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A condition-dependent carbon dioxide fraction at which a specified candle flame is extinguished in a specified protocol. Distinguish a demonstrated sufficient fraction from the least sufficient fraction.

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.

The wick supplies liquid wax by capillary action; wax vapour reacts with atmospheric oxygen, releasing the heat that keeps the supply going. The wick is a delivery system, rather than the principal fuel.

First, an external flame warms the wick and adjacent wax. Melting produces a small liquid reservoir, and capillary action draws it into the spaces between the wick fibres. Near the hot tip, evaporation and some pyrolysis supply gaseous fuel. Melting and evaporation are physical changes; pyrolysis and combustion change the chemical substances present. Once established, the candle flame transfers enough heat back to the wax to maintain this sequence.^[ref]

The candle flame is a diffusion flame. Its relatively dark inner region contains newly supplied fuel with limited access to oxygen. In the yellow luminous region, incomplete conversion of the hydrocarbons produces small soot particles, which become incandescent. Farther out, mixing supplies enough oxygen to consume most of the remaining fuel, carbon monoxide and soot. Thus the yellow light is largely thermal emission from hot particles, rather than a yellow gas.^[ref]

For a representative alkane component of paraffin wax, complete combustion has the chemical equationReal candle materials are mixtures, and some, such as fatty materials, already contain oxygen; the displayed chemical equation is an illustrative wax model. The principal products of complete combustion are carbon dioxide and water vapour. Convection carries the hot gases upward and brings fresh air into the flame. A cold collector can reveal condensed water; collecting the gases and passing them into limewater gives a calcium carbonate cloudiness from carbon dioxide.

Removing the oxygen supply, cooling the reaction zone, or cutting off wax delivery extinguishes the flame. The smoking wick immediately afterwards can still emit combustible vapour; without sufficient heat at the mixing zone, that vapour need not sustain a flame.

A controlled test in which a taper is exposed to a specified gas mixture to determine whether its candle flame persists under a fixed protocol. The result depends on composition, flow, time, taper and thermal conditions; it is not a general test of whether the gas can safely be breathed.