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The manganese oxidation state is $+4$ when each oxygen is assigned $-2$.

oxidation of an enol or enolate can generate a carbon-centred radical that adds intramolecularly to an alkene. Further oxidation or oxygen capture determines the final functional group.

A mass spectrometry instrument with a photographic readout. In the 1919 apparatus described in Chapter V: The Mass-Spectrograph, a gas discharge produced positive ions. Two narrow slits formed a ribbon beam in a vacuum; plates applied an electric field to spread it, an aperture selected part of it, and a magnetic field bent it oppositely. Focusing reduced the spread caused by differing ion speeds, concentrating a given mass-to-charge ratio into a line on a photographic plate.

The observed quantity was line displacement from a fiducial spot. Known reference lines calibrated displacement against mass-to-charge ratio; repeated exposures with changed magnetic field tested the calibration. Evacuation limited collisions. Comparing line shapes with narrow and wide apertures helped distinguish geometric broadening from photographic spreading. Finite slit widths, plate response, and overlapping molecular or multiply charged ions limited interpretation. See Chapter V: The Mass-Spectrograph (§§33–40: apparatus and photographic procedure; §§43 and 45–46: calibration, aperture comparisons, and accuracy).

In Mass spectra and isotopes by Francis William Aston (Nobel lecture, 12 December 1922), the reported neon lines at 20 and 22 have companions at 10 and 11 from doubly charged ions. That paired pattern and comparison with reference lines support different atomic masses within one chemical element, rather than an atomic mass concentrated at the bulk average. The lecture also describes an earlier failed separation by distillation and partial separation by diffusion, showing why the focused mass spectrum supplied stronger evidence. These numbers used a historical oxygen-based reference scale. The lecture's whole-number rule was an empirical approximation at its stated accuracy, not the modern exact definition $A=Z+N$.^[ref]

The chemical compound $\mathrm{HgO}$. Thermal decomposition can release oxygen and produce mercury; historical preparations of the red oxide featured in Joseph Priestley's and Antoine Lavoisier's investigations.

A mesylate is a methanesulfonate, $\mathrm{ROS}{\mathrm{O}}_2\mathrm{Me}$. Converting an alcohol to its mesylate improves leaving-group ability without initially cleaving the original carbon–oxygen bond.

Mesylation installs a methanesulfonyl group on a heteroatom, often alcohol oxygen. An alcohol attacks electrophilic sulfur of a sulfonylating reagent, and base removes the O–H proton.

Metachloroperbenzoic acid is a peroxycarboxylic acid used for concerted oxygen transfer to alkenes. A neighboring allylic hydroxyl can direct its approach through hydrogen bonding.

Metal ion catalysis uses a coordinated metal ion to activate a reagent, orient reactants or stabilize charge. Zinc can lower the acidity constant of coordinated water and support attack by the resulting oxygen nucleophile without a metal redox step.

The fraction of total mass in chemical elements heavier than helium, so the hydrogen mass fraction, helium mass fraction and metal mass fraction satisfy $X+Y+Z=1$. Despite the astronomical name, this includes elements such as carbon and oxygen that are not chemical metals.

A mitochondrion is an organelle with an outer mitochondrial membrane and an inner mitochondrial membrane. The latter encloses the mitochondrial matrix and folds into cristae; the intermembrane space lies on its opposite side. This architecture separates a chemical workspace from a membrane that couples electron transport to ATP formation.^[ref]

For an original location exercise, place soluble label A in the mitochondrial matrix and soluble label B in the interior of a crista. In the depicted geometry, B can reach the peripheral intermembrane space through the fold's opening without crossing a lipid bilayer. A must cross the inner mitochondrial membrane to reach either location. A fold projecting into the mitochondrial matrix therefore does not make its enclosed fluid part of the mitochondrial matrix. Following a continuous path through the colored regions proves the distinction; merely asking whether a label is “inside the mitochondrion” loses it.

The functional connection is equally spatial. The mitochondrial respiratory chain pumps protons from the mitochondrial matrix side across the inner mitochondrial membrane. Their return through ATP synthase can drive ATP formation. Oxidative phosphorylation develops the mechanism and chemiosmosis gives its free energy bookkeeping. Compartmentalization is useful because it lets a shared electrochemical gradient couple different proteins without direct transfer of a chemical intermediate between each pair.

Under aerobic conditions, mitochondria supply much of the ATP in many eukaryotic biological cells; the contribution varies with biological tissue, demand and oxygen supply. Glycolysis also makes ATP in the cytosol. Mature mammalian red blood cells lack mitochondria, and bacteria have no mitochondria at all. Neither all ATP production nor all biological cells fit the familiar mitochondrial picture.^[ref]

Mitochondria descend from a bacterial endosymbiosis and retain a genome and ribosomes, although many required proteins are encoded by nuclear genes. Endosymbiotic theory develops the ancestry argument; organelle protein import explains delivery of nuclear-encoded proteins. A functioning isolated mitochondrion demonstrates biochemical autonomy under supplied conditions, rather than independently establishing that ancestry.

The mitochondrial matrix is the compartment enclosed by the inner mitochondrial membrane, containing mitochondrial DNA, ribosomes and many enzymes. Most citric acid cycle steps occur here; succinate dehydrogenase is membrane-associated. The citric acid cycle supplies NADH for the mitochondrial respiratory chain.^[ref]

Distinguish the location of a chemical reaction from the location of its detection. An external oxygen electrode can report consumption by an intact preparation without entering the mitochondrial matrix. That signal does not locate every intermediate, establish protein targeting or directly count newly formed ATP.

In Respiratory enzymes in oxidative phosphorylation. I. Kinetics of oxygen utilization (1955), Britton Chance and G. R. Williams examined isolated liver mitochondria in isotonic medium with substrate and inorganic phosphate. A one-millilitre optical cuvette held the suspension. A vibrating platinum electrode lay outside the light path; calibrated electric current followed dissolved oxygen, with rapid changes recorded by a galvanometer oscillograph. Air-saturated and oxygen-depleted readings checked sensitivity. Their Figure 2 shows ADP additions accelerating oxygen consumption, followed by return to slow respiration; repeated additions restored acceleration. Figure 4B compares delayed substrate addition after ADP incubation with the reverse order, supporting little unrelated ADP loss in that preparation. These comparisons support coupling to ADP utilization. The authors discuss dilution, sensitivity changes and atmospheric oxygen entry, which especially biases slow respiration. The readout did not directly measure the membrane potential or prove the later chemiosmosis mechanism.^[ref]

A control can test either the instrument or the biology. Calibrating electric current against oxygen checks the former; comparing responses before and after an ADP addition checks the latter. A valid calibration cannot by itself establish ATP formation, and a repeatable biological response cannot by itself fix an instrument's sensitivity.

NADH supplies two electrons to respiratory complex I, then ubiquinone, respiratory complex III, cytochrome c and cytochrome c oxidase; terminal oxygen reduction forms water. Succinate dehydrogenase, or respiratory complex II, supplies another entry to ubiquinone. Respiratory complex I, respiratory complex III and cytochrome c oxidase move protons outward; respiratory complex II does not.^[ref]

For an original electron balance, supply exactly $6\mu \mathrm{mol}$ of NADH to an ideal preparation with no other electron donor or competing electron acceptor. The donor supplies $12\mu \mathrm{mol}$ of electrons. Complete reduction of one oxygen molecule needs four electrons, so the corresponding oxygen consumption is $3\mu \mathrm{mol}$. Adding the two formal half-reactions makes the result explicit:The cancelling electrons determine the donor-to-oxygen ratio. These chemical equations do not count transmembrane protons or determine an ATP yield. Chemical protons consumed in water formation and transported protons have different roles in the ledger.

A mixture contains two or more chemical substances combined in proportions that need not be fixed. A chemical compound instead has a definite composition: water has two hydrogen chemical atoms per oxygen chemical atom, whereas a sucrose and water mixture can contain different sugar proportions. A homogeneous mixture has uniform composition on the scale of representative samples; a heterogeneous mixture has distinguishable regions of different composition. A chemical solution is homogeneous, whereas sand dispersed in water is a particle suspension.^[ref]

The distinction concerns the sample, not merely its ingredient list. A vessel with dissolved sodium chloride and excess undissolved sodium chloride contains a chemical solution and an ionic crystal thermodynamic phase. The liquid portion can be homogeneous while the whole vessel is heterogeneous. Similarly, molecular oxygen dissolved in water is part of a chemical solution; visible gas bubbles introduce a separate gas thermodynamic phase.

The following original model chooses piecewise constant oxygen consumption rates in a closed, well-mixed $2\mathrm{mL}$ suspension. It assumes no gas exchange, negligible addition volume, a corrected sensor and sufficient oxygen throughout. The curves are invented teaching examples, not measured traces, fitted data or a reconstruction of Figure 6.

Start at $c(0)=220\mu \mathrm{mol}{\mathrm{L}}^{-1}$. On successive one-minute intervals, choose positive slope magnitudes $5,25,5,25,6,32,1\mu \mathrm{mol}{\mathrm{L}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$. Integration gives the endpoint concentrations $220,215,190,185,160,154,122,121\mu \mathrm{mol}{\mathrm{L}}^{-1}$. This is just the recurrence $c_{i+1}=c_i-r_i\Delta t$, with $\Delta t=1\min$; the step plot shows $r_i=-dc/dt$. The trace remains above zero by construction.

During the second ADP interval, the total consumption rate isWith a stipulated mitochondrial protein mass of $0.20\mathrm{mg}$, that is $250\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}\mathrm{m}{\mathrm{g}}^{-1}$. Using a denominator twice as large would halve this reported rate without changing the raw oxygen trace. Comparisons therefore need both loading and the chosen denominator.

For a second bookkeeping check, the modeled post-antimycin A slope of $1\mu \mathrm{mol}{\mathrm{L}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$ corresponds to $2\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ background. If that background is additive and unchanged in earlier windows, subtraction gives $48$, $10$ and $62\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ for excess ADP, oligomycin and FCCP, respectively. The oligomycin-sensitive difference is $48-10=38\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$. It is a difference in oxygen consumption under the chosen interventions, not an ATP production rate. Converting it into one requires additional coupling assumptions or an independent ATP measurement; the FCCP interval shows why slope alone cannot supply that conversion.

Across the whole seven-minute example, consumption is $V(c(0)-c(7))=198\mathrm{nmol}$, also the sum of the seven interval consumptions. This equality checks the rate-to-amount accounting independently of how the intervals are named. Actual records require attention to calibration, mixing transients, background stability and decreasing oxygen availability; a line that steepens or flattens alone does not identify the cause.

Molar mass turns a weighed sample into a count of specified particles. For a pure chemical substance with specified chemical formula and isotopic abundances, its molar mass iswhere $m$ is the sample mass and $n$ its amount of substance. The SI unit is $\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$; the common laboratory unit is $\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, with $1\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}=10^{-3}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. Equal values of amount of substance correspond to equal counts of specified entities, but heavier entities give greater masses.

Combining this definition with molecular count and amount of substance givesThe Avogadro constant is exact under the modern definition of the mole. The mass $M/N_{\mathrm{A}}$ is the mean mass per specified entity; if isotopes differ within the sample, individual molecules need not all have that mean mass.^[ref]

Specify what $n$ counts: water molecules, hydrogen chemical atoms, and oxygen chemical atoms give different values of amount of substance for the same sample. For a mixture, dividing total mass by total amount of substance of its chosen entities gives a composition-dependent mean. A polymer sample can contain many chain molar masses; its number-average molar mass and weight-average molar mass answer different averaging questions. Relating either to degree of polymerization also requires a unit-mass convention and end-group accounting.

A molecular formula gives the number of chemical atoms of each chemical element in a molecule. For urea, ${\mathrm{CH}}_4{\mathrm{N}}_2\mathrm{O}$ counts one carbon, four hydrogen, two nitrogen and one oxygen chemical atom. It records composition rather than the arrangement of chemical bonds.

In the International Union of Pure and Applied Chemistry (IUPAC) mass spectrometry convention, a molecular ion is formed by removing or adding one or more electrons to a molecule without fragmentation of its molecular structure.^[ref] For example, removing one electron from intact water gives ${\mathrm{H}}_2{\mathrm{O}}^{\bullet +}$: two hydrogen and one oxygen chemical atom, total electric charge $+e$, and an unpaired electron, hence a radical cation. Atom inventory, net electric charge, and electronic state are separate pieces of information. Hydronium, ${\mathrm{H}}_3{\mathrm{O}}^{+}$, has a different inventory; it is a polyatomic ion, rather than the molecular ion obtained by electron removal from water.

The diatomic form of oxygen. Modern terrestrial abundance is maintained largely by oxygenic photosynthesis, balanced by chemical and biological sinks.

A molecule, using the International Union of Pure and Applied Chemistry (IUPAC) convention, is an electrically neutral entity containing two or more chemical atoms. Its constituents form a bound unit through chemical bonds; merely drawing a boundary around neighboring particles does not make a molecule. The neutrality requirement concerns total electric charge, not the absence of internal charge separation: water is a polar molecule with zero total electric charge.^[ref]

One water molecule, ${\mathrm{H}}_2\mathrm{O}$, contains two hydrogen and one oxygen chemical atom. One molecular oxygen molecule, ${\mathrm{O}}_2$, contains two oxygen chemical atoms; a molecule need not contain different chemical elements. One carbon dioxide molecule, $\mathrm{C}{\mathrm{O}}_2$, contains one carbon and two oxygen chemical atoms. The molecular formula records these inventories, while molecular geometry describes their arrangement. Water and carbon dioxide are chemical compounds; molecular oxygen is a form of one chemical element.

Ordinary crystalline sodium chloride, $\mathrm{NaCl}$, contains an extended arrangement of sodium cations $\mathrm{N}{\mathrm{a}}^{+}$ and chlorine anions $\mathrm{C}{\mathrm{l}}^{-}$. Its formula unit specifies one of each for compositional accounting, without selecting a unique isolated pair. Bulk neutrality therefore does not imply a material consists of neutral molecules. This statement concerns the ionic crystal; the physical state and conditions matter when deciding what particles a chemical formula represents.^[ref]

A polyatomic ion is a charged bound group of chemical atoms, such as hydronium, ${\mathrm{H}}_3{\mathrm{O}}^{+}$. A molecular ion formed by removing an electron from intact water, ${\mathrm{H}}_2{\mathrm{O}}^{\bullet +}$, retains the same atom inventory but has net electric charge $+e$. Neither satisfies the neutral-molecule definition. Distinguishing these entities makes molecular count and amount of substance and mass spectrometry interpretable: say whether the count is of chemical atoms, neutral molecules, ions, or formula units.

The useful surprise is that a molecule can be treated as one particle for motion and counting while retaining internal structure. Its molar mass connects a particle inventory to bulk mass; molecular rotation and molecular vibration reveal internal organization. The continuum approximation uses bulk fields in place of individual molecular positions and motions.