Infra-red spectroscopy: principles, interpretation

Infra‑red (IR) Spectroscopy – Cambridge AS/A‑Level Chemistry (9701)

1. How IR Spectroscopy Relates to the Syllabus

• AO1 – Knowledge & Understanding: Explain the physical basis of IR absorption (energy‑wavenumber relationship, selection rules) and link it to bonding concepts (dipole moment, polarity, bond strength).
• AO2 – Application & Analysis: Use IR spectra to identify functional groups, interpret the fingerprint region, and evaluate quantitative data (Beer‑Lambert law).
• AO3 – Evaluation: Assess the reliability of IR results, discuss sources of error, and compare IR with other analytical techniques.

2. Fundamental Principles (AO1)

2.1 Energy – Wavenumber Conversion

The energy of a photon absorbed in a vibrational transition is

\[ E = hu = hc\tilde{u} \]

• h = 6.626 × 10⁻³⁴ J s (Planck’s constant)
• c = 2.998 × 10⁸ m s⁻¹ (speed of light)
• \tilde{u} = wavenumber (cm⁻¹). 1 cm⁻¹ = 1.986 × 10⁻²³ J.

Because \tilde{u} is expressed in cm⁻¹, the product hc\tilde{u} gives the energy directly in joules, allowing a quick estimate of the bond‑energy change associated with a given band.

2.2 Selection Rules

• IR‑active vibration: a net change in the molecular dipole moment during the vibration (Δμ ≠ 0).
• Raman‑active vibration: a change in polarizability (Δα ≠ 0). Symmetric stretches of non‑polar molecules (e.g., O₂) are Raman‑active but IR‑silent.
• Example – CO₂:
  • Symmetric stretch: Δμ = 0 → IR‑inactive, Raman‑active.
  • Asymmetric stretch: Δμ ≠ 0 → IR‑active, Raman‑inactive.

2.3 Bond Strength & Frequency

Higher bond force constants (k) give higher stretching frequencies (ν) according to the harmonic‑oscillator approximation:

\[ \tilde{u} = \frac{1}{2\pi c}\sqrt{\frac{k}{\mu}} \] where μ is the reduced mass of the vibrating atoms. This explains why C≡C/C≡N (large k, low μ) appear at 2100–2260 cm⁻¹, whereas C–H (smaller k) appear at 2850–2960 cm⁻¹.

3. Instrumentation – FT‑IR (AO1)

1. Radiation source: Globar (SiC) – continuous mid‑IR (4000–400 cm⁻¹).
2. Michelson interferometer: Beam splitter → moving mirror & fixed mirror → recombined beams produce an interferogram.
3. Fourier transform: Mathematical conversion of the interferogram to an intensity‑vs‑wavenumber spectrum.
4. Sample compartment
   • Solids – KBr/NaCl pellets or pressed films.
   • Liquids – Thin film (≈0.01 mm) between IR‑transparent windows (KBr, NaCl, CaF₂).
   • Gases – Long‑path gas cell (≈10 cm).
5. Detector: DTGS (general use) or MCT (high sensitivity, cooled).

Suggested diagram: Michelson interferometer showing source, beam splitter, moving mirror, fixed mirror, sample cell, and detector.

4. Sample Preparation & Practical Planning (AO2 / AO3)

Sample Type	Typical Procedure	Key Practical Points
Solid	Grind ~1 mg sample with ~100 mg dry KBr; press into a clear 1 mm pellet.	Avoid moisture (KBr hygroscopic); ensure uniform pressure; record pellet thickness.
Liquid	Place a drop (≈0.1 mL) between two IR‑transparent windows; seal to prevent evaporation.	Check film is uniform; use a spacer (~0.01 mm) for reproducible path length.
Gas	Introduce gas into a sealed cell of known path length; pressurise if necessary.	Measure pressure and temperature for concentration calculations; purge cell between runs.

Practical Planning Checklist

• Choose appropriate sample holder (pellet, liquid cell, gas cell).
• Record ambient temperature and humidity (affects baseline).
• Run a background spectrum with an empty holder.
• Verify instrument resolution (typically 4 cm⁻¹) and number of scans.
• Apply baseline correction and, if needed, atmospheric subtraction (CO₂, H₂O).
• Document any observed artefacts (e.g., moisture bands, scratches).

5. Regions of an IR Spectrum

• Functional‑group region (4000–1500 cm⁻¹) – sharp, characteristic absorptions used for functional‑group identification.
• Fingerprint region (1500–400 cm⁻¹) – complex pattern unique to each molecule; useful for confirming identity by comparison with a reference spectrum.

6. Interpreting an IR Spectrum (AO2)

1. Identify the most intense peaks in the functional‑group region.
2. Match each wavenumber with the appropriate functional‑group range (see Table 1).
3. Check for complementary bands (e.g., C=O together with C–O for esters; N–H with C=O for amides).
4. Examine the fingerprint region; compare with a known spectrum or use computer‑matched libraries.
5. If quantitative data are required, apply the Beer‑Lambert law (see Section 8).
6. Evaluate reliability (AO3): consider band overlap, concentration, instrument resolution, and sample‑preparation artefacts.

7. Functional‑Group Table (AO1)

Functional Group (IUPAC name)	Typical ν (cm⁻¹)	Band Shape / Diagnostic Features	Example & Reaction Highlight
Alcohol – O–H (primary, secondary)	3200–3600 (broad)	Broad, rounded; free OH sharp ≈ 3600 cm⁻¹.	CH₃CH₂OH → oxidation (PCC) → CH₃CHO (aldehyde).
Carboxylic acid – O–H & C=O	2500–3300 (very broad O–H) ; 1700–1725 (C=O)	Very broad O–H often masks C=O; C=O sharp, strong.	CH₃CH₂COOH → esterification → CH₃CH₂COOCH₃.
Aldehyde – C=O	1720–1740	Strong, sharp; often accompanied by C–H stretch ≈ 2720 cm⁻¹.	CH₃CHO (acetaldehyde) – oxidation → CH₃COOH.
Ketone – C=O	1705–1725 (non‑conjugated) ; 1680–1700 (conjugated)	Very strong, sharp; conjugation lowers ν by 20–30 cm⁻¹.	CH₃COCH₃ (acetone) – reduction → isopropanol.
Ester – C=O & C–O	1735–1750 (C=O) ; 1150–1250 (C–O stretch)	C=O slightly higher than ketone; two strong C–O bands.	CH₃COOH + CH₃OH → CH₃COOCH₃ + H₂O (acid‑catalysed).
Amide – C=O & N–H	1650–1690 (C=O) ; 3300–3500 (N–H, two bands for primary)	C=O shifted lower; N–H bands medium‑broad.	CH₃CONH₂ (acetamide) – hydrolysis → CH₃COOH + NH₃.
Amine – N–H	3300–3500 (primary: two bands; secondary: one band)	Medium‑broad; often coupled with C–H stretches.	CH₃NH₂ (methylamine) – alkylation → CH₃NHCH₃.
Alkene – C=C & =C–H	1600–1680 (C=C) ; 3020–3100 (=C–H stretch)	Medium intensity; out‑of‑plane bends 650–900 cm⁻¹ indicate substitution pattern.	CH₂=CH₂ → hydrogenation → CH₃CH₃.
Alkyne – C≡C or C≡N	2100–2260 (sharp)	Sharp, medium intensity; terminal alkyne shows ≈ 3300 cm⁻¹ ≈ C–H stretch.	HC≡CH → addition → CH₂=CH₂.
Aromatic – C–H & C=C	3000–3100 (C–H) ; 1500–1600 (C=C) ; 650–900 (out‑of‑plane bends)	Multiple sharp peaks; substitution pattern deduced from bend region.	Benzene → nitration → nitrobenzene.
Metal–O (inorganic)	400–700 (broad, often weak)	Broad, low‑frequency; useful for metal oxides, carbonates.	CaO + H₂O → Ca(OH)₂ (hydroxide stretch ≈ 3600 cm⁻¹).

8. Factors Influencing Band Position & Intensity (AO1)

• Hydrogen bonding: Shifts O–H / N–H bands to lower wavenumber and broadens them (e.g., alcohol O–H ≈ 3400 cm⁻¹, carboxylic acid O–H ≈ 2500–3300 cm⁻¹).
• Conjugation: Delocalisation lowers C=O stretching frequency by 20–30 cm⁻¹.
• Electron‑withdrawing/donating substituents: EW groups raise ν(C=O); ED groups lower it.
• Isotopic substitution: Replacing ¹H with ²H (D) reduces frequency by ≈ √(m_H/m_D) ≈ 0.71 (e.g., O–D stretch ≈ 2500 cm⁻¹).
• Mass effect (reduced mass μ): Heavier atoms → lower frequency (e.g., C–Cl stretch ≈ 700 cm⁻¹).
• Band intensity: Proportional to (Δμ)²; weak bands may disappear if concentration is low.

9. Quantitative IR Spectroscopy (AO2)

The Beer‑Lambert law applies to solution IR measurements:

\[ A = \varepsilon \, c \, l \]

• A – absorbance (unitless)
• ε – molar absorptivity (L mol⁻¹ cm⁻¹)
• c – concentration (mol L⁻¹)
• l – path length (cm) – usually the thickness of the liquid film or the length of the gas cell.

Worked Quantitative Example

A 0.250 mm liquid cell (l = 0.025 cm) is filled with an unknown solution. The absorbance of the carbonyl band at 1720 cm⁻¹ is 0.420. The molar absorptivity for this ketone at that wavelength is 150 L mol⁻¹ cm⁻¹. Calculate the concentration.

\[ c = \frac{A}{\varepsilon l}= \frac{0.420}{150 \times 0.025}= \frac{0.420}{3.75}=0.112\;\text{mol L}^{-1} \]

If the balance reads 0.500 g of sample dissolved in 25 mL, the experimental concentration is 0.200 mol L⁻¹, indicating a systematic error (e.g., path‑length mis‑measurement). Propagating the uncertainties (±0.002 abs, ±5 % ε, ±0.001 cm l) gives a combined relative uncertainty of ≈ 7 %.

Key Points for AO3 Evaluation

• Linear range of Beer‑Lambert law is typically 0.1 – 1.0 A; dilute or concentrate accordingly.
• Check for band saturation (flattened peaks) – dilute sample.
• Verify baseline stability; correct for atmospheric CO₂/H₂O.
• Report concentration with appropriate significant figures (same as least‑precise measurement).

10. Limitations, Accuracy & Reliability (AO3)

• IR‑inactive vibrations: Homonuclear diatomics (O₂, N₂) and symmetric stretches of non‑polar molecules do not appear.
• Band overlap: Broad O–H/N–H can mask nearby C=O or C–H bands.
• Concentration effects: Too concentrated → saturation; too dilute → poor signal‑to‑noise.
• Sample‑preparation artefacts: Moisture in KBr pellets, uneven film thickness, bubbles in liquid cells, or gas‑cell leaks.
• Instrumental factors: Resolution (typically 4 cm⁻¹), detector noise, stray light, and number of scans affect peak position and intensity.
• Evaluation strategy:
  1. Compare the spectrum with a known reference (library match or literature).
  2. Cross‑check functional‑group assignments with another technique (e.g., NMR for carbonyl carbon, MS for molecular weight).
  3. Discuss any ambiguous or missing bands and possible reasons (e.g., symmetry, low dipole change).

11. Comparison with Other Analytical Techniques (AO2)

Technique	Primary Information	Strengths vs. IR	Weaknesses vs. IR
IR Spectroscopy	Functional‑group identification (dipole‑change vibrations)	Fast, inexpensive, works for solids, liquids, gases; quantitative (Beer‑Lambert).	Cannot see IR‑inactive groups; overlapping bands; limited structural detail.
NMR Spectroscopy	Atomic‑level connectivity, chemical environment of H/C	Complete structural information; distinguishes isomers.	More costly, requires deuterated solvents, larger sample amounts.
Mass Spectrometry (MS)	Molecular mass, fragmentation pattern	Accurate molecular weight; useful for unknowns.	No direct functional‑group info; requires ionisation.
UV‑Vis Spectroscopy	Electronic transitions of conjugated systems	Very sensitive for chromophores; good for quantitative analysis.	Only applicable to compounds with π‑π* or n‑π* transitions; limited structural detail.
Elemental Analysis (CHN)	Empirical formula (percent composition)	Provides elemental ratios; confirms molecular formula.	No information on functional groups or connectivity.

12. Inorganic Context Box (AO1)

13. Worked Example (Full AO1‑AO3 Application)

Spectrum (selected peaks)

• 3400 cm⁻¹ – broad, very strong (O–H, hydrogen‑bonded)
• 1720 cm⁻¹ – very strong, sharp (C=O, non‑conjugated)
• 2950 & 2850 cm⁻¹ – medium, sharp (C–H sp³)
• 1240 & 1080 cm⁻¹ – strong (C–O stretches)
• Fingerprint region matches reference spectrum of butanoic acid.

Interpretation (AO1‑AO2)

1. Broad 3400 cm⁻¹ → hydrogen‑bonded O–H, typical of carboxylic acids.
2. 1720 cm⁻¹ C=O → carbonyl of a non‑conjugated acid (acid carbonyls 1700–1725 cm⁻¹).
3. C–O bands (1240 & 1080 cm⁻¹) confirm an –COOH group.
4. Sp³ C–H region confirms an aliphatic chain.
5. Fingerprint match → butanoic acid (CH₃CH₂CH₂COOH).

Quantitative Check (AO2)

Using a 0.250 mm liquid cell, the absorbance at 1720 cm⁻¹ is 0.650. ε = 180 L mol⁻¹ cm⁻¹.

\[ c = \frac{0.650}{180 \times 0.025}= \frac{0.650}{4.5}=0.144\;\text{mol L}^{-1} \]

If the prepared solution was intended to be 0.150 mol L⁻¹, the result is within experimental error.

Evaluation (AO3)

• Band overlap: the broad O–H slightly obscures the C=O shoulder; baseline correction was applied.
• Instrument resolution (4 cm⁻¹) is sufficient to separate the C=O from nearby C–H overtone.
• Possible error sources: slight variation in cell thickness, residual moisture in KBr pellet (if solid reference used).
• Cross‑validation: ^1H NMR shows a singlet at δ 12.2 ppm (acidic proton) and a quartet/multiplet pattern consistent with butanoic acid.

14. Summary Checklist for Students (AO1‑AO3)

1. Recall the selection rule (Δμ ≠ 0) and be able to state why a given vibration is IR‑active.
2. Memorise the key wavenumber ranges (Table 1) and associate each with an IUPAC‑named functional group.
3. When given a spectrum, follow the step‑by‑step interpretation procedure (Section 6).
4. For quantitative questions, apply Beer‑Lambert law, watch the linear range, and propagate uncertainties.
5. Always comment on reliability: consider concentration, overlapping bands, instrument resolution, and compare with another technique.