057 – The relationship between gas solubility and temperature

Every carbonated drink is a gas held in a liquid under pressure, and every one of them eventually goes flat. The relationship behind that everyday observation is not a curiosity: it governs how much oxygen a river can hold for its fish, how much carbon dioxide the ocean takes up from the atmosphere, how a brewery carbonates its product, how a treatment plant strips dissolved gas out of boiler feedwater before it corrodes the pipework, and why a blood-gas sample has to be kept cold on its way to the laboratory. In each case the quantity that matters is the concentration of a gas dissolved in a liquid, and two things set it: the pressure of that gas above the liquid, and the temperature of the liquid itself.

The governing relationship is Henry’s law — at equilibrium, the concentration of a dissolved gas is proportional to its partial pressure above the solution. The constant of proportionality depends strongly on temperature, and for a gas it moves in the opposite direction to most solids: warming a liquid drives dissolved gas out rather than allowing more in. The reason is that dissolving a gas releases heat, so by Le Chatelier’s principle adding heat pushes the equilibrium back towards the gas phase. In this laboratory you will hold three sealed test tubes of sparkling water at three different temperatures — one in an ice bath, one in hot water, one standing on the bench — and then remove the stoppers and time how long the effervescence lasts in each. Temperature is the only thing that differs between the tubes; the liquid, the volume and the initial pressure are identical in all three, so any difference in the result belongs to temperature alone.

Educational Goals

Familiarization with the laboratory environment

• Locate the three sealed test tubes of carbonated water, the two 1000 mL beakers, the two stands with their universal clamps and the test tube rack, and set the bench up completely before any sample is disturbed.
• Recognise that a stoppered tube of carbonated water is a pressurised container, and open it deliberately and away from the face rather than abruptly.

Construction of a controlled comparison

• Identify temperature as the single independent variable, and name the quantities deliberately held constant — the liquid, the sample volume and the initial pressure.
• Explain why the tube left on the bench is the control against which the other two are read, rather than simply a third result.

Operation of stands and universal clamps

• Assemble a stand so that a clamp holds a test tube upright and immersed over the centre of its beaker, at a depth that does not change during the run.
• Prepare an ice bath and a hot-water bath to a repeatable fill level, so that both tubes exchange heat over the same wetted area.

Observation and timing

• Agree a consistent endpoint for “effervescence has stopped” before the first stopper is removed, and apply exactly the same criterion to all three tubes.
• Record the three durations in a table beside the condition each belongs to, rather than as loose notes, so that the comparison can be read at a glance.

Application of Henry’s law

• State Henry’s law and use it to predict, before any tube is opened, which one will fizz longest and which will finish first.
• Convert a dissolved concentration into a mass of carbon dioxide in the sample and into the volume that gas would occupy at room conditions.

Thermodynamic reasoning

• Relate the sign of the enthalpy of solution to the direction in which solubility moves with temperature, and explain why gases behave oppositely to most solids.
• Use the van ’t Hoff relation to estimate how much the solubility changes over a stated temperature interval.

Critical evaluation of the evidence

• Identify what a single unreplicated trial, with no temperature measurement, can and cannot establish.
• Distinguish clearly between how much gas is dissolved and how quickly it comes back out, and recognise that a longer effervescence is consistent with either.

Protocol

1. Locate the three test tubes of carbonated water (with carbon dioxide (CO2)).
2. Fill the 1000 mL beaker with ice, then add about 500 mL of cold tap water.
3. Place the ice beaker to the right of the left support.
4. Fill the second 1000 mL beaker with about 500 mL of hot tap water.
5. Place the beaker of hot water to the right of the right-hand stand.
6. Hang a universal clamp on each stand so that they are positioned just above the center of each beaker.
7. Hang test tube 1 on the clamp of the left universal stand above the beaker containing cold water.
8. Hang test tube 2 on the clamp of the right universal stand above the beaker containing hot water.
9. Leave test tube 3 on the test tube rack at room temperature.
10. Wait 30 sec for the temperature of the samples to be cold enough or hot enough before continuing.
11. Remove the rubber stopper from test tube 3 left at room temperature and note the observed reaction (e.g., duration of effervescence).
12. Remove the rubber stopper from test tube 2 left in the hot water and note the observed reaction (e.g., duration of effervescence).
13. Remove the rubber stopper from test tube 1 left in the cold water and note the observed reaction (e.g., duration of effervescence).

Anticipated Outcomes

All three tubes hold the same sparkling water, sealed under the same carbon dioxide pressure of about 150 kPa, and differ only in the temperature of the bath they have been standing in. When the stoppers come off, all three effervesce, but they do not effervesce for the same length of time. The tube from the ice bath fizzes longest, the tube from the bench is intermediate, and the tube from the hot water finishes first. These are the durations the simulation records:

Henry’s law sets how much gas is there. At equilibrium the concentration of a dissolved gas is proportional to its partial pressure above the liquid: C = k_H × P. For carbon dioxide in water at 20 °C, k_H = 0.039 mol L⁻¹ bar⁻¹, and the tubes are sealed at 150 kPa = 1.50 bar, so C = 0.039 × 1.50 = 0.059 mol/L. Multiplied by the molar mass of 44.01 g/mol, that is 2.6 g of carbon dioxide in every litre of the water — a concentration typical of a lightly carbonated mineral water and about seventy times what water in contact with ordinary air would hold.

Temperature moves the constant, and the van ’t Hoff relation says by how much. Dissolving carbon dioxide is exothermic, with ΔH_soln ≈ −20 kJ/mol, so the Henry constant falls as the liquid warms: ln(k₂/k₁) = −(ΔH_soln/R)(1/T₂ − 1/T₁), where −ΔH_soln/R = 20 000 / 8.314 = 2400 K. Going from 20 °C to 40 °C: ln(k₂/k₁) = 2400 × (1/313 − 1/293) = 2400 × (−2.18 × 10⁻⁴) = −0.52, so k₂/k₁ = e^−0.52 = 0.59. A twenty-degree rise costs the water about 41 % of its capacity to hold the gas. Cooling from 20 °C to 2 °C works the other way and raises it by 71 %.

Applying that correction at each of the three bath temperatures gives the amount of dissolved gas each tube starts with, and hence the volume that has to escape before the fizzing can stop:

The two tables agree in direction and very nearly in size. The predicted dissolved amounts stand in the ratio 2.9 : 1.7 : 1.0 from cold to hot, and the measured durations in the ratio 2.2 : 1.4 : 1.0. The ordering is reproduced exactly, and the durations are compressed relative to the amounts, which is what should happen: the warmer tube not only holds less gas, it also gives up what it holds more quickly, so its shorter run time is doing double duty. Worked the other way, the numbers also say that a 20 mL sample straight out of the ice bath releases about 48 mL of gas — nearly two and a half times the volume of the liquid it came from — in 42 seconds.

Why the cold tube holds more but the hot tube empties faster. Two separate physical arguments are at work and it is worth keeping them apart. The first is thermodynamic and answers how much: a gas molecule in solution sits in a favourable, slightly ordered arrangement of water molecules, and warming the liquid gives it enough thermal energy to leave that arrangement, which is exactly what the negative ΔH_soln expresses. The second is kinetic and answers how fast: once the stopper is off, the dissolved gas must diffuse to a bubble or to the surface, and the diffusion coefficient scales roughly as D ∝ T/η (the Stokes–Einstein form). Water’s viscosity falls from 1.67 mPa·s at 2 °C to 1.00 at 20 °C and 0.65 at 40 °C, so T/η runs 165, 293 and 482 — carbon dioxide diffuses about 2.9 times faster through the hot sample than through the ice-cold one. Both effects shorten the hot tube’s effervescence, which is why the experiment gives such a clean ordering, and also why one trial cannot tell you which of the two dominates.

The dissolved gas is also an acid, which gives a second way to see it. Carbon dioxide reacts with water: CO₂(aq) + H₂O ⇌ H₂CO₃ ⇌ H₃O⁺ + HCO₃⁻. Only about 0.2 % of the dissolved gas is genuinely present as carbonic acid, so the composite constant K_a1 = 4.5 × 10⁻⁷ already accounts for that. For the room-temperature tube, [H₃O⁺] = √(K_a1 × C) = √(4.5 × 10⁻⁷ × 0.059) = 1.6 × 10⁻⁴ mol/L, giving pH 3.8 — and the same calculation gives pH 3.7 for the cold tube and pH 3.9 for the hot one. Sparkling water is a genuine acid with no acid added to it, and if this laboratory is run alongside 046 or 048 a pH meter dipped into each tube before and after opening makes the loss of gas visible as a rise in pH of about half a unit.

Where this matters outside the tube. Oxygen behaves the same way as carbon dioxide, and the numbers are stark: fresh water in contact with air holds 14.6 mg/L of dissolved oxygen at 0 °C, 9.1 mg/L at 20 °C and 7.6 mg/L at 30 °C. A river warmed by five degrees, whether by a summer heatwave or by cooling water returned from a power station, loses roughly 9 % of its oxygen at the same moment that the metabolic demand of the fish living in it rises. The ocean absorbs carbon dioxide by the same law, so a warming ocean is a weaker sink for it; a can of soft drink left in a warm car loses its fizz for precisely the reason tube 2 finishes first.

Summary of Assignment by Grade Range

Grade 9–10

Focus: Observing that temperature changes how much gas a liquid can hold, and describing it in the right vocabulary.

Activities: Write down a prediction, before any stopper is removed, of which tube will fizz longest and why. Time each tube against an agreed endpoint and record the three durations in a table with the condition written beside each one. State the finding as a single sentence of the form “the colder the water, the longer the gas stays dissolved”. List what was kept the same in all three tubes and explain why that matters. Name two everyday situations that depend on this behaviour, such as a warm soft drink going flat faster than a cold one, or fish moving to deeper water in a heatwave.

Grade 11

Focus: Quantitative treatment with Henry’s law.

Activities: Write C = k_H × P and use it to calculate the dissolved concentration at room temperature from the stated 150 kPa. Convert that concentration into a mass of carbon dioxide in a 20 mL sample and into the volume the gas would occupy at 101 kPa and 20 °C. Compare the ratio of the three measured durations (2.2 : 1.4 : 1.0) with the ratio of the predicted dissolved amounts (2.9 : 1.7 : 1.0), and account for the fact that the durations are the more compressed of the two. Explain, using Le Chatelier’s principle and an exothermic dissolution, why the direction of the temperature effect for a gas is the opposite of what most solids show — and contrast this directly with laboratory 039, where warming the water dissolves more solid.

Grade 12 / College Level

Focus: Derivation, error analysis and independent interpretation.

Activities: Derive the van ’t Hoff form of the temperature dependence and use ΔH_soln = −20 kJ/mol to compute the ratio of Henry constants across a stated interval, showing the substitution in full. Estimate the pH of each tube from K_a1 and explain why sparkling water is an acid although no acid was added to it. Separate the thermodynamic factor from the kinetic one and design a measurement that would isolate them — weighing each tube before and after opening is the obvious candidate — then state what result would distinguish the two. Evaluate the experiment’s weakest point, that no temperature is measured, and specify the instrument, the placement and the waiting time that would fix it. Finally, use published dissolved-oxygen solubilities to estimate the effect of a 5 °C warming on a river and discuss the consequences for the organisms living in it.

Laboratory essentials

Instruments

• Test tubes (3), each holding about 20 mL of carbonated water
• Rubber stoppers (3), one sealing each test tube
• Beakers, 1000 mL (2) — one for the ice bath and one for the hot-water bath, each filled to about 500 mL
• Laboratory stands (2)
• Universal clamps (2), one on each stand
• Test tube rack (holds tube 3 at room temperature)
• Timer or stopwatch, to record the duration of the effervescence

Products

• Carbonated water (CO₂ at about 150 kPa above the liquid), in three sealed test tubes
• Ice
• Cold tap water (about 500 mL)
• Hot tap water (about 500 mL)