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A diprotic acid can donate two protons per molecule through successive acid-base steps. The name counts ionizable protons in the stated chemistry, rather than all hydrogen atoms in a molecular formula. The intermediate after the first loss is itself able to act as an acid in the second step. Carbonic acid and sulfuric acid provide examples with different dissociation strengths.^[ref]

For ${\mathrm{H}}_2\mathrm{A}$ in water, write the equilibria as ${\mathrm{H}}_2\mathrm{A}\rightleftharpoons {\mathrm{H}}^{+}+\mathrm{H}{\mathrm{A}}^{-}$ and $\mathrm{H}{\mathrm{A}}^{-}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{2-}$, suppressing the explicit water/hydronium notation. There are two acid dissociation constants, $K_1$ and $K_2$. In an ideal dilute approximation let $h$ be hydrogen-ion concentration divided by the standard concentration, soSquare brackets denote concentrations. With total acid concentration $C_T=[{\mathrm{H}}_2\mathrm{A}]+[\mathrm{H}{\mathrm{A}}^{-}]+[{\mathrm{A}}^{2-}]$, the fractions in the three forms areTheir sum is one by construction; this is a species balance, not a claim that every molecule has already released both protons.

For illustrative constants $K_1=10^{-3}$ and $K_2=10^{-6}$, a maintained $h=10^{-4}$ gives fractions approximately $(0.0901,0.9009,0.00901)$. The singly deprotonated form dominates in this chosen regime. These are stipulated parameters, not measured constants for the named example acids.

If the acid is placed in initially pure water, $h$ is generally unknown: species balance must be combined with charge neutrality, water ionization and any other ions. Holding pH fixed, as in the example, is a different boundary condition. Likewise, two available protons do not imply two resolved features in every acid-base titration: the separation of the two dissociation steps and the experimental conditions determine how distinguishable they are.

The product is carbonic acid, $\mathrm{HO}-\mathrm{C}(=\mathrm{O})-\mathrm{OH}$. The oxygen lone pair Homo of water donates into the carbon-centred component of the carbon dioxide ${\pi }^{\ast }$ LUMO. Draw an electron-pair arrow from the water oxygen to carbon and a second from one C=O pi bond onto its oxygen:The first step bends the original linear electrophile and gives carbon three oxygen neighbours; carbon is approximately trigonal planar in the resulting carbonate framework. Proton transfer from the oxonium oxygen to the negatively charged oxygen produces the neutral acid. In real water, solvent molecules relay that proton rather than requiring a strained isolated intramolecular transfer. The forward mechanism does not assert that most dissolved carbon dioxide is present as carbonic acid at equilibrium.

Prepare carbon dioxide, make measured mixtures with air, and test a standardized lighted taper in fresh mixtures to find an extinction boundary. In this taper extinction experiment, “carbonic acid gas” means gaseous carbon dioxide, not liquid carbonic acid. The proportion should be reported as a fraction of the final mixture, with the conditions of the test.

A documented sufficient mixture is available from a later first-hand experiment: one volume of carbon dioxide with two volumes of air extinguished the introduced taper in the apparatus used. ThusThis is a conditional literature result, not an invented observation from the Oxford examination. In The True Position of Oxygen as a Restorative in Carbonic Acid Poisoning by W. Ernest Thomson, Experiment XLVIII directly compares one-third carbon dioxide mixed with two-thirds oxygen and with two-thirds air; the latter extinguished the taper. The experiment was published in 1894, so it supplies a later physical comparison rather than evidence of what the 1866 candidate measured.^[ref]

The question asks for an approximately sufficient proportion; it does not explicitly require a universal minimum. The cited condition supplies one sufficient point. To find approximately the least sufficient proportion for the proposed apparatus, determine the lower boundary by the following procedure instead of treating one-third as that boundary.

Prepare the carbon dioxide in a small gas-generating flask by adding dilute hydrochloric acid to calcium carbonate:Fit a delivery tube, keep the outlet unobstructed, and discard the first gas while the original air is being displaced from the apparatus. A wash bottle and droplet trap can reduce acid carry-over before collection in a freely moving gas syringe or suitable gas holder. This acid-carbonate preparation is also used in a current Royal Society of Chemistry demonstration.^[ref] A separate sample may be checked with limewater:The turbidity is a qualitative check for carbon dioxide; it is not a measurement of the fraction in the flame-testing mixture. Avoid using a water-filled collecting vessel for the quantitative mixing stage without allowing for dissolved carbon dioxide and water vapour.

For the mixing stage, use two calibrated gas syringes and a closed mixing vessel with a means of transferring the mixture into a larger flame-testing jar. Measure the component gas volumes at the same temperature and pressure. Mix the gases thoroughly before the flame test. If the gases behave approximately as an ideal gas mixture, their measured volume fractions then approximate their mole fractions. For example, an intended one-third mixture can be prepared from one measured portion of carbon dioxide and twice that volume of air. These are preparation instructions, not recorded trial outcomes.

Keep the taper's material, exposed wick, initial candle flame, insertion depth, gas volume and test duration fixed. Give the flame a reproducible exposure, using a gas-filled jar and a narrow insertion opening with a loose collar to limit entry of fresh air. The observation period must be specified before testing; a fixed five-second exposure is one possible chosen protocol, not a reported condition of the historical reference experiment. Use a large mixture volume relative to the small taper, introduce it briefly, and use a fresh mixture for every trial; prolonged burning changes the mixture by consuming oxygen and producing carbon dioxide and water vapour. Do not seal a burning vessel into an improvised pressure-tight apparatus.

Start with an air control that sustains the taper. Test successively richer, separately prepared carbon dioxide mixtures until extinction occurs within the specified observation period. Retest with a less rich mixture and subdivide the interval. Repeat mixtures near the boundary to detect inconsistent results. A completed experiment would report, for example, the greatest tested fraction $x_b$ at which burning consistently persists and the smallest tested fraction $x_e$ that consistently extinguishes the taper. If the responses are ordered and reproducible under the fixed protocol, reportA midpoint and half-interval may describe the resolution of that bracket; they are not a statistical confidence interval. No numerical values of $x_b$ or $x_e$ are supplied by the source, and none are asserted here.

For a useful model check, let $y_{{\mathrm{O}}_2,0}$ denote the initial oxygen fraction in air, and let $x$ denote the fraction of added pure carbon dioxide in the final mixture. Before the taper changes the gas, an ideal, uniformly mixed replacement model givesTaking dry air to have $y_{{\mathrm{O}}_2,0}=0.2095$ is an explicit model input. For the documented one-third mixture, this gives $y_{{\mathrm{O}}_2}\approx 0.140$, or about $14\%$ oxygen. It is a calculation from an assumed starting composition, not a measured oxygen analysis or a general extinction rule. Also distinguish a fraction of the final mixture from an addition relative to the original air: the volume ratio $r=V_{\mathrm{C}{\mathrm{O}}_2}/V_{\mathrm{air}}$ satisfies $x=r/(1+r)$, so a 1:2 addition ratio means $x=1/3$, not $x=1/2$.

Carbon dioxide affects the thermal balance of a diffusion flame as well as the oxidizer fraction. Extinction therefore depends on the taper, mixing, gas flow, temperature, pressure and heat loss; an oxygen-dilution calculation alone cannot predict its value. The official account of carbon dioxide suppression describes its predominantly thermophysical action.^[ref]

Finally, distinguish this experiment from covering a burning candle and waiting for it to go out. That procedure simultaneously changes gas composition, temperature and spatial distribution. A modern experimental study using gas and temperature sensors found different conditions at different heights and extinction before all oxygen was consumed.^[ref] A pouring demonstration with unmixed carbon dioxide likewise does not determine a uniform bulk fraction. A sufficient, condition-labelled literature mixture and a reproducible bracketing procedure answer the available task; an actual examination threshold or a universal minimum is not claimed.