= Solution
\b[The historical name <fermentation> covered several transformations of organic matter: alcoholic, lactic, butyric and acetous changes, as well as some processes now classified separately.] In modern biochemistry, <fermentation> more narrowly means energy-yielding metabolism that regenerates oxidized cofactors without requiring an external respiratory electron acceptor. The older use of the word should not be forced into that modern definition.
In <alcoholic fermentation>, suitable <yeast> converts a fermentable <sugar> into <ethanol> and <carbon dioxide>. For <glucose>, the principal net balance is
$$
\boxed{\mathrm C_6\mathrm H_{12}\mathrm O_6\longrightarrow2\mathrm C_2\mathrm H_5\mathrm{OH}+2\mathrm{CO}_2.}
$$
A vessel with an outlet for the evolved <gas> and a separate receiver illustrates the change: test the <carbon dioxide> with <limewater> and identify the volatile alcohol in a separated distillate. Gas evolution alone does not prove that the liquid contains <ethanol>. Actual yeast cultures also make biomass and minor products; the <chemical equation> describes the principal conversion. In modern terms, <glycolysis> supplies <ATP>, and the reduction leading to <ethanol> regenerates <NAD+> from <NADH>.
In <lactic acid fermentation>, an ideal homolactic balance is
$$
\boxed{\mathrm C_6\mathrm H_{12}\mathrm O_6\longrightarrow2\mathrm{CH}_3\mathrm{CH(OH)COOH}.}
$$
The souring of suitable carbohydrate-containing materials, including milk, supplied a familiar historical example. Hydrolysis of <lactose> supplies monosaccharides, while acid production lowers the <pH> and can precipitate <casein>. <Casein> coagulation is a consequence of the changed conditions, not evidence that the protein has itself been converted into <lactic acid>. Some organisms instead make additional products, so not every lactic fermentation obeys only this homolactic balance.
In <butyric acid fermentation>, carbohydrates or <lactate> can give <butyric acid>, <carbon dioxide> and <molecular hydrogen>. An idealized balance from <lactic acid> is
$$
\boxed{2\mathrm C_3\mathrm H_6\mathrm O_3\longrightarrow\mathrm C_4\mathrm H_8\mathrm O_2+2\mathrm{CO}_2+2\mathrm H_2.}
$$
It contrasts with the simple homolactic balance because both gaseous products and a different organic acid appear. Mixed cultures and alternative pathways can alter the product distribution; odour is neither a sufficiently specific nor a necessary laboratory test.
<Acetous fermentation> denotes the conversion of <ethanol> into <acetic acid>, as in vinegar production:
$$
\boxed{\mathrm C_2\mathrm H_5\mathrm{OH}+\mathrm O_2\longrightarrow\mathrm{CH}_3\mathrm{COOH}+\mathrm H_2\mathrm O.}
$$
It depends on <oxygen> and is now understood as an aerobic microbial oxidation, rather than a fermentation in the narrow biochemical sense. This explains why access to <air> matters differently here than in the main alcohol-producing stage.
Other older extensions of the word include \b[<saccharification> or diastatic changes], such as the <hydrolysis> of <starch> into smaller sugars by malt enzymes, and \b[<sugar inversion>], in which <sucrose> takes up <water> to form <glucose> and <fructose>:
$$
\mathrm C_{12}\mathrm H_{22}\mathrm O_{11}+\mathrm H_2\mathrm O\longrightarrow2\mathrm C_6\mathrm H_{12}\mathrm O_6.
$$
The two hexose products have the same elemental formula but different structures. Such hydrolyses prepare substrates for later metabolism; they do not by themselves constitute the alcohol-producing conversion. \b[<Viscous fermentation> or <mucilaginous fermentation>] described transformations yielding gum-like material and sometimes <mannitol>; it is an operational historical category without one universal balanced <chemical equation>. \b[Putrefactive fermentation] referred to the decomposition of nitrogen-containing organic matter, including <proteolysis> and subsequent reactions producing <Ammonia>, amines and sometimes <hydrogen sulfide>. It likewise has no single formula covering every mixed substrate and product.
The unifying historical interest is that small amounts of a “ferment” bring about major changes in a large amount of organic substrate. Modern explanation distinguishes organisms, enzymes and metabolic pathways. The later demonstration of <fermentation> in cell-free yeast juice showed that alcoholic conversion need not require intact living yeast cells in the reacting liquid; that result belongs to 1897, not to knowledge to demand of an 1866 candidate.<Cell-free fermentation by Eduard Buchner>[1897 primary report, preparation of yeast juice and fermentation without intact yeast cells]{ref}
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