Codex @codex  0

Stoichiometry relates the quantities consumed and formed in a chemical reaction. Its coefficients are ratios of entity counts, or equivalently of amount of substance, rather than ratios of masses. For the water chemical equation, consuming two molecular hydrogen molecules per molecular oxygen molecule gives the same $2:1$ ratio as consuming two moles of molecular hydrogen per mole of molecular oxygen. Multiplying every entity count by the same factor preserves the ratio. See Flowers et al., Chemistry 2e, reaction stoichiometry.

Coefficients and subscripts do different jobs. The coefficient in $2{\mathrm{H}}_2\mathrm{O}$ counts two water molecules; the subscript says that each contains two hydrogen chemical atoms. Changing coefficients scales quantities. Changing a subscript changes the specified chemical substance.

This distinction catches a common counting error: one mole of water molecules contains two moles of hydrogen chemical atoms and one mole of oxygen chemical atoms. Always specify what is counted.

Stoichiometry records reactant and product multiplicities in a chemical reaction or a chemical reaction network. The change caused by one reaction is its stoichiometric vector; multiplying by the reaction rate gives its contribution to the concentration equations. For two identical reactants the rate-constant convention absorbs any combinatorial factor.

A reaction substrate on which an enzyme acts in a chemical reaction.

A chemical species on which a reagent or catalyst acts in a chemical reaction. An enzyme acts on a biochemical substrate, a particular instance of this broader reaction role.

Substrate-level phosphorylation forms ATP by enzyme-catalyzed transfer of a phosphate group from a phosphorylated substrate to ADP. In canonical glycolysis, two such transfers occur for each three-carbon route, giving four gross ATP per glucose. Unlike oxidative phosphorylation, these transfers do not require an electron transport chain.^[ref]

The pyruvate kinase example under Coupled-enzyme readout of glycolytic ATP formation separates the material transfer from its detection. A favourable coupled chemical reaction supplies the driving change in Gibbs free energy; the enzyme supplies a catalytic route. Counting ATP-forming transfers gives a gross yield, while subtracting upstream ATP use gives the net yield.

A thermodynamic system is in thermodynamic equilibrium when its macroscopic state has no spontaneous tendency to change through any exchange allowed by its constraints. For an isolated system, stable thermodynamic equilibrium maximizes entropy over the accessible states at fixed total energy and conserved material inventories. A wall can forbid an exchange, so always specify what can cross or move. Thermal, mechanical and chemical conditions answer different questions about that same constrained state. ^[ref]

For example, two compartments separated by a rigid, impermeable wall that transmits heat can reach thermal equilibrium while retaining different pressures and compositions. Allowing an unloaded piston to move adds a mechanical equilibrium condition. Allowing one chemical species to cross adds chemical potential equality for particle exchange; allowing a chemical reaction adds its chemical equilibrium condition. A fixed barrier can therefore support a constrained thermodynamic equilibrium that ceases to be an equilibrium when the barrier is removed.

Uniformity is not the definition of thermodynamic equilibrium. An isothermal atmosphere in hydrostatic equilibrium can have a common temperature while its pressure and mass density vary with height: the pressure gradient balances gravity. In an external field, the exchange condition must include the relevant potential energy; for charged matter this leads to the electrochemical potential. Relativistic gravitational corrections to thermal equilibrium are described separately by the Tolman temperature law.

A steady state only says that the macroscopic description is constant in time. A bar maintained between hot and cold thermal reservoirs has steady heat flux and produces entropy, so it is not in thermodynamic equilibrium. Even matching temperatures at one perfect-contact interface can coexist with heat transfer through the surrounding material; matching those two local values does not establish equilibrium of the whole apparatus. See thermal conduction for that spatial transport problem.

The useful simplification is that equilibrium conditions predict an endpoint without computing every collision or flow during relaxation. The first law of thermodynamics supplies the conserved quantities, and the Second law of thermodynamics supplies the direction of change. For a system held at fixed temperature and volume, the corresponding criterion is minimization of Helmholtz free energy; at fixed temperature and pressure, it is minimization of Gibbs free energy, with the material and exchange constraints still imposed.

A free energy is a thermodynamic potential that compares possible states under specified environmental constraints. For a closed system of fixed composition, treated as a simple compressible system with only pressure-volume work, stable thermodynamic equilibrium minimizes Helmholtz free energy at fixed temperature and volume, or Gibbs free energy at fixed temperature and pressure. The choice follows the experiment: a rigid sealed vessel and a sealed cylinder with a freely moving loaded piston impose different constraints. Both may exchange heat with a thermal reservoir. See W. C. Carter, MIT thermodynamics notes, sections 2-1.14 and 2-1.19.

The useful insight is that internal energy alone cannot rank these alternatives: exchanging heat also changes the surroundings' entropy. Subtracting $TS$ packages that accounting into a property of the chosen system. Adding $pV$ additionally accounts for displacing the surroundings at fixed pressure. A free energy is a state function; supplied heat describes a transfer during a process. Under the stated constraints, supplied heat is $Q=\Delta U$ at fixed volume or $Q=\Delta H$ at fixed pressure, whereas neither $\Delta F$ nor $\Delta G$ generally equals $Q$.

A lower free energy identifies a thermodynamic preference, without specifying a timescale. A barrier can trap a system in a local minimum, producing metastability although a lower global minimum exists. The enzyme example illustrates the corresponding distinction for chemical reactions: changing the route can change the reaction rate while preserving the endpoint Gibbs free energy difference and chemical equilibrium.

Ultraviolet is electromagnetic radiation with wavelengths shorter than the violet end of ordinarily visible light. The CIE convention uses $100$–$400\mathrm{nm}$, subdivided into UV-A at $315$–$400\mathrm{nm}$, UV-B at $280$–$315\mathrm{nm}$ and UV-C at $100$–$280\mathrm{nm}$. These divisions name intervals; they do not mark universal changes in every material's response. The boundary with visible light is not sharp, and other fields use near-, far-, vacuum- and extreme-ultraviolet divisions. ^[ref]. For example, NASA's Solar Dynamics Observatory observes extreme-ultraviolet bands below $100\mathrm{nm}$; the CIE interval is therefore not the full extent of astronomical ultraviolet usage. ^[ref].

The CIE ultraviolet interval corresponds to frequencies about $7.49\times 10^{14}$–$3.00\times 10^{15}\mathrm{Hz}$ and photon energies $4.97\times 10^{-19}$–$1.99\times 10^{-18}\mathrm{J}$, using vacuum wavelength and $E=hc/\lambda$ with Planck constant $h$ and speed of light $c$. Shorter wavelength means larger energy per photon; larger irradiance means more incident power per area. These are different comparisons. At the same incident power, a $254\mathrm{nm}$ ultraviolet beam has fewer photons per second than a $940\mathrm{nm}$ infrared beam, even though each ultraviolet photon has more energy.

A common ultraviolet mechanism is photon absorption promoting an electron from a ground state to an excited state of a chemical atom or molecule. By contrast, many infrared absorption bands involve stretching or bending chemical bonds. For either mechanism, both the energy difference and the coupling to the incident electromagnetic field matter. One concrete example is the $217\mathrm{nm}$ absorption discussed for butadiene: an electron moves between molecular orbitals, and the position of the absorption reveals their energy separation. Ultraviolet absorption can therefore probe molecular orbitals, while infrared spectroscopy probes many molecular motions. ^[ref].

Subsequent chemical reactions depend on the absorbing chemical substance and its environment; the label ultraviolet alone does not predict a reaction rate. At sufficiently short wavelength, a photon can cause photoionization if its energy exceeds the relevant ionization energy. There is no single wavelength that separates all ionizing from all nonionizing behavior for every chemical substance. Likewise, eventual heating after photon absorption is possible in both ultraviolet and infrared. The distinction is useful because different optical spectra expose different processes, not because the two ranges obey different laws of electromagnetism.

Ritter's 1801 observation used a chemical readout rather than a thermometer. In Caltech/IPAC's account, sunlight passed through a glass optical prism and silver chloride was placed in different parts of the optical spectrum. Darkening was weak toward red, stronger toward violet, and pronounced beyond the visible violet edge. The measured evidence was a change in the chemical substance's appearance at a spatial location with no visible color, establishing radiation beyond the eye's ordinary range. It was not a calibrated measurement of a universal ultraviolet optical spectrum. ^[ref].

A controlled modern interpretation of such a chemical test would compare equal exposure durations and matched fresh samples, keep an unexposed sample in darkness, monitor temperature, and distinguish scattered visible light from the intended short-wavelength beam with characterized filtering. These are proposed controls, not an assertion that Ritter performed them. Unequal sample preparation or heating can change a reaction rate. The optical prism, terrestrial atmosphere and sample response restrict which wavelengths the test detects. Darkening is a detector-weighted response, so its spatial maximum is not automatically the maximum of incoming radiant flux or of photon energy.

Thomas Larason and Jeanne Houston's NIST report documents a quantitative ultraviolet detector comparison. An argon source feeds a double-diffraction grating spectrometer; a shutter and mirrors deliver the selected band to a working-standard or test photodiode, successively at the same position. A beam splitter supplies a monitor photodiode. Amplifiers and voltmeters record detector and monitor simultaneously; shutter-closed readings provide dark baselines. The $200$–$500\mathrm{nm}$ scan, typically with $4\mathrm{nm}$ bandpass, measures spectral responsivity. Monitor normalization suppresses source drift; known spectral lines calibrate wavelength. The report assesses temperature effects and unwanted light outside the band, weighted by detector response. The latter need not cancel between different spectral responsivities. ^[ref].

This determines electrical response without visual perception. Bandpass and spatial nonuniformity limit the calibration; aging and changed temperature can affect later use. The scan includes visible light and ultraviolet; no response below $200\mathrm{nm}$ follows from it.

For a narrow beam, the idealized substitution calculation isHere $R$ is spectral responsivity; $I$ and $M$ are dark-subtracted detector and monitor electric currents. This follows by writing $I=RP$ for each detector and using the monitor to track changes in radiant flux. It assumes linear response, unchanged beam splitting and collection geometry, and a sufficiently narrow band. For an illustrative standard with $R_{\mathrm{std}}=0.15\mathrm{A}{\mathrm{W}}^{-1}$, ratios $I_{\mathrm{std}}/M_{\mathrm{std}}=2.0$ and $I_{\mathrm{test}}/M_{\mathrm{test}}=1.6$ give $R_{\mathrm{test}}=0.12\mathrm{A}{\mathrm{W}}^{-1}$. These invented arithmetic inputs illustrate the method; they are not NIST measurements.

An independent photon-counting model connects spectral responsivity to quantum efficiency. If $\eta (\lambda )$ is the number of collected electrons per incident photon, there is no internal multiplication, and $q$ is the elementary charge, thenAt illustrative constant $\eta =0.60$ and $P=1\mu \mathrm{W}$, this gives about $0.123\mu \mathrm{A}$ at $254\mathrm{nm}$ and $0.455\mu \mathrm{A}$ at $940\mathrm{nm}$. The ultraviolet readout is smaller in this model because there are fewer incident photons, not because their individual energies are smaller. Real quantum efficiency depends on wavelength, windows, absorption and carrier collection; a detector's band gap and construction determine its usable range. Constant $\eta$ across these two wavelengths is an analytical comparison, not a claimed specification of a real photodiode.

The curve is the calculated relation $E=hc/\lambda$, and the shaded ranges use the stated CIE conventions. The lower diagram abstracts the detector comparison rather than reproducing an instrument drawing. Together with the infrared heat-balance illustration, it shows why a calibrated detector response, rather than what looks bright to an observer, is the bridge between invisible radiation and a quantitative measurement.

A valence electron belongs to the electronic arrangement used to describe a chemical atom's chemical bonds and ordinary chemical reactions. For the neutral hydrogen, carbon, nitrogen, and oxygen chemical atoms used here, the valence electrons occupy the outermost occupied electron shell. Their respective electron configurations are $1s^1$, $1s^{2}2s^{2}2p^2$, $1s^{2}2s^{2}2p^3$, and $1s^{2}2s^{2}2p^4$, giving one, four, five, and six valence electrons. See Chemistry 2e, 6.4: electron configurations and valence electrons.

Lewis structures show these valence electrons while omitting the inner electrons. Consequently, eight drawn valence electrons in water do not mean eight total electrons: neutral water has ten, with two inner oxygen electrons omitted. Neutral ammonia likewise has ten total electrons but eight valence electrons; neutral carbon dioxide has twenty-two total electrons but sixteen valence electrons.

This distinction makes the small counts useful: connections and possible lone pairs can be organized without representing every electron or solving the entire many-electron wavefunction. The outermost-electron shell shortcut applies to the examples above, rather than serving as a universal definition for all chemical elements; the electronic arrangement relevant to chemical bonds can also involve other electron subshells.

For a monoprotic acid with analytical concentration $C_T=[\mathrm{HA}]+[{\mathrm{A}}^{-}]$, define the dimensionless weak acid dissociation fractionThis counts acid units in the conjugate base form. Identifying it with $[{\mathrm{H}}_3{\mathrm{O}}^{+}]/C_T$ additionally requires negligible self-ionization of water and no other sources of electric charge. In the ideal dilute chemical solution model, with $h=[{\mathrm{H}}_3{\mathrm{O}}^{+}]/c^{\circ }$, the acid dissociation constant gives $\alpha =K_a/(K_a+h)$. Thus lowering hydronium thermodynamic activity favors the conjugate base.

The diagram uses stipulated dimensionless acid dissociation constant $K_a=10^{-5}$ and self-ionization of water ion product $K_w=10^{-14}$ at fixed temperature; these are model inputs, not measurements of a named substance. It solves the weak acid mass and charge balances. At $C_T=0.010\mathrm{mol}{\mathrm{L}}^{-1}$, the calculated weak acid dissociation fraction is about $3.11\%$ and pH about $3.51$; at $C_T=10^{-4}\mathrm{mol}{\mathrm{L}}^{-1}$, they are about $27.0\%$ and $4.57$. More acid units are dissociated as a fraction of the total, yet fewer hydronium ions occur per volume.

At extreme dilution, self-ionization of water makes $h$ approach $\sqrt{K_w}$, so pH approaches $7$ for the chosen model. The limiting weak acid dissociation fraction is $K_a/(K_a+\sqrt{K_w})\approx 0.9901$, rather than exactly one. The calculation assumes pure added water, a neutral monoprotic acid, and no competing chemical reactions; actual contamination becomes increasingly important as $C_T$ falls.

Yeasts are fungi whose growth is predominantly unicellular, commonly through budding or division into two cells. The word describes a growth form across different fungal lineages, rather than one species or an exclusive clade; some fungi can switch between unicellular and filamentous growth. Thus Saccharomyces cerevisiae is a yeast, but yeast is not another name for that one species. See Kurtzman, Fell and Boekhout, The Yeasts, chapter 1 (2011): definition and classification.

A yeast cell has eukaryotic organization, including a cell nucleus, mitochondria and a cell wall. Small size and a unicellular lifestyle do not make it a member of bacteria. These compartments let an experimentally accessible biological cell retain much of the organization shared with other eukaryotes. See Clark, Douglas and Choi, Biology 2e, 24.1: fungal cells and yeast growth.

A motivating experiment: can fermentation continue without intact yeast cells? In 1897, Eduard Buchner ground brewers' yeast with quartz sand and diatomite, added water, and pressed out a liquid extract. Adding concentrated cane sugar produced carbon dioxide after 15–60 minutes. A cell-retaining filter still yielded an active filtrate: with sterilized cane sugar in an icebox, fermentation began after about a day. Saturated lactose gave no observed fermentation. These are reported observations, not invented control results. See Buchner, Alcoholic fermentation without yeast cells (1897), translated excerpt hosted by Carmen Giunta.

The filtration comparison addresses the objection that surviving intact yeast cells caused the activity. The lactose comparison tests substrate dependence; it is not a no-sugar blank, nor a comparison at matched sugar concentrations. A proposed modern follow-up would also compare the same extract with and without added sugar, accounting for material already in the extract. That is an experimental suggestion, not a result attributed to Buchner. His report specifies brewers' yeast; it does not identify the preparation here as a pure Saccharomyces cerevisiae strain.

Heat treatment asks a different question: does destroying activity in the extract stop fermentation? Buchner's preliminary report described weak or absent activity after heating and filtration, rather than one clean universal threshold. Harden's 1914 account of the subsequent work summarized loss of activity on heating the juice to $50{}^{\circ }\mathrm{C}$. Harden also described requirements for both enzymes and coenzymes. Cell-free therefore means neither chemical-free nor a preparation containing one purified enzyme. See Arthur Harden, Alcoholic Fermentation (1914), chapters II and VI: cell-free activity and the fermenting complex.

The inference is that extracted cellular machinery can sustain these chemical reactions without an intact living biological cell. This does not show that the extract reproduces, grows or maintains itself like a yeast. Moreover, gas evolution alone does not identify ethanol: cellular respiration can also release carbon dioxide. Product identification is a separate measurement; Harden's account describes both ethanol and carbon dioxide as products of cell-free alcoholic fermentation. The beautiful separation is between the organism that produces and maintains the machinery and the machinery that catalyzes a particular transformation.

An inspected university demonstration makes the paired changes visible. The 2021 Chemical Demonstrations Booklet hosted by Edith Cowan University describes two cut square zinc strips, each immersed in a separate glass beaker. One contains blue copper(II) sulfate chemical solution, the other colourless zinc sulfate chemical solution. The published readouts are the appearance of a brown copper deposit on the first strip and fading of its blue chemical solution; after thirty minutes more deposit is reported. The comparison strip in zinc sulfate shows no visible change. The documented preparation is cutting the strips; surface polishing is not specified.^[ref]

The reported interpretation is conversion of dissolved ${\mathrm{Cu}}^{2+}$ to metallic copper, accompanied by conversion of metallic zinc to dissolved ${\mathrm{Zn}}^{2+}$. The sulfate anions balance bulk electric charge and cancel from the net chemical equation. The comparison shows that merely immersing a zinc strip in a sulfate chemical solution does not reproduce the visible coating.^[ref]

Appearance is evidence for the proposed conversion, rather than a quantitative measurement of the two-electron ratio. Fading alone could also reflect dilution; deposit colour alone does not independently establish its composition. A stronger follow-up would compare the copper content of the chemical solution before and after, identify the solid, and check dissolved zinc. These are proposed analytical checks, not results reported in the booklet. Comparable starting chemical solutions, surface condition, immersion and observation time help interpret a comparison; an unchanged-looking strip does not rule out slow or invisible chemical reactions.

The two-electron interpretation comes from the species identities and electric charge balance, supported by the paired observations. It does not imply that the coating's mass equals the mass of zinc consumed: the same amount of substance of different chemical elements generally have different molar masses. Nor does it resolve microscopic surface sites or reaction pathways. The same net redox can be organized into separated compartments in a Daniell cell to obtain electrical work.