EGA110 — Definitions & Diagrams

Definitions with Diagrams

Key terms illustrated. Diagrams built from the lecture notes — every label corresponds to an exam target.

Topic 1 — Data & Errors

Accuracy vs Precision — dartboard analogy

ACCURATE + PRECISE PRECISE, NOT ACCURATE ACCURATE, NOT PRECISE NEITHER ✓ Low error, low SD High error, low SD Low error, high SD High error, high SD
Accuracy vs precision — four possible combinations

Gaussian distribution

x p(x) μ μ−σ μ+σ μ−2σ μ+2σ 68% 95% 99.7%
Gaussian distribution — 68-95-99.7 rule. Shaded area = ±1σ = 68% of measurements.
Absolute error
Eᵢ = |xᵢ − xₜ|. Magnitude of deviation from true value. Same units as measurement.
Relative error
Rᵢ = |xᵢ − xₜ| / xₜ. Dimensionless fraction (or %). Allows comparison across different magnitudes.
Sample standard deviation
s = √[Σ(xᵢ−x̄)²/(N−1)]. Uses N−1 (Bessel's correction). Measures scatter of replicate measurements.
Standard error of the mean
Sₘ = s/√N. Uncertainty in the mean x̄. Decreases with more measurements. NOT the same as s.

Topic 4 — Spectroscopy

Beer-Lambert law — light path through a cuvette

I₀ SAMPLE SOLUTION (concentration c) path length b (cm) I (transmitted) analyte molecules absorb photons T = I/I₀ A = εbc A = −log T
Beer-Lambert law — incident intensity I₀ reduced to I as analyte molecules absorb photons

UV-Vis spectrometer — signal path

SOURCE D₂ lamp (UV) W-halogen (Vis) λ SELECTOR Diffraction grating nλ = d sinθ SAMPLE Quartz cuvette (UV + Vis) DETECTOR PMT or Photodiode OUTPUT A or %T
UV-Vis spectrometer signal path — source → wavelength selector → sample → detector → output
Molar absorptivity (ε)
Species- and wavelength-specific proportionality constant in Beer-Lambert law. Units: L mol⁻¹ cm⁻¹. Maximum at λ_max.
λ_max
Wavelength of maximum absorbance/molar absorptivity. Most sensitive measurement point; Beer-Lambert most linear here.
Standard addition advantage
Compensates for matrix effects — any species that affects absorbance in the sample also affects the spiked sample equally, so the effect cancels out in the ratio.
PMT (photomultiplier tube)
Detector with cascade of dynodes; each dynode multiplies electrons ~5×; total gain ~10⁶. Range 150–1000 nm. Used in high-sensitivity instruments.

Topic 5 — Titrations

Strong acid / strong base titration curve

Volume NaOH added (mL) → pH → 0 2 4 6 8 10 12 EQ pH=7 excess HCl excess NaOH steep jump near EQ →
Strong acid / strong base titration curve — S-shaped, equivalence point at pH 7, steep jump indicates correct region for indicator selection

EDTA structure — hexadentate ligand

M^n+ N N O O O O N donor (×2) O donor (×4) --- coordinate bond Total: 6 bonds → hexadentate
EDTA — hexadentate ligand with 2 N and 4 O donors forming 6 simultaneous coordinate bonds with the central metal ion. Ratio is always 1:1 regardless of metal charge.
Chelate effect
Polydentate ligands form more stable complexes than equivalent monodentate ligands. Driven by entropy — releasing multiple water molecules is thermodynamically favourable.
Volhard method
Back-titration for halides. Add excess AgNO₃ → precipitate AgX → FILTER → add Fe³⁺ indicator → back-titrate excess Ag⁺ with KSCN → red FeSCN²⁺ endpoint.
Filter step is critical — omitting it gives wrong result.
Self-indicating titrant
KMnO₄ is self-indicating. Purple MnO₄⁻ is immediately decolourised by Fe²⁺. First permanent purple = endpoint. No external indicator required.
KMnO₄ : Fe²⁺ stoichiometry
1 MnO₄⁻ + 5 Fe²⁺ + 8 H⁺ → Mn²⁺ + 5 Fe³⁺ + 4 H₂O. Mn goes from +7 → +2 (gains 5e⁻); each Fe²⁺ loses 1e⁻. Ratio 1:5.