= Solution
\b[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.<Hydrogen cyanide emergency response information by NIOSH>[Agent Characteristics; Routes of Exposure; warning that smell does not provide adequate protection]{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.<Pharmacopoeia Castrensis Ruthenica in The British and Foreign Medical Review (1842)>[Processes for obtaining Hydrocyanic Acid]{ref} At the level of the released <cyanide>, the essential <acid-base reaction> is $\mathrm{CN^-+H^+\rightarrow HCN}$. 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 is
$$
\mathrm{H_2C_2O_4\longrightarrow HCOOH+CO_2}.
$$
The <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>.<Verfahren zur Darstellung der Ameisensäure by Marcellin Berthelot>[Polytechnisches Journal 140 (1856), p.78, report of the March 1856 communication]{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.<Polytechnisches Journal volume 117 (1850)>[p.466, “Verfahren das Salpetergas in Salpetersäure zu verwandeln”, opening example]{ref} An alternative already established before 1864 is alkaline treatment of <sawdust>, producing an <oxalate> which can be purified through sparingly soluble <calcium oxalate>.<Polytechnisches Journal volume 162 (1861)>[report on chemical manufacture in South Lancashire, Oxalsäure section: alkaline sawdust route]{ref} Decomposing the isolated <calcium oxalate> with <sulfuric acid> separates much of the <calcium> as <calcium sulfate>:
$$
\mathrm{CaC_2O_4+H_2SO_4\longrightarrow H_2C_2O_4+CaSO_4}.
$$
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 $\mathrm{H_2C_2O_4}$.
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 is
$$
\mathrm{HgSO_4+Hg+2NaCl\longrightarrow Hg_2Cl_2+Na_2SO_4}.
$$
The 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.<Polytechnisches Journal volume 87 (1843)>[pp.209 onward, “Ueber Darstellung des Calomels als höchst zartes Pulver”, condensation and collecting chamber]{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:
$$
\mathrm{HgSO_4+2NaCl\longrightarrow HgCl_2+Na_2SO_4}.
$$
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. <Dictionary of Arts, Manufactures and Mines by Andrew Ure>[Mercury, p.141, bichloride preparation and the following calomel account]{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 by
$$
\mathrm{4As+3O_2\longrightarrow2As_2O_3}.
$$
Actual <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.<Polytechnisches Journal volume 156 (1860)>[p.77, report on the antimony content of glassy arsenious acid from Andreasberg]{ref} The product intended here is dry $\mathrm{As_2O_3}$; dissolving it does not make the bottled solid a pure crystalline hydrate $\mathrm{H_3AsO_3}$.
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.<Chemical News volume 9 (1864)>[30 January 1864, p.53, Antimonium Tartaratum: paste, standing, boiling and the oxide–bitartrate route]{ref} In the traditional antimonyl notation the underlying reaction, before assigning crystal <water of crystallization>, is
$$
\mathrm{Sb_2O_3+2KHC_4H_4O_6\longrightarrow2K(SbO)C_4H_4O_6+H_2O}.
$$
This 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.<Antimony potassium tartrate by the National Poisons Information Service>[Toxicity; gastrointestinal effects and systemic poisoning]{ref}
For <potassium chlorate>, pass <chlorine> into hot concentrated <potassium hydroxide>. The <disproportionation> gives <potassium chloride> together with <potassium chlorate>:
$$
\mathrm{3Cl_2+6KOH\longrightarrow KClO_3+5KCl+3H_2O}.
$$
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 is
$$
\mathrm{6Cl_2+6Ca(OH)_2+2KCl\longrightarrow2KClO_3+6CaCl_2+6H_2O}.
$$
The 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.<Polytechnisches Journal volume 118 (1850)>[pp.424 onward, “Die neue Bereitungsart des chlorsauren Kalis”]{ref}
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