UV–VIS Spectrophotometry: Comprehensive Exam Notes

DEFINITIONS

• Spectroscopy: study of interaction of energy (EM-radiation, acoustic waves, particle beams) with matter.
• Spectrometry: quantitative measurement of radiation intensity $I$ with electronic device.
• Spectrometer: instrument measuring radiation intensity vs. $\lambda,\;\nu,\;\sigma,\;E_{\text{photon}}$.
• Spectrophotometer: spectrometer employing photon detector to record incident power $P_0$ and emergent power $P$ (gives absorbance).
• Spectrophotometry: all procedures using light to quantify chemical concentrations.

UV–VIS SPECTROPHOTOMETRY – GENERAL PRINCIPLES

• Measures absorbance in 200–400 nm (UV) and 400–800 nm (VIS).
• Two requirements for absorption:
  • Photon energy exactly matches energy gap $\Delta E$ between two quantised states of analyte.
  • Electric/magnetic field of radiation must couple with analyte’s electrons.
• In UV–VIS, interaction involves electronic energy of valence electrons ➔ changes valence-electron configuration.

ELECTRONIC ENERGY LEVELS & TRANSITIONS

• Occupied molecular orbitals (MOs): $\sigma$-bonding, $\pi$-bonding, non-bonding $n$.
• Vacant MOs: $\sigma^{<em>},\;\pi^{</em>}$.
• Four principal electronic transitions:
  • $\sigma \rightarrow \sigma^{*}$ (usually <200 nm)
  • $n \rightarrow \sigma^{*}$ (≈185–195 nm)
  • $n \rightarrow \pi^{*}$ (≈300 nm for C=O)
  • $\pi \rightarrow \pi^{*}$ (≈190 nm; shifts with conjugation)
• Importance hierarchy: $n\rightarrow\pi^{<em>}$ and $\pi\rightarrow\pi^{</em>}$ dominate analytical work (characteristic wavelengths, accessible range).

Tabulated Typical Transitions

• $\sigma$ electrons (C–C, C–H): $\sigma\rightarrow\sigma^{*}$ < 200 nm.
• Isolated lone pair O, N: $n\rightarrow\sigma^{*}$ ≈ 185–195 nm.
• Carbonyl >!C=O: $n\rightarrow\pi^{<em>}$ ≈ 300 nm; $n\rightarrow\sigma^{</em>}$ ≈ 190 nm.
• Isolated $\pi$ electron systems: $\pi\rightarrow\pi^{*}$ ≈ 190 nm.

CHROMOPHORES & AUXOCHROMES

• Chromophore: structural moiety whose electrons undergo electronic transition upon UV-VIS absorption; confers colour/absorbance.
• In VIS region only molecules with well-defined chromophores absorb noticeably.
• Conjugation (alternating double/single bonds) lowers $\Delta E$; shifts $\lambda_{\text{max}}$ to longer wavelength (bathochromic/red shift).
  • Ethylene: $\lambda_{\text{max}} = 190\;\text{nm}$.
  • 1,3-butadiene: 217 nm.
  • 1,3,5-hexatriene: 258 nm.
  • $\lambda<em>{\text{max}}$ ↑ further with extended conjugation (e.g. (\beta)-carotene $\lambda</em>{\text{max}} = 455\;\text{nm}$ ➔ orange colour).
• Auxochrome: substituent extending a chromophore, creating new chromophore; typically contains lone pairs (e.g. >C=O + NH2R \rightarrow >C=NR, $\lambda</em>{\text{max}}$ 190 → 230 nm).
• Bathochromic effect (red shift) = move to longer $\lambda$; Hypsochromic (blue) shift = shorter $\lambda$. Caused by substitution, solvent polarity, pH, loss of conjugation etc.

MO Scheme Illustration

• 1,3-Butadiene: four $p$ orbitals combine ➔ two filled MOs ((\psi1,\psi2)), two empty ((\psi3,\psi4)). HOMO→LUMO transition yields broad band at 217 nm. Reduced HOMO–LUMO gap with longer conjugated chains.

UV–VIS SPECTRA CHARACTERISTICS

• Each electronic transition couples with numerous vibrational levels → many closely spaced lines merge into broad absorption bands often exhibiting multiple maxima.
• $\lambda<em>{\text{max}}$: wavelength of peak molar absorptivity $\varepsilon</em>{\max}$.
• Molar absorptivity increases with conjugation (polyene example shows higher $\varepsilon$ and red-shifted peaks).
• Solvent and pH can alter both $\lambda_{\text{max}}$ and $\varepsilon$ (polarity, hydrogen bonding, protic vs. aprotic).

INSTRUMENTATION

Single-Beam Spectrophotometer

• Optical path: light source → wavelength selector (monochromator) → sample cuvette → detector → readout.
• Requires manual blanking (record $P_0$) then sample (record $P$). Variations in lamp intensity/time are not auto-compensated.

Double-Beam Spectrophotometer

• Rotating chopper/mirror alternately directs beam through reference (blank) and sample cells many times per second.
• Detector receives alternating $P_0$ and $P$, providing:
  • Automatic source & detector drift correction.
  • Continuous wavelength scanning with real-time absorbance recording.

Practical Issues

• Choose measurement wavelength at or very near $\lambda_{\text{max}}$ (maximises sensitivity, minimises interference).
• Always run reagent blank (solvent + reagents, no analyte) to correct for extraneous absorbance.
• Non-absorbing analytes can be derivatised chemically to form absorbing species (e.g. $\text{Fe}^{2+} + 3\,\text{phen} \rightarrow [\text{Fe(phen)}_3]^{2+}$).

BEER–LAMBERT LAW

• When monochromatic beam passes through absorbing solution:
  • Transmittance $T = P/P_0$; $\%T = 100T$.
  • Absorbance $A = \log<em>{10}\frac{P</em>0}{P} = \log<em>{10}\frac{1}{T} = 2 - \log</em>{10}\%T$.
• Linear relation with concentration and path length: $A = \varepsilon \; b \; c$ where
  • $\varepsilon$: molar absorptivity $\big(\text{L mol}^{-1}\,\text{cm}^{-1}\big)$.
  • $b$: optical path length (cm).
  • $c$: molarity (mol L$^{-1}$).
• Advantages of absorbance scale:
  • Linear with $b$ and $c$.
  • Independent of incident intensity fluctuations.

Interpretive Benchmarks

• $A = 0$ ⇒ no absorption (\%T = 100 %).
• $A = 1$ ⇒ 90 % photons absorbed (\%T = 10 %).
• $A = 2$ ⇒ 99 % photons absorbed (\%T = 1 %).

Limitations & Deviations

1. Polychromatic light: Significant bandwidth relative to absorption band causes non-linearity. Remedy: employ narrow-bandwidth monochromator.
2. High concentration (>0.01 M): Close proximity induces electrostatic interactions altering $\varepsilon$.
3. Chemical changes: Association/dissociation, complex formation or pH-dependent speciation (e.g. methyl orange IndH ⇌ Ind⁻) create multiple absorbing species.
4. Stray light, scattering (turbidity), refractive-index changes, or detector non-linearity.
5. Validity prerequisites (six key conditions): independent absorbers, homogeneous medium, negligible scattering, parallel rays/constant $b$, monochromatic beam, non-perturbative intensity (avoid saturation).

Multi-Component Systems

• For non-interacting species: $A<em>T = \sum</em>{i=1}^n \varepsilon<em>i b c</em>i$ (linear additive).

QUANTITATIVE APPLICATIONS

Calibration Curve Method

1. Prepare stock of analyte (primary standard) and serially dilute to at least five standards spanning expected concentration range.
2. Prepare reagent blank (all solvents/reagents, no analyte).
3. Measure blank, standards (low→high), then unknown at selected $\lambda_{\text{max}}$.
4. Correct absorbances (sample – blank).
5. Plot $A_{\text{corrected}}$ (y) vs. $c$ (x); apply least-squares to obtain slope $m$ and intercept $b$.
6. Determine unknown concentration by interpolation (only within linear region). If outside, dilute sample or adjust standard range.

Serial Dilution Scheme

• Repeated fixed-ratio dilutions, producing geometric concentration series (e.g. 1/10, 1/100, 1/1000 …).
• Ensures accurate low-level standards when direct weighing becomes impractical.

Cuvette Handling Guidelines

• Use quartz cuvettes for UV (glass absorbs <~300 nm).
• Inspect clear faces for scratches; wipe with lint-free lens tissue.
• Hold by frosted/ribbed sides only; cap to avoid evaporation.
• Remove bubbles; rinse with small volume of new solution before filling.
• Align orientation mark consistently; ideally use same cuvette for all measurements.

Chelation & Metal Analysis

• Transition-metal aqua ions often show weak $d\rightarrow d$ bands (low $\varepsilon$). Complexation with chelating agents converts them to intensely absorbing charge-transfer complexes.
• Chelation: ligand with two or more donor atoms forms ring with metal (ex. dimethylglyoxime with Ni$^{2+}$, 1,10-phenanthroline with Fe$^{2+}$, 8-hydroxyquinoline with Mg$^{2+}$, acetylacetone, dithizone, APDC, crown ethers, cryptands).
• Reaction often releases $\text{H}^+$ ➔ maintain buffer.
• Charge-transfer bands typically appear in VIS with very high \varepsilon (>50{,}000).
  • Ligand→metal CT (e.g. $\text{MnO}_4^-$, $\text{Fe(SCN)}^{2+}$).
  • Metal→ligand CT (aromatic $\pi^{*}$ acceptors, e.g. Fe–phenanthroline).

MATRIX EFFECT & STANDARD ADDITION

• Matrix: all sample constituents other than analyte; can alter analytical signal via additive absorbance, chemical reactions, viscosity, refractive index, etc.
• Matrix effect: any change in signal attributable to matrix, not analyte.
• Calibration with pure standards may be invalid if matrix differs markedly.

Standard Addition (SA) Technique

• Spike unknown with small, known amount of standard analyte → observe signal increase.
• Basic proportionality:$\frac{[X]<em>i}{A</em>x} = \frac{[S]<em>f + [X]</em>f}{A_{s+x}}$ (after accounting for dilution).
• Graphical SA: divide sample into equal aliquots, add incremental standard volumes, dilute to equal volumes, measure responses. Plot signal vs. added standard concentration.
  • Extrapolation to x-axis intercept (negative added concentration) gives original $[X]_i$.
• Ensures standards and unknown share identical matrix.
• Keep spike volume small to minimise dilution; correct with dilution factor when necessary.

Worked Example Synopsis

• Na⁺ in serum: initial signal 4.27 mV; after +0.104 M spike signal 7.98 mV.
  $\displaystyle [\text{Na}^+]_\text{orig} = 0.120\;\text{M}$ (via SA equation).

INTERNAL STANDARDISATION (IS)

• Especially valuable when sample prep/handling may cause variable analyte loss.
• Internal standard: compound chemically/physically similar to analyte, absent from original sample (e.g. C$<em>6$D$</em>5$Cl for chlorobenzene GC-MS, nor-leucine for amino-acid GC-MS).
• Added in constant amount to all blanks, standards, samples.
• Ratio of signals (analyte/IS) compensates for volume changes, detector fluctuations, extraction losses.
• Calibration: plot $(A/IS)<em>{\text{signal}}$ vs. analyte concentration; use ratio measured in sample to derive $c</em>{\text{unknown}}$.
• Fundamental relationship:$\frac{c<em>x}{c</em>{IS}} = \frac{(A<em>x/A</em>{IS})<em>{\text{sample}}}{(A</em>x/A<em>{IS})</em>{\text{std}}}$ (assuming identical response factors).

EXEMPLAR CALCULATIONS / PROBLEMS

• Benzene $\varepsilon$ determination: 25.8 mg benzene in 250 mL (1 cm path, $A=0.266$ @ 200 nm) ⇒ $\varepsilon = 2.6\times10^{3}\;\text{L mol}^{-1}\,\text{cm}^{-1}$.
• Unknown concentration: given $A<em>1=0.43\;(c</em>1=0.14\,M),\;A<em>2=0.37$ ⇒ $c</em>2 = 0.12\,M$.
• Photometer question: blank 73.6 µA, sample 24.9 µA.
  • $T = 24.9/73.6 = 0.338$ ⇒ $\%T = 33.8\%$.
  • $A = -\log_{10}T = 0.470$.
  • If concentration $1/3$ original ⇒ $A/3 = 0.157$ ⇒ $T = 0.697$ ⇒ $\%T=69.7\%$.
  • If double concentration ⇒ $A\times2 = 0.940$ ⇒ $T = 0.115$ ⇒ $\%T = 11.5\%$.

ETHICAL & PRACTICAL IMPLICATIONS

• Careful blank subtraction prevents false positives/negatives.
• Sample matrices (environmental, biological) often complex ➔ SA or IS mandatory to ensure data integrity.
• High-ε charge-transfer complexes enable trace metal detection but require control of toxic ligands (e.g. dithizone, crown ethers) – proper waste disposal.
• UV sources (deuterium lamps) emit harmful UV-C; shielding and eye protection necessary.

CONNECTIONS & REAL-WORLD RELEVANCE

• Conjugated pigments underpin vision (retinal) and plant coloration (carotenoids).
• Beer–Lambert framework parallels attenuation laws in acoustics, NMR, X-ray absorption.
• Instrumental design concepts (double-beam correction) echoed in FT-IR beam-splitter modulation.
• Chelation principles exploited in medicinal chelators (EDTA therapy), water softening, and catalysis.