Analytical Chemistry

What a measurement is worth, and how to make one you can defend

About this course

Chemical measurement from error and calibration through acid-base and titration equilibria, electrochemical methods, chromatography, mass spectrometry and quantitative spectroscopy, ending with method validation.

What you will be able to do

  • Propagate uncertainty and determine a detection limit from blank measurements
  • Build a calibration by least squares or standard addition, and judge its reliability
  • Calculate titration curves and buffer behaviour from the systematic equilibrium treatment
  • Apply the Nernst equation and activity to potentiometric and voltammetric measurements
  • Optimise a chromatographic separation and quantify an analyte by spectroscopy or mass spectrometry

What this course covers

  • Why five of six validation criteria are blind to systematic bias
  • Precision as self-comparison versus accuracy as external comparison
  • Accuracy and the critical role of the reference material
  • One recurring shape: a comparison corrects only what both sides share
  • R-squared as a test of range, not linearity
  • Detection limit as two conflated questions
  • Robustness as experimental derivative and its structural blind spot
  • What validation actually delivers and its characteristic failure
  • Two independent approximations in the textbook pH formula
  • The five-percent rule and its conservatism
  • Neutral pH and temperature dependence of Kw
  • The exact cubic and the systematic treatment
  • When water dominates: the second approximation fails
  • Unlisted species: the exact solver's blind spot
  • Nernst Slope and Its Temperature Dependence
  • Isopotential Point and Calibration Structure
  • Automatic Temperature Compensation: Scope and Limits
  • Liquid Junction Potential and Ionic-Composition Error
  • What pH Actually Is: Convention vs. Measurable Quantity
  • Worked Problem: Diagnosing Inter-Laboratory pH Disagreement
  • Resolution as square root of column length
  • Theoretical plates as variance in disguise
  • Van Deemter equation and the optimum flow rate
  • What smaller particles actually buy
  • Extra-column variance and instrument contribution
  • Selectivity as the only linear lever
  • Precision vs. accuracy: two distinct quantities
  • Random vs. systematic error
  • The 1/√N law for random error
  • Systematic error is unaffected by averaging
  • The blank and its limits
  • Confidence intervals and Student's t with small samples
  • Resolution equation: three non-comparable factors
  • Saturation of the retention term
  • Selectivity as the near-linear, highest-return lever
  • Resolution per unit time and the throughput optimum
  • Zero selectivity: the impossible separation
  • Capstone decision and lecture summary
  • Activity vs. concentration in ion-selective electrodes
  • Why single-ion activity is unmeasurable
  • Imposing ionic strength with TISAB
  • Swamping as a general analytical strategy
  • Selectivity coefficient and the usable pH window
  • Detection limit as membrane solubility
  • Activity vs. concentration: which did you want?
  • Four-formula piecewise titration curve and its real failure regions
  • Drop size as the practical resolution limit of titration
  • One-equation titration curve: solving for volume given pH
  • Buffer capacity as the unifying quantity behind titration sharpness
  • Equivalence point, inflection point, and observable endpoint distinguished
  • Distinguishing effect existence from effect magnitude
  • Worked problem: titrating a dilute weak acid of high pKa
  • Quadrature combination of uncertainties
  • Variance shares and where to spend effort
  • General propagation law via partial derivatives
  • Significant figures and the subtraction failure mode
  • Detection limit and its two error rates
  • Budgeting and method specification: worked synthesis
  • Henderson-Hasselbalch's omitted variable
  • pH versus dilution: exact system check
  • Buffer capacity and its linear dependence on total concentration
  • Crossover: water out-buffering the buffer
  • The concentration dilemma: capacity versus ionic-strength error
  • Worked problem: designing a buffer by capacity, not just pH
  • Voltammetric current as a flux, not an amount
  • Cottrell equation and the decaying current
  • Expiry date: natural convection ends the Cottrell regime
  • Rotating disc electrode and the 'impose, don't correct' principle
  • The 'impose over correct' rule across three modules
  • Diffusion coefficient, speciation, and the flaw-or-feature question
  • Standard addition as the required method in voltammetry
  • Pulse voltammetry: separating signals by time dependence
  • Mass axis as a second separation dimension
  • Resolving power and its costs
  • Exact mass, formula shortlists, and the precision–specificity distinction
  • Ion suppression and matrix effects in electrospray
  • Isotope-labelled internal standards for suppression correction
  • Complementary blind spots: why column and detector are both required
  • Worked suppression case: drug assay in plasma
  • Calibration as inverse prediction
  • Hourglass confidence band: interpolation vs. extrapolation
  • Placement of calibration standards: spread vs. distinct levels
  • R-squared versus residual plots as calibration diagnostics
  • Standard addition: bias removal and precision cost
  • Worked problem and lecture synthesis
  • Optimum absorbance as a noise-model property
  • Stray light and the hard absorbance ceiling
  • Slit width, bandwidth error, and the peak-measurement rule
  • Diagnosing calibration curvature at the dilute end
  • Usable absorbance range and linear dynamic range
  • Worked diagnostic: stray light vs. chemical deviation
  • Sampling error: scale and irreversibility
  • The mass law: sampling error vs. sample size
  • Particle size and the cube law
  • Uncertainty budget: sampling vs. analytical variance
  • Increments: what they cure and what they do not
  • Protocol design and module-one synthesis
  • The Conditional Formation Constant
  • The pH Window: Lower and Upper Bounds
  • The Auxiliary Ligand and Its Concentration Window
  • The Conditional Constant as a Shrinking Budget
  • Non-Selectivity of EDTA: Total Hardness vs. Calcium
  • Worked Problem: Determining Calcium in a Complex Water Sample

Syllabus

  1. Error, Calibration and Sampling

    1. L1 · What a Measurement Is: Error, Precision and the Blank
    2. L2 · Propagation, Significant Figures and the Detection Limit
    3. L3 · Calibration: Least Squares, Leverage and Standard Addition
    4. L4 · Sampling: the Error You Cannot Fix Later

  2. Equilibria and Titrations

    1. L5 · Acid-Base Equilibria and the Systematic Treatment
    2. L6 · Titration Curves from First Principles
    3. L7 · Buffers, and Where the Simple Formula Breaks
    4. L8 · Complexometric and Precipitation Titrations

  3. Electroanalytical Methods

    1. L9 · Potentiometry and the Nernst Equation
    2. L10 · Ion-Selective Electrodes, and Activity
    3. L11 · Voltammetry and the Diffusion Layer

  4. Separations and Instrumental Detection

    1. L12 · Chromatography: Plates, Rates and Resolution
    2. L13 · Optimising a Separation, and What Cannot Be Optimised
    3. L14 · Mass Spectrometry as a Detector
    4. L15 · Quantitative Spectroscopy: Beer-Lambert, and When It Fails

  5. Method Validation

    1. L16 · Method Validation, and the Course as One Argument