Analytical Chemistry: Voltammetry, Electrophoresis, and Spectroscopy Notes on Spectroscopy

Definition: Voltammetry is electrolysis on a microscale using microworking electrodes (e.g., Platinum wire). It is a current-voltage technique where the potential is scanned and the resulting current is recorded as a VOLTAMMOGRAM.
Conventions: By Contention, a cathodic (reduction) current is positive and an anodic (oxidation) current is negative.
Limiting Current ( $I_l$ ): In dilute solutions, current reaches a limiting value proportional to the analyte concentration because mass transport becomes diffusion controlled.
Three-Electrode Setup: Consists of a Working electrode, Counter or auxiliary electrode, and a Reference electrode (usually Ag/AgCl or Saturated Calomel Electrode, SCE).
Potential Conversion: $E_{vs\,SCE} = E_{vs\,NHE} - 0.242$ .
Nernst Equation at $25^\circ C$ ( $298\,K$ ): $E = E^o - \frac{0.0592}{n} \log\left(\frac{1}{C}\right)$ .
Half-Wave Potential ( $E_{1/2}$ ): The potential at which the current is half the limiting current; it is independent of concentration and serves as a qualitative tool for identifying species.
Supporting Electrolyte: An inert substance (e.g., $KNO_3$ ) added at high concentration (at least $100-fold$ or $0.1\,M$ ) to eliminate MIGRATION CURRENT and decrease $IR$ drop.

Conditions: Distinct voltammetric waves are recorded if electroactive species have half-wave potentials ( $E_{1/2}$ ) differing by at least $0.2\,V$ .
Examples:
- $Cu^{2+}$ in $NH_3$ reduces to $Cu^+$ at $-0.2\,V$ vs SCE, then to $Cu$ metal at $-0.5\,V$ .
- Mixtures: Pb reduces at $-0.4\,V$ and Co reduces at $-0.6\,V$ ; wave heights are proportional to relative concentrations.

General Principle: Separates substances based on charge-to-mass ratio using an electric field. Widely used for proteins, nucleic acids, and polysaccharides.
Zone Electrophoresis: Uses solid supports like starch gels, polyurethane foam, or polyacrylamide gels. Separation depends on electric charges, sizes, and shapes.
Capillary Zone Electrophoresis (CZE): High-resolution technique using fused capillary tubes ( $10-100\,\mu m$ diameter). Employs high voltage ( $1000 - 30,000\,V$ ) and separates minute quantities (nanoliters or less).
MICELLAR ELECTROKINETIC CAPILLARY CHROMATOGRAPHY (MECC): Involves adding detergents to the background electrolyte to resolve neutral molecules through micelle interaction.

Beer-Lambert's Law: The fundamental law of photometry stating absorbance ( $A$ ) is proportional to concentration ( $c$ ) and path length ( $l$ ): $A = \epsilon cl$ .
Transmittance ( $T$ ): The ratio of transmitted intensity ( $I$ ) to incident intensity ( $I_o$ ): $T = \frac{I}{I_o}$ .
Absorbance Relationship: $A = \log\left(\frac{I_o}{I}\right) = -\log(T)$ .
Limitations: Valid for monochromatic radiation, dilute solutions (typically < 10^{-2}\,mol/dm^3), and non-participating chemical equilibria.
Colorimeter: Invented by Louis J. DuBosc in 1870. Operation involves a light source, monochromator (filter/lens), cuvette, and photocell.

Fluorescence: Instantaneous emission ( $10^{-9}$ to $10^{-7}\,seconds$ ) following excitation from ground singlet state ( $S_0$ ) to excited singlet state ( $S_1$ ). Features high energy and shorter emission duration.
Phosphorescence: Delayed emission (milliseconds to hours) involving Intersystem Crossing (ISC) to a triplet excited state ( $T_1$ ). The transition to the ground state ( $T_1 \rightarrow S_0$ ) is spin-forbidden.

Principle: Measures the Refractive Index ( $n$ ), which is the ratio of the speed of light in a vacuum ( $c$ ) to the speed in the substance ( $v$ ): $n = \frac{c}{v}$ .
Snell's Law: Governs the bending of light: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$ .
Applications: Determining sugar content in juices, purity in pharmaceuticals, and identifying gemstones in gemology.

Spectrometer Components: Source of radiation, Analyzer (monochromator/filter), and Detector.
AAS Burner Types:
- Total-Consumption Burner: All aspirated sample enters the flame; noisier, shorter path length.
- Premix Chamber / Laminar Flow Burner: Selective aspiration; gentle, longer path length, less noise.
Flames: Air-acetylene is common; Nitrous oxide-acetylene is used for heat-stable samples (e.g., Calcium Pyrophosphate, $Ca_2P_2O_7$ ).

History: Discovered by Wilhelm Conrad Rontgen in 1895 (Nobel Prize 1901).
Properties: Electromagnetic radiation with wavelength ( $\lambda$ ) range of $0.005$ to $10\,nm$ ( $5-100\,\text{\u00c5}$ ).
X-Ray Diffraction (XRD): Based on Bragg's Equation: $n\lambda = 2d \sin(\theta)$ . Used for crystal structure identification.
Applications: X-ray absorption (XRA) for identifying internal cracks/flaws, medical radiography, and security screening at airports.