= Solution
\b[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: \b[one volume of <carbon dioxide> with two volumes of <air> extinguished the introduced taper in the apparatus used.] Thus
$$
\boxed{x_{\mathrm{CO_2}}=\frac{V_{\mathrm{CO_2}}}{V_{\mathrm{CO_2}}+V_{\mathrm{air}}}=\frac13\approx 33\% \text{ by volume.}}
$$
This 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.<The True Position of Oxygen as a Restorative in Carbonic Acid Poisoning by W. Ernest Thomson>[p. 36, Experiment XLVIII (Physical Experiment), especially preparation (2)]{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>:
$$
\boxed{\mathrm{CaCO_3(s)+2HCl(aq)\longrightarrow CaCl_2(aq)+CO_2(g)+H_2O(l).}}
$$
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.<Fire stopper by the Royal Society of Chemistry>[Teaching goal, calcium carbonate–hydrochloric acid preparation and equation]{ref} A separate sample may be checked with <limewater>:
$$
\mathrm{CO_2(g)+Ca(OH)_2(aq)\longrightarrow CaCO_3(s)+H_2O(l)}.
$$
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, report
$$
\boxed{x_b<x_{\mathrm{ext}}\leq x_e.}
$$
A 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 gives
$$
\boxed{y_{\mathrm{O_2}}=(1-x)y_{\mathrm{O_2},0}.}
$$
Taking dry <air> to have $y_{\mathrm{O_2},0}=0.2095$ is an explicit model input. For the documented one-third mixture, this gives $y_{\mathrm{O_2}}\approx0.140$, 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 $r=V_{\mathrm{CO_2}}/V_{\mathrm{air}}$ 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.<Carbon Dioxide as a Fire Suppressant: Examining the Risks by the United States Environmental Protection Agency>[Extinguishing Mechanism of Carbon Dioxide]{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.<Changes of CO2 Concentration and Heat Illustrate Why the Flame Is Extinguished in the Candle-and-Cylinder Experiment>[Abstract, sensor measurements at different heights and remaining oxygen]{ref} A pouring demonstration with unmixed <carbon dioxide> likewise does not determine a uniform bulk fraction. \b[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.]
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