Real vs ideal gases

Clinical relevance in anaesthesia

• Most anaesthetic gases behave nearly ideally at typical theatre pressures and temperatures, but deviations matter when pressure is high, temperature is low, or near condensation/critical point.
  • Examples: compressed gas cylinders, pipeline pressures, CO2 absorbent canisters (heat), cryogenic storage, nitrous oxide near its critical temperature.
• Understanding real gas behaviour helps explain: cylinder contents/pressure relationships, Joule–Thomson cooling/heating, why N2O cylinder pressure stays ~constant until near empty (two-phase behaviour), and why ideal gas assumptions can fail for CO2 at high pressures.
• Measurement devices (flowmeters, spirometers, gas analysers) often assume ideal behaviour, errors increase with humidity, high pressure, and non-ideal mixtures.

Ideal gas: definition and key equations

• An ideal gas is a theoretical gas in which molecules have negligible volume, no intermolecular forces, and collisions are perfectly elastic.
• Equation of state: PV = nRT (or PV = NkT).
  • R = 8.314 J·mol⁻¹·K⁻¹, k = 1.38×10⁻²³ J·K⁻¹, n = moles, N = number of molecules.
• Ideal gas laws derived from PV=nRT: Boyle (P∝1/V at constant T), Charles (V∝T at constant P), Gay-Lussac (P∝T at constant V), Avogadro (V∝n at constant P,T).
• For an ideal gas, internal energy depends only on temperature: U = U(T) (no potential energy from intermolecular forces).

Real gases: why they deviate

• Real gases deviate because molecules have finite volume and experience intermolecular forces (attractive at moderate distances, repulsive at very short distances).
• Deviations become important when molecular spacing decreases: high pressure, low temperature, and near the critical point (where gas and liquid phases become indistinguishable).
• At moderate pressures, attractive forces reduce measured pressure vs ideal (molecules pulled back from the wall). At very high pressures, finite molecular volume/repulsion increases pressure vs ideal.

Compressibility factor (Z): quick way to express non-ideality

• Define Z = PV/(nRT). Ideal gas: Z = 1.
• Z &lt, 1: attractions dominate (gas more compressible than ideal). Z &gt, 1: repulsions/finite volume dominate (less compressible).
• Z approaches 1 at low pressure and high temperature for most gases.

Van der Waals equation (common FRCA model for real gases)

• One real-gas equation of state: (P + a(n/V)²)(V − nb) = nRT.
• Meaning of constants:
  • a corrects for intermolecular attractions (reduces effective pressure). Larger a → stronger attractions.
  • b corrects for finite molecular volume (reduces free volume). Larger b → bigger molecules/excluded volume.
• Interpretation: measured pressure is increased by adding a(n/V)² (because attractions made the measured P too low), available volume is reduced by nb.

Critical point and reduced variables (high-yield concepts)

• Critical point: defined by critical temperature (Tc) and critical pressure (Pc), above Tc, a gas cannot be liquefied by pressure alone.
• Reduced temperature and pressure: Tr = T/Tc, Pr = P/Pc. Many gases show similar behaviour when compared at the same Tr and Pr (principle of corresponding states).
• Anaesthetic relevance: N2O has Tc close to room temperature, so it readily exists as a liquid–vapour mixture in cylinders at room temperature, O2 and air have much lower Tc so are stored as compressed gases at room temperature.

Dalton’s law and mixtures: ideal vs real

• For ideal gases: total pressure = sum of partial pressures (Dalton) and each component obeys PV=nRT independently.
• Real gas mixtures can deviate due to interactions between different molecules, at typical anaesthetic conditions these deviations are usually small but can matter at high pressures (e.g., hyperbaric medicine).

Joule–Thomson effect: real-gas hallmark

• Joule–Thomson coefficient μJT = (∂T/∂P)H. For an ideal gas, μJT = 0 (no temperature change on throttling at constant enthalpy).
• Real gases: throttling (pressure drop through a valve) can cause cooling or heating depending on temperature relative to the inversion temperature.
• Clinical link: cylinder regulators and pipeline pressure reduction can cause cooling, risk of regulator icing is greater with gases showing significant JT cooling at ambient temperatures.

Practical anaesthetic examples

• N2O cylinder: pressure reflects saturated vapour pressure while liquid is present (temperature dependent), not ideal-gas PV behaviour, mass/contents estimation requires weighing or using known liquid volume relationships.
• O2/air cylinders: largely compressed gas at room temperature, pressure falls approximately proportionally with contents (closer to ideal behaviour), though still not perfectly ideal at high pressures.
• CO2: more non-ideal than O2/N2 at higher pressures, relevant to insufflation systems and high-pressure storage/transport (less common in theatre but examinable).

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