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 < 1: attractions dominate (gas more compressible than ideal). Z > 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).