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Laboratory reference

The science desk

Reference material for laboratory work: the arithmetic that gets redone every week, the constants worth keeping to hand, and a plain account of what the common analytical instruments actually measure — and what they cannot tell you.

Units & constants Analytical methods
A note on precision: a measurement carries only as much precision as the instrument earned. Writing 99.400% when the method resolves to one decimal claims two digits that were never measured. Extra digits read as confidence; they are usually noise.

Quick reference

Units, constants and conversions

The numbers worth having in one place. Since 20 May 2019 the SI has been built on constants fixed by definition rather than by artefact — these are exact, not measurements with error bars.

NAAvogadro constantThe number of entities in one mole. Exact by definition since 2019.6.02214076 × 10²³ mol⁻¹ hPlanck constantFixed exactly, and the kilogram is now derived from it rather than from a cylinder in a vault near Paris.6.62607015 × 10⁻³⁴ J·s cSpeed of lightExact. The metre is defined from it, not the other way round.299 792 458 m·s⁻¹ RMolar gas constantFollows from the Boltzmann and Avogadro constants, both of which are exact.8.314462618 J·mol⁻¹K⁻¹ C₁V₁ = C₂V₂DilutionConcentration times volume is conserved. Any consistent pair of units works, so long as both concentrations share one and both volumes share another.V₁ = (C₂ × V₂) ÷ C₁ c = ρ ÷ MMolar concentrationMolarity counts particles; mass concentration weighs them. Moving between the two needs the molar mass. mg/mL and g/L are the same number.mol·L⁻¹

Everything above is standard laboratory practice, not house style. Where a value is exact by definition it is marked as such; everything else carries the uncertainty of the method behind it.

Working principles

Things worth remembering

None of this is complicated. All of it is routinely got wrong, usually by trusting a number further than the method that produced it.

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Significant figures

Multiplying or dividing keeps the fewest significant figures of the inputs. Adding or subtracting keeps the fewest decimal places. Rounding at the end, not at every step, avoids compounding the error.

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Accuracy is not precision

Accuracy is how close a result sits to the true value; precision is how closely repeats agree with each other. A method can be reliably, repeatably wrong — tight scatter around the wrong number.

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Every method has a blind spot

Each technique answers one narrow question well and is silent on the others. Most misreadings come from treating one method's answer as a general verdict.

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Beer–Lambert has a ceiling

Absorbance rises linearly with concentration and path length until it does not. Above roughly A = 1 the relationship bends as the detector runs out of light to lose. Dilute into range rather than extrapolating out of it.

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Detection and quantification differ

The limit of detection is the smallest amount distinguishable from noise. The limit of quantification — the smallest amount you can put a reliable number on — is higher, usually by around three times.

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Blanks and controls

A result without a blank is a number without a baseline. Controls are what separate a real signal from an artefact of the solvent, the vessel, or the instrument itself.

Common questions

Analytical methods FAQ

What does HPLC actually measure?

It separates a mixture by how strongly components partition between a mobile and a stationary phase, then measures what comes off the column. It answers how much of what was detected is one substance. It does not identify that substance, and anything that does not elute or does not absorb at the detector's wavelength is invisible to it.

What does a purity percentage not tell you?

A figure from a chromatogram means that proportion of the signal the detector saw was one peak. It is silent on anything the detector could not see — residual solvent, water, counter-ions, inorganic salts. Purity, identity and content are three separate questions and one number answers only one of them.

How does mass spectrometry differ from NMR?

Mass spectrometry ionises molecules and sorts them by mass-to-charge ratio, answering what mass is present — strong evidence of identity, though isomers share a mass. NMR reads how nuclei behave in a magnetic field and reports on their chemical environment, answering how the atoms are connected. NMR is far less sensitive and needs much more material.

Why is content found sometimes higher than the labelled amount?

Containers are often deliberately overfilled. A figure above the label means more material is present than stated, which covers residue left behind during reconstitution and transfer so the usable amount still meets the label.

What is the difference between molarity and molality?

Molarity is moles per litre of solution and shifts with temperature, because volume expands. Molality is moles per kilogram of solvent and does not, since mass is temperature-independent. For careful work across temperatures, molality is the safer measure.

Why do exact constants have no uncertainty?

Since the 2019 redefinition, seven constants are fixed by definition rather than measured. The uncertainty moved: instead of measuring the Planck constant against a kilogram, the kilogram is now realised from a Planck constant that is exact by fiat. The error bars sit on the realisation, not on the number.