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A simple motivating comparison is visible gas evolution from hydrogen peroxide, whose net chemical equation isThe products are water and oxygen. The Royal Society of Chemistry's teaching resource uses small test tubes and droppers, hydrogen peroxide labelled 5–10 volumes, solutions of metal salts including copper(II) sulfate, and approximately $1\mathrm{mol}{\mathrm{L}}^{-1}$ sodium hydroxide. Its qualitative procedure tests additions singly and in pairs to tubes containing about $1\mathrm{cm}$ depth of hydrogen peroxide. It reports the expected classroom result that the additions individually are not effective under those conditions, whereas the solids produced by mixing metal-salt solution with sodium hydroxide give effective heterogeneous catalysis. This is the resource's expected observation, not a newly measured ranking.^[ref]

A focused adaptation compares four matched tubes: no addition, copper(II) sulfate alone, sodium hydroxide alone, and the pair. Use equal initial hydrogen peroxide amounts, identical tubes and the same starting temperature. Record stock concentrations and added volumes; add water to the other tubes to match the total added liquid. Additions can first be checked without hydrogen peroxide to distinguish precipitation from gas evolution. Start a timer at contact, mix consistently, and observe gas evolution over the same interval. These matching controls are proposed improvements to the qualitative resource, not claimed details of its original trials. Follow its supervised chemical-handling requirements; the stated strengths describe its teaching protocol rather than an unrestricted recipe.

The immediate readout is relative bubbling, together with whether a solid appears. More vigorous bubbling in the paired tube supports faster conversion under the comparison conditions; it does not identify the solid's exact composition or establish a unique reaction mechanism. Bubble counts are not a calibrated reaction rate: bubble sizes, gas retention and warming can differ. For a quantitative extension, use a freely moving gas syringe to record collected volume $V(t)$ and compare early slopes $dV/dt$ at matched temperature and pressure; check for leaks and repeat runs. This extension is a measurement proposal, not source-reported gas traces.

The paired treatment also changes pH and produces a surface, so the four tubes alone cannot assign the whole effect to one microscopic catalytic step. A filtered-liquid comparison and a separated, washed-solid comparison would help distinguish dissolved and solid contributions, although washing itself can change the active material. More gas at one time establishes neither a changed equilibrium constant nor indefinite catalyst reuse. The open gas-evolution experiment is especially unsuitable as a demonstration that two closed mixtures reach the same chemical equilibrium: the escaping oxygen changes the constraints. The reversible model above supplies that separate explanation. No numerical experimental rate constants, barrier heights or gas volumes are asserted here.

A gas syringe traps a gas in a graduated barrel with a movable plunger, allowing its volume to be varied and read. In an isothermal gas syringe experiment, the relevant total volume also includes any connected tubing and sensor cavity containing the same gas.

In a gas syringe, the graduated barrel reading $V_{\mathrm{read}}$ can omit a fixed connecting or sensor volume $V_d$ occupied by the same sealed gas. For a common settled temperature, Boyle's law then requiresThis second relation makes a graph of $1/p$ against $V_{\mathrm{read}}$ a straight line; its intercept divided by its slope estimates $V_d$ under these assumptions. Unequal temperatures between the barrel and the connecting space require a different correction, analogous to the gas thermometer dead-space correction.

For an original hypothetical example, let $V_d=1\mathrm{c}{\mathrm{m}}^3$, $V_{\mathrm{read},1}=20\mathrm{c}{\mathrm{m}}^3$, $p_1=100\mathrm{kPa}$, and $V_{\mathrm{read},2}=10\mathrm{c}{\mathrm{m}}^3$. The total volume falls from $21$ to $11\mathrm{c}{\mathrm{m}}^3$, so $p_2=100(21/11)\mathrm{kPa}\approx 190.91\mathrm{kPa}$, rather than $200\mathrm{kPa}$. The omitted volume makes the total compression ratio smaller than the barrel-reading ratio. These stipulated values are independent of the manufacturer's apparatus correction and are not measurements.

Vernier's Boyle's Law: Pressure-Volume Relationship in Gases, Experiment 6 of Chemistry with Vernier, specifies a graduated $20\mathrm{mL}$ gas syringe, a pressure sensor and LabQuest recording. Preparation sets the disconnected syringe to $10.0\mathrm{mL}$, then attaches it to the sensor valve, trapping air. At several plunger positions, the displayed pressure is allowed to stabilize before the paired volume is entered. The analysis tests whether $pV$ remains approximately constant. It adds $0.8\mathrm{mL}$ to each syringe reading for the sensor's internal volume; this correction belongs to that apparatus. The worksheet supplies a blank results table, not measured values.^[ref]

The manufacturer's Gas Pressure Sensor User Manual identifies a membrane sensor referenced to a vacuum, hence an absolute pressure readout. Its calibration section uses the actual local atmospheric pressure for an ambient reference check, rather than a weather report corrected to sea level. Checking this baseline before sealing separates an offset error from compression physics.^[ref]

Additional controls follow from the model. Keep the same sealed amount of substance, connections and ambient temperature; persistent pressure drift at held volume after thermal equilibrium suggests a leak or another uncontrolled change. Small steps and waiting allow compression heat to leave the gas; avoiding hand warming reduces another heat input. Compare settled readings when approaching a position from either direction. Plunger friction affects the applied force and position reproducibility, so record actual pressure and actual plunger position rather than predicting pressure from the load. These are proposed controls, not reported experimental outcomes.

Nearly constant $pV$ across equilibrated states supports the fixed-temperature ideal gas approximation over the tested range. Stabilized pressure alone does not demonstrate uniform or constant temperature; the isothermal gas syringe experiment adds a temperature readout to distinguish a transient from its cooled endpoint. Finite sensor accuracy and uncertain total volume limit the test, and agreement does not establish ideal behavior at every pressure. Repeated return readings help distinguish reproducibility from a one-direction trend.

A gas syringe makes the distinction between a constant-temperature path and equal-temperature endpoints observable. The Ideal Gas Law Apparatus (TD-8596A), Instruction Manual 012-08420B by PASCO scientific specifies a TD-8596A gas syringe with a mechanical stop, an internal thermistor, an attached pressure sensor and data acquisition. Record the stop volume with the coupling disconnected, then set $40\mathrm{mL}$ and seal the coupling. Record pressure and temperature, compress quickly to the stop near $20\mathrm{mL}$, and hold until both readouts settle. The manual gives roughly $30\mathrm{s}$ for settling and about $0.5\mathrm{s}$ for the thermistor response. Releasing the plunger gives a second transient and a final volume to record.^[ref]

The manual describes a pressure overshoot and temperature rise during rapid compression, followed by cooling at the held volume; the settled pressure remains higher than initially. This illustrates approximately adiabatic compression followed by heat rejection, rather than an isothermal compression throughout. Use the settled initial and compressed readings to test Boyle's law, correcting both syringe readings by the unmarked tubing volume $V_d$:Use absolute pressure, not gauge pressure. A transient comparison of $pV/T$ must pair simultaneous pressure and temperature readings: the sensor lag can separate their peaks.^[ref]

For an additional test of the path, repeat with small compression steps, wait for stable temperature and pressure at every step, and repeat in reverse. Keep the sealed amount of substance, connecting tubing and ambient temperature fixed; prevent hand warming of the barrel and check for leaks by watching for continued pressure drift at held volume after thermal equilibrium. These are proposed controls, rather than reported measurements. Agreement of equilibrated points with Boyle's law supports the fixed-temperature ideal gas law approximation, but does not prove that the rapid segments between them were isothermal processes. A single local temperature sensor can miss temperature gradients; plunger friction can produce direction-dependent readings. The pressure and volume data estimate reversible work only insofar as the path approaches a reversible thermodynamic process; they do not directly measure heat. After motion stops, cooling at fixed volume has zero boundary work and $Q=\Delta U<0$, even though the complete equal-endpoint-temperature ideal gas run has $\Delta U=0$.

TODO: Solid substance g is an unidentified supplied specimen. Without its identity or relevant observations, the particular gas and conditions for obtaining it cannot be determined.

Neither the gas nor the conditions required to obtain it from g can be identified. The word “fixed” does not supply a chemical formula, and the existence of a labelled solid does not establish that it is a carbonate or any other particular chemical compound.

A defensible investigation would first characterise g and distinguish physical release of an absorbed gas from a chemical reaction that produces a new gas. Whether heating, contact with a solvent, or a selected reagent is relevant depends on that characterisation. An arbitrary thermal decomposition equation would therefore assume the very composition that is missing.

If an identified reaction produced a gas, the apparatus would be chosen for its actual properties: a reaction vessel and delivery system, a means of distinguishing the product from initially enclosed air, and a compatible collection or detection method. Collection over water would be unsuitable when dissolution or reaction with water materially changes the product; a gas syringe is an alternative only when compatible with the substances and conditions. The gas would then require discriminating chemical tests, and the residue could help check the proposed reaction. No evolution, odour, combustion behaviour, precipitation result or residue is reported for g, so none of those observations can be supplied as its answer.

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.