What analytical chemistry is: the analytical process

Every day, analytical chemists answer questions that matter to someone. Is the lead in this school's drinking water below the guideline? How much active ingredient is in this batch of tablets? Has the nitrate in a farm well risen since last spring? Is this athlete's urine sample clean? Did the mine's effluent meet its permit last month? Each question ends in a number, and each number carries consequences: a boil-water advisory, a recalled product, a fine, a disqualification, or a family's decision to buy a filter. Analytical chemistry is the science of obtaining such numbers, knowing how good they are, and reporting them so that people can act on them.

This course builds on the stoichiometry, equilibrium, acid–base and electrochemistry you met in CHEM-101 and CHEM-102. There, a titration was mainly an exercise in moles. Here it becomes a measurement with an uncertainty, a choice among methods, and part of a quality system. By the end of the course you will be able to plan an analysis, carry out the classical wet-chemical methods (acid–base, complexometric, precipitation and redox titrations, and gravimetry), treat the data statistically, and defend the result in a written report.

Qualitative and quantitative analysis

Analytical chemistry has two broad branches. Qualitative analysis asks what is present: is there chloride in this solution, is this white powder caffeine or something else, which pesticide residues are on this lettuce? Quantitative analysis asks how much: what is the mass fraction of iron in this ore, what is the concentration of fluoride in this tap water? Most modern work is quantitative, and it is the focus of this course, although every quantitative method assumes you already know the identity of what you are measuring.

The substance being measured is the analyte. Everything else in the sample is the matrix. Iron in a vitamin tablet is the analyte; the starch, sugar coating, binder and other minerals are the matrix. Matrix components that respond to the method as if they were the analyte, or that suppress or enhance its signal, are called interferences. A method's ability to measure the analyte without interference from the matrix is its selectivity, and much of the art of analytical chemistry lies in achieving it, either by choosing a selective reaction or by separating the analyte from the interferences before measurement.

Classical and instrumental methods

Classical methods, also called wet-chemical methods, rely on chemical reactions and on measurements of mass and volume. Gravimetric analysis weighs a pure product formed from the analyte; titrimetric (volumetric) analysis measures the volume of a reagent of known concentration that reacts exactly with the analyte. These methods developed in the eighteenth and nineteenth centuries and are still in daily use, because they can be very accurate and need no calibration curve: the result follows directly from stoichiometry and from masses traceable to the kilogram. Many reference materials are still certified by titration or gravimetry.

Instrumental methods measure a physical property that depends on the analyte's amount: absorption or emission of light, an electrode potential, a current, a mass-to-charge ratio, or the time a compound takes to pass through a chromatographic column. They are usually faster, more sensitive and better at handling many samples, but nearly all are relative: the instrument must be calibrated with standards of known concentration. CHEM-311 Instrumental Analysis develops these methods. In this course we use the simplest instrumental measurements, pH and absorbance, to illustrate calibration and to follow titrations.

The analytical process

An analysis is much more than the measurement step. Analytical chemists describe it as a sequence of decisions and operations, each of which can introduce error. The figure shows the process as a loop, because results that fail quality checks send the analyst back to an earlier step.

1. Define the problem. What is the question behind the request? Which analyte, in what kind of sample, at what concentration, with what accuracy, how fast and at what cost? A request for the arsenic in rice for a regulatory decision needs a validated method with a low detection limit; a quick screen of a hundred soil samples for gross contamination needs speed more than exactness. Talking to the client before starting saves more mistakes than any statistical test.

2. Choose a method. Match the method's sensitivity, selectivity, accuracy, speed and cost to the problem. Standard methods published by bodies such as ASTM International, the International Organization for Standardization (ISO), the American Public Health Association (Standard Methods for the Examination of Water and Wastewater) and national regulators are often required for regulatory work.

3. Obtain a representative sample. The result can be no better than the sample. A grab of the top centimetre of a grain truck, or tap water collected after the tap has run for ten minutes when the question is about lead standing in the pipes overnight, gives a precise answer to the wrong question. Sampling plans specify where, when and how much to collect, how to store it and how long it can be held.

4. Prepare the sample. Most samples must be dried, ground, weighed, dissolved or digested, and sometimes the analyte must be separated from interferences or concentrated. Losses, contamination and incomplete dissolution at this stage are common sources of error.

5. Measure. Carry out the measurement on replicate portions, usually three or more, along with blanks (samples with no analyte, carried through every step) and check standards.

6. Calculate. Convert the raw signal into the quantity requested, using stoichiometry or a calibration, and keep track of units and dilutions.

7. Evaluate. Estimate the uncertainty, test for outliers, compare replicates, and check quality-control results. Are they good enough to answer the question?

8. Report. State the result with its uncertainty, the method, and any limitations, in a form the client can use.

Absolute and relative methods

An absolute method gives the amount of analyte from fundamental quantities: mass, volume, stoichiometry and atomic masses. Gravimetry and titration with a standardized titrant are absolute in this sense. A relative method compares the sample's signal with the signals of standards. Spectrophotometry, chromatography and most electrochemical methods are relative. The distinction matters for traceability: an absolute method inherits its accuracy from the balance and the glassware, while a relative method inherits it from the standards, and errors in the standards pass straight into every result.

Units of concentration

Analytical results are reported in many units, and conversion errors are among the most common mistakes in practice. The table collects the units you will use most.

Parts per million and parts per billion are convenient but ambiguous, because they can be on a mass, volume or mole basis. In water analysis, 1 L of dilute solution has a mass of almost exactly 1 kg, so 1 mg/L is 1 mg per 10⁶ mg, or 1 ppm by mass. For gases, ppm usually means a volume (mole) ratio. Always state the basis, and prefer mg/L or µg/L for water.

# Unit conversions an analyst does every day
M = {'Ca': 40.078, 'Mg': 24.305, 'CaCO3': 100.087, 'Fe': 55.845, 'NO3': 62.004, 'N': 14.007}

def mg_per_L_to_mM(mg_L, species):
    return mg_L / M[species]

def as_CaCO3(mg_L, species):
    # hardness: one mol of a divalent cation corresponds to one mol of CaCO3
    return mg_L / M[species] * M['CaCO3']

ca, mg = 52.0, 14.6
hard = as_CaCO3(ca, 'Ca') + as_CaCO3(mg, 'Mg')
print(f"Ca {ca} mg/L = {mg_per_L_to_mM(ca, 'Ca'):.3f} mM = {as_CaCO3(ca, 'Ca'):.0f} mg/L as CaCO3")
print(f"Mg {mg} mg/L = {mg_per_L_to_mM(mg, 'Mg'):.3f} mM = {as_CaCO3(mg, 'Mg'):.0f} mg/L as CaCO3")
print(f"total hardness = {hard:.0f} mg/L as CaCO3")

# nitrate is often reported as nitrate-N; convert 10 mg/L as N to mg/L as nitrate
print(f"10.0 mg/L nitrate-N = {10.0 * M['NO3'] / M['N']:.1f} mg/L as nitrate")

Ca 52.0 mg/L = 1.297 mM = 130 mg/L as CaCO3
Mg 14.6 mg/L = 0.601 mM = 60 mg/L as CaCO3
total hardness = 190 mg/L as CaCO3
10.0 mg/L nitrate-N = 44.3 mg/L as nitrate

The last line shows a classic trap. Nitrate guidelines are often written as nitrate-nitrogen (10 mg/L as N in both Canada and the United States), which is equivalent to about 45 mg/L as nitrate ion. A laboratory that reports 30 mg/L without saying which form has given an answer that could be read as safe or unsafe.

Figures of merit

Methods are compared by figures of merit, numbers that describe how well a method performs. You will meet each of them in detail later in the course.

A brief history

Quantitative chemistry began when chemists started to weigh. Antoine Lavoisier's careful balance work in the 1770s and 1780s, showing that mass is conserved in reactions, made chemistry a quantitative science. Gravimetric analysis flourished in the nineteenth century, when Jöns Jacob Berzelius determined atomic masses of many elements with remarkable accuracy, and Theodore Richards later refined them so well that he received the 1914 Nobel Prize in Chemistry. Titration developed alongside: Joseph Louis Gay-Lussac published a volumetric method for silver in 1832 and introduced the words burette and pipette in the 1820s, Karl Friedrich Mohr designed the burette with a pinchcock and published his influential textbook on titration in 1855, and Jacob Volhard described his back-titration for silver and halides in 1874. Statistics entered the laboratory in the twentieth century: William Sealy Gosset, publishing as Student in 1908 while working at the Guinness brewery in Dublin, gave analysts the t distribution for small samples, and Walter Shewhart's control charts of 1924 created statistical quality control.

Analytical chemistry and society

Most analytical results are used to make decisions, and many decisions are written into regulations. Drinking-water guidelines, food standards, workplace exposure limits and environmental permits all set numerical limits, and only analytical measurements can show whether they are met. Because the stakes are high, laboratories that produce results for regulatory or legal use are usually accredited to the international standard ISO/IEC 17025, which requires documented methods, trained staff, calibrated equipment, traceable standards, quality-control records and participation in proficiency tests. Lesson 12 returns to this system.

In Canada, Health Canada publishes the Guidelines for Canadian Drinking Water Quality, which the provinces and territories adopt into their own regulations, and the Canadian Council of Ministers of the Environment (CCME) publishes environmental quality guidelines. Laboratories are commonly accredited by the Canadian Association for Laboratory Accreditation (CALA) or the Standards Council of Canada. Lead is a good example of how analytical capability and health knowledge move together: Health Canada lowered its maximum acceptable concentration for lead from 0.010 mg/L to 0.005 mg/L in 2019, a level that requires methods able to measure reliably at about 1 µg/L.

Safety in the analytical laboratory

Analytical work uses corrosive acids and bases, oxidizers, toxic metal salts and sometimes flammable solvents, usually in small amounts but repeatedly. The habits from CHEM-101 apply every day: wear eye protection and a lab coat, read the safety data sheet before using a new reagent, add acid to water rather than water to acid when diluting, never pipette by mouth, label every container with its contents and date, and dispose of metal-containing and halogenated wastes in the designated containers rather than down the drain. Silver, mercury, chromium(VI) and lead reagents deserve special care, and modern methods are chosen partly to avoid them.