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The chemical element with atomic number eighteen. Argon is a colourless noble gas. It can provide a protective atmosphere around hot, reactive materials, for example in welding, where excluding oxygen limits oxidation. Commercial production separates it by distillation of liquid air.^[ref]

Its discovery shows why a small disagreement can matter more than a reassuringly repeatable result. Two preparations can each give consistent measurements while producing different mixtures. The Rayleigh-Ramsay argon density experiment investigated just such a discrepancy. Gas density links the weighing to a mean molar mass; a separate separation process tests which component accounts for it.

Co-distillation is the vaporization and collection of multiple components together during distillation. A component can enter the collected vapor alongside another volatile substance instead of being isolated as a pure vapor. Steam distillation is the case in which water supplies a volatile carrier; co-distillation is not restricted to water.

The result depends on vapor-liquid equilibrium. In an ideal, fully mixed binary liquid at a specified temperature, Raoult's law gives $p_A=x_A{p}_A^{\ast }$ and $p_B=x_B{p}_B^{\ast }$. The vapor fraction is $y_A=p_A/(p_A+p_B)$. The McMaster distillation manual uses liquid/vapor composition diagrams to explain why the vapor can be enriched in one component while still containing both.^[ref]

For original hypothetical data, let $x_A=0.25$, $p_A^{\ast }=80\mathrm{kPa}$ and $p_B^{\ast }=20\mathrm{kPa}$. Then $p_A=20$ and $p_B=15\mathrm{kPa}$, giving $y_A=20/35\approx 0.571$. Both components co-distil, but the vapor is richer in $A$ than the starting liquid. These are equilibrium pressures at the stated temperature; boiling additionally requires their sum to match the external pressure.

With two persistent immiscible liquid phases, a different limiting model uses the pure-component vapor pressures directly, rather than multiplying each by its fraction of a homogeneous mixture. An azeotrope is another special equilibrium situation. Specify the phase behavior before assigning a distillate composition, and use a distillation material balance to distinguish enrichment from total recovery. Collecting a component together with a carrier does not itself establish complete separation from every impurity.

Creosote is a mixture obtained from distillation of organic material, historically including wood tar. Its composition depends strongly on origin and processing.

Distillation separates a mixture by producing vapor from a liquid and collecting the condensed liquid, called the distillate. The more volatile component can have a higher mole fraction in the vapor. Simple distillation collects this condensate directly; fractional distillation adds repeated contact in a fractionating column.^[ref]

Two questions must be kept separate. Vapor-liquid equilibrium describes which compositions can coexist. A distillation material balance accounts for how much of each component leaves in each product. A product can be enriched without containing all the original component, and even a feasible distillation material balance does not establish that an apparatus can make those products.

Water purified by distillation, used as a defined solvent in many pharmaceutical preparations.

Harold Urey identified deuterium through the spectrum of a hydrogen sample enriched by low-temperature distillation. Ordinary hydrogen and deuterium have the same atomic number but different atomic mass; the small spectral displacement offered a way to recognize the heavier isotope.^[ref]

A physical chemist whose name is used in the planetary Urey ratio.

An ideal solution is a chemical solution whose component chemical potentials depend on composition throughHere $n_i$ is an amount of substance, $x_i$ its mole fraction, $R$ the molar gas constant, and ${\mu }_i^{\ast }$ the pure-component liquid reference at the same temperature $T$ and pressure $P$. This model applies to every component across the composition range; it is stronger than an approximation valid only near a pure solvent.^[ref]

With this pure-liquid standard state convention, the thermodynamic activity satisfies ${\mu }_i={\mu }_i^{\ast }+RT\ln a_i$, so an ideal solution has $a_i=x_i$, or activity coefficient ${\gamma }_i=a_i/x_i=1$.^[ref] This statement concerns the liquid. Assuming that a coexisting vapor is an ideal gas mixture is an additional approximation. Its mole fractions $y_i$ generally differ from the liquid mole fractions $x_i$.

For an original two-component example, stipulate $T=300\mathrm{K}$ and pure-component vapor pressures $p_A^{\ast }=80\mathrm{kPa}$ and $p_B^{\ast }=20\mathrm{kPa}$. A and B are invented distinguishable components; these numbers are chosen model inputs, not material data. Combine an ideal solution with an ideal gas vapor, neglect the pure-liquid reference's pressure correction, and exclude other gases. At liquid mole fractions $x_A=0.4$ and $x_B=0.6$, Raoult's law and addition of partial pressures giveThus the coexisting vapor contains about $72.73\%$ A by amount of substance, although the liquid contains only $40\%$. The total pressure is neither pure-component vapor pressure, and $x_A$ cannot be substituted for $y_A$. This enrichment is the basis of distillation.

The usefulness of the ideal solution is that one composition law connects chemical potentials, vapor-liquid equilibrium, entropy of mixing and Gibbs free energy of mixing. Its liquid components can interact strongly: the defining condition is their composition dependence, rather than the absence of all interactions as in an ideal gas model.

A laboratory condenser removes heat from vapor so that it becomes liquid. In distillation, the downstream laboratory condenser makes collectable distillate. Complete condensation, without loss or reaction, preserves the entering vapor's overall component mole fractions; cooling alone does not give another enrichment step. Partial condensation can instead leave two streams of different composition, requiring both vapor-liquid equilibrium and a distillation material balance.

Liquid air is a cryogenic liquid mixture produced from atmospheric gases, chiefly nitrogen and oxygen. It does not behave as a pure substance with a single composition-independent boiling temperature.

Because its components have different volatilities, evaporation changes the mixture's composition. Fractional distillation uses that difference to separate major atmospheric gases, linking phase equilibrium with industrial gas production.

A concrete motivating experiment is the acetone–chloroform mixture in Truman State University's Liquid-Vapor Equilibrium of a Binary System, Procedure and Figure 1. A two-neck flask feeds a distillation head with a water-cooled laboratory condenser, condensate sampling arm and temperature probe. Starting with one pure liquid, the procedure adds the other component successively and waits for stable temperature with returning condensate. Small paired samples from the flask and condensate are read on an Abbé refractometer; a tabulated refractive index–composition relation gives the two compositions. Controls include three-point thermometer calibration, corrected atmospheric pressure readings, and agreement of the initial pure-liquid and condensate refractive indices with the reference value. Small withdrawals and little retained condensate reduce disturbance of composition. Sample evaporation can bias the readout. The inferred paired mole fractions, temperature and pressure describe vapor-liquid equilibrium, subject to the conversion from mass fraction to mole fraction and to representative sampling. This teaching protocol reports no measured results of a particular student run.^[ref]

How does such a measurement expose activity coefficients? Let $x_i$ and $y_i$ be the mole fractions in the liquid and gas thermodynamic phases, respectively, and let $p_i^{\ast }(T)$ be the pure-component vapor pressure. Assume the gas thermodynamic phase is an ideal gas mixture and neglect the change of the pure-liquid reference chemical potential between its saturation pressure and the experimental pressure. Equality of each component's chemical potential between the two thermodynamic phases then givesThis turns the paired composition readings into estimates of the activity coefficients. The approximation needs refinement when the gas departs appreciably from ideal gas behavior or the neglected liquid pressure effect matters.

The apparatus measures a boiling-composition series in which temperature changes as the mixture changes. Its readings therefore cannot be inserted directly into the fixed-temperature, fixed-pressure activity coefficient constraint. They motivate the more general task: test whether the measured mixture properties can arise from a common Gibbs free energy while accounting for changing state variables. A failure can reveal incompatible property fits or experimental bias; a pass supplies a consistency check, not proof that every reading is correct.

A suitable historical answer gives both the chemical transformation and the means of isolating a reasonably pure product. The following are preparative principles, with modern chemical formulas; they are not instructions for self-preparation of medicines. In particular, hydrogen cyanide, mercury compounds and arsenic compounds present serious toxicity hazards. Hydrogen cyanide is extremely volatile, can be absorbed by several routes, and its odour is an unreliable warning.^[ref]

For hydrocyanic acid, a customary early nineteenth-century route is the controlled distillation of potassium ferrocyanide with dilute sulfuric acid and water. Hydrogen cyanide passes into the distillate; nonvolatile salts remain behind. A generating flask, efficient laboratory condenser and chilled receiver are needed because hydrogen cyanide is readily lost. The contemporary account of hydrocyanic acid preparation in Pharmacopoeia Castrensis Ruthenica in The British and Foreign Medical Review (1842) specifically describes the ferrocyanide–sulfuric acid method and its losses on imperfect condensation. The concentration must be determined analytically before any defined dilution: a nominal starting mixture does not establish the final strength.^[ref] At the level of the released cyanide, the essential acid-base reaction is $\mathrm{C}{\mathrm{N}}^{-}+{\mathrm{H}}^{+}\to \mathrm{HCN}$. This equation alone is not a complete equation for decomposing the stable ferrocyanide coordination complex. Concentrated sulfuric acid can lead to different decomposition chemistry, so the specified dilution is meaningful.

For formic acid, gently heat oxalic acid with glycerol and some water, then separate the aqueous formic acid by distillation. The useful net transformation isThe glycerol participates through intermediate esters and is regenerated rather than consumed in this net equation. Marcellin Berthelot's 1856 account describes the carbon dioxide evolution, subsequent water addition and distillation, and reuse of the residual glycerol. Overheating is disadvantageous because the formic acid can decompose further to carbon monoxide and water. The method therefore separates a volatile acid from a much less volatile carrier; it is not merely the dry destructive heating of oxalic acid.^[ref]

For oxalic acid, oxidize a carbohydrate, such as sucrose or starch, with nitric acid; concentrate the resulting chemical solution appropriately and cool it to obtain crystals, followed by recrystallization. Nitrogen oxides evolve, and excessive oxidation can carry carbon onward to carbon dioxide, so an idealized single-product equation would conceal losses. The use of starch and nitric acid for oxalic acid production is explicitly documented in an 1850 account of nitric oxide recovery.^[ref] An alternative already established before 1864 is alkaline treatment of sawdust, producing an oxalate which can be purified through sparingly soluble calcium oxalate.^[ref] Decomposing the isolated calcium oxalate with sulfuric acid separates much of the calcium as calcium sulfate:Filter off the calcium sulfate and crystallize the oxalic acid from the filtrate. The usual crystals contain two water of crystallization; a calculation for the anhydrous acid must not treat their entire mass as ${\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4$.

For calomel, intimately combine mercury(II) sulfate, metallic Mercury and dry sodium chloride, then collect the volatile mercury(I) chloride in a cooler receiving chamber. The net change isThe extra metallic Mercury lowers the average oxidation state from +2 to +1. The product is purified by appropriate sublimation and washing to remove soluble contamination, particularly mercury(II) chloride. Both the chemical composition and the fine subdivision of the product matter: condensation through a chamber can give a powder rather than an adherent crystalline crust. This physical part of calomel preparation is described in the 1843 primary account in Polytechnisches Journal volume 87 (1843); the account's historical therapeutic claims are not adopted here.^[ref]

For corrosive sublimate, heat dry mercury(II) sulfate with sodium chloride and collect the mercury(II) chloride in the cooler part of a suitable sublimation apparatus:Here no metallic Mercury is added. Nonvolatile sodium sulfate stays behind, while mercury(II) chloride is transferred and condensed. Further sublimation or recrystallization separates impurities. ^[ref] The crucial distinction from calomel preparation is whether Mercury remains in the +2 oxidation state or is converted to +1.

For the solid called arsenious acid, roast an arsenic-bearing ore in air and collect the volatile arsenic trioxide in cooler chambers; purify by resublimation. The essential oxidation is represented byActual ores also contain other chemical elements, so their roasting equations and gaseous by-products depend on composition. A contemporary 1860 report describes roasting arseniferous ores, collecting the volatile arsenic trioxide in chambers and refining it by another sublimation. It also demonstrates that apparently good material could contain antimony(III) oxide: physical appearance alone does not establish purity.^[ref] The product intended here is dry $\mathrm{A}{\mathrm{s}}_2{\mathrm{O}}_3$; dissolving it does not make the bottled solid a pure crystalline hydrate ${\mathrm{H}}_3\mathrm{As}{\mathrm{O}}_3$.

For tartar emetic, react antimony(III) oxide with potassium hydrogen tartrate in water. A small amount of water first gives intimate contact in a paste; subsequent heating with more water completes formation of the soluble potassium antimony tartrate. Filter away unreacted insoluble matter and cool the clear filtrate to crystallize the product. This sequence is directly described in a January 1864 discussion of the newly issued British Pharmacopoeia, rather than inferred from its later editions.^[ref] In the traditional antimonyl notation the underlying reaction, before assigning crystal water of crystallization, isThis notation expresses the overall composition; tartrate coordination complexes and water of crystallization need the qualification given in 4. The historical pharmaceutical use of tartar emetic does not make it a safe contemporary emetic.^[ref]

For potassium chlorate, pass chlorine into hot concentrated potassium hydroxide. The disproportionation gives potassium chloride together with potassium chlorate:Concentration and cooling permit fractional crystallization of the much less soluble cold-water potassium chlorate, leaving much of the potassium chloride in the mother liquor; recrystallization improves purity. Cold dilute alkali instead favours hypochlorite, so the heating condition is essential. An economical contemporary manufacturing alternative uses hot calcium hydroxide and potassium chloride; the overall accounting isThe 1850 account in Polytechnisches Journal volume 118 (1850) describes a steam-heated stirred vessel and recovery by cooling, rather than an electrical manufacturing process introduced retrospectively.^[ref]

Confirm hydrogen cyanide by chemical tests on a suitable separated fraction, then estimate its amount with a defined quantitative assay. Here “hydrocyanic acid” means $\mathrm{HCN}$ in water, also historically called prussic acid. Smelling or tasting is not an analytical test: hydrogen cyanide is acutely poisonous, and its characteristic odour is not reliably perceived.^[ref]

A coloured or complex liquid can mask the tests or contain interfering ions. Historically, controlled distillation separated volatile hydrogen cyanide from many nonvolatile constituents; a receiving solution captures the analyte. In a modern analytical apparatus, the closed transfer system includes a condenser and an alkaline gas absorber. The receiver converts volatile hydrogen cyanide into less volatile cyanide:The measured fraction must be defined: free hydrogen cyanide in the original liquid is not automatically identical to “total cyanide” released from complexes by a more aggressive preparation. A blank, a known positive control and recovery checks help distinguish a negative sample from failed separation or reagent failure.^[ref]

For the historical iron test, make a separate test portion alkaline, introduce fresh iron(II) salt together with an iron(III) source, and finally acidify as specified by the historical procedure. Cyanide first forms ferrocyanide with iron(II); iron(III) then gives the characteristic Prussian blue precipitate. Idealized balances explaining the recognition chemistry areReal Prussian blue can be hydrated and nonstoichiometric; the second chemical equation is a useful idealization. The acid stage also removes obscuring iron hydroxide precipitates. These steps explain the old mixed iron-salt test, rather than assuming that cyanide simply reacts directly with any iron salt to give blue material.^[ref]

A second aliquot can be examined with silver nitrate. Silver cyanide is white, but whiteness alone is not specific because silver chloride and other precipitates can interfere:For a purified aliquot, precipitate the cyanide quantitatively with silver nitrate, separate the silver cyanide, wash it free of soluble salts, dry it to constant mass and weigh it. The precipitation conditions must avoid losses as volatile hydrogen cyanide and dissolution as dicyanoargentate; interfering precipitates must be excluded. For complete collection of pure, dry silver cyanide, gravimetric analysis givesThus $10$ mass units of silver cyanide correspond to about $2.02$ mass units of hydrogen cyanide. The 1867 pharmacopoeial check was $10$ grains of dry silver cyanide from $100$ grains of the diluted acid, corresponding approximately to its stated $2\%$ strength by mass.^[ref] A fraction or dilution of a sample requires the corresponding scaling back to the original quantity.

Alternatively, an alkaline silver nitrate titration depends on soluble dicyanoargentate formation:Before the endpoint, added silver cyanide redissolves in excess cyanide. In the classical version, the first persistent turbidity marks the end of this clear-solution stage. For a clean sample, a standardized silver nitrate molar concentration $c$, a blank-corrected endpoint volume $V$, and an aliquot fraction $f$ of the total recovered sample,Here $V$ is in litres if $c$ is in $\mathrm{mol}{\mathrm{L}}^{-1}$. Divide by the original sample mass for a mass fraction, or by its original volume for a mass concentration. No numerical sample amount is supplied, so no particular measured concentration can be inferred.

Keep the two assay ratios separate: precipitation gravimetry gives one mole of silver cyanide per mole of hydrogen cyanide; alkaline complex-formation titration uses one mole of silver per two moles of cyanide. A modern version of the latter uses a rhodanine indicator and a blank, as in EPA Method 9014; that indicator procedure is a modern comparison, not a detail assigned to 1867.^[ref]

Reflux is condensed liquid returned toward the heated part of a distillation apparatus. In a fractionating column, descending reflux contacts rising vapor. Returning more condensate also changes the amount available for collection, so enrichment and product recovery must be considered together.^[ref]

Vacuum distillation carries out distillation at reduced pressure.