beam. This knocks an electron off the molecule, forming a molecular ion ($M^{+\bullet}$).

  2. Fragmentation: The unstable molecular ion often breaks into smaller fragments (cations and radicals).

  3. Detection: Magnetic fields deflect ions based on their mass-to-charge ratio ($m/z$). Since the charge ($z$) is typically $+1$, the detector effectively measures the mass ($m$).

• The Mass Spectrum: A plot of relative abundance (%) versus the mass-to-charge ($m/z$) ratio.

  • Molecular Ion ($M^{+\bullet}$) Peak: The peak representing the entire molecule minus one electron. It indicates the molar mass of the compound.

  • Base Peak: The most stable fragment, which appears as the tallest peak in the spectrum (assigned $100\%$ abundance).

Analyzing Mass Spectrometry Peaks

• The Nitrogen Rule:

  • An odd-numbered molecular ion peak ($M^{+\bullet}$) indicates the presence of an odd number of nitrogen atoms.

  • An even-numbered molecular ion peak indicates an even number of nitrogens or zero nitrogens.

• The $(M+1)^{+\bullet}$ Peak: Results from the presence of the $^{13}C$ isotope. Since $1.1\%$ of all carbon is $^{13}C$, the intensity of this peak increases with the number of carbon atoms in the molecule.

• The $(M+2)^{+\bullet}$ Peak (Halogen Detection):

  • Chlorine: Naturally occurs as $^{35}Cl$ ($\approx 76\%$) and $^{37}Cl$ ($\approx 24\%$). Compounds with one Chlorine atom show an $M^{+\bullet}$ and $(M+2)^{+\bullet}$ in a $3:1$ ratio.

  • Bromine: Naturally occurs as $^{79}Br$ ($\approx 51\%$) and $^{81}Br$ ($\approx 49\%$). Compounds with one Bromine atom show an $M^{+\bullet}$ and $(M+2)^{+\bullet}$ in a roughly $1:1$ ratio.

Fragmentation Patterns

• Common Fragment Losses:

  • $M - 15$: Loss of a methyl radical ($\cdot CH_3$).

  • $M - 29$: Loss of an ethyl radical ($\cdot CH_2CH_3$).

  • $M - 43$: Loss of a propyl radical ($\cdot CH_2CH_2CH_3$).

  • $M - 57$: Loss of a butyl radical ($\cdot CH_2CH_2CH_2CH_3$).

  • $M - 18$: Loss of water ($H_2O$), characteristic of alcohols.

  • $M - X$ (where $X$ is an even number): Result of a McLafferty rearrangement in ketones or aldehydes.

• Specific Rearrangements:

  • Alpha-Cleavage: Occurs in alcohols and amines to form resonance-stabilized oxonium or iminium ions.

  • McLafferty Rearrangement: Occurs in carbonyl compounds containing a $\gamma$-hydrogen, leading to the loss of a neutral alkene.

Advanced Mass Spectrometry Techniques

• High-Resolution Mass Spectrometry (HRMS): Measures $m/z$ with up to four decimal places. This allows for the differentiation of compounds that have identical nominal masses but different molecular formulas (e.g., distinguishing between $C_{12}H_{24}$ and $C_{11}H_{20}O$).

  • Atomic Masses: Based on $^{12}C = 12.0000\,amu$.

  • $^{1}H = 1.0078\,amu$; $^{16}O = 15.9949\,amu$; $^{14}N = 14.0031\,amu$.

• Gas Chromatography-Mass Spectrometry (GC-MS): A combination technique where mixtures are first separated by a gas chromatograph and then identified individually by a mass spectrometer. The GC provides ‘retention time,’ while the MS provides the molecular identity.

• Electrospray Ionization (ESI): A ‘soft’ ionization technique used for large biomolecules (proteins, nucleic acids) that would otherwise fragment too extensively under standard electron impact (EI) conditions.

Degrees of Unsaturation

• Hydrogen Deficiency Index (HDI): Used to determine the number of rings or $\pi$ bonds in a molecular formula.

• Saturated Alkanes: Follow the formula $C_nH_{2n+2}$.

• Changes in HDI:

  • Each degree of unsaturation (one ring or one $\pi$ bond) reduces the hydrogen count by two.

  • Halogens ($X$): Treat as a hydrogen atom.

  • Oxygen ($O$): Ignore when calculating HDI.

  • Nitrogen ($N$): Subtract one hydrogen from the count (or add one to the saturation reference).

• HDI Formula:     $HDI = \frac{1}{2} (2C + 2 + N - H - X)$     (Where $C$ is carbon, $N$ is nitrogen, $H$ is hydrogen, and $X$ is halogen).