Amagat (amg): Number Density Benchmark for Gas Mixtures

The amagat (amg) expresses gas number density relative to an ideal gas at standard temperature and pressure (STP). One amg equals 2.686 781 1 × 10²⁵ molecules per cubic metre under 1 atm and 273.15 K. By scaling densities to this reference, scientists and engineers compare laboratory and atmospheric conditions without repeatedly converting units.

Combine this resource with the amount-of-substance guide and the kelvin explainer to integrate amagat-based reasoning into thermodynamic calculations.

Definition, Equations of State, and Conversions

Relating amagat to number density and pressure

Number density n (m⁻³) relates to amagat value f via n = f × n₀, where n₀ equals the Loschmidt constant under the chosen reference conditions. For the conventional amagat, n₀ = 2.686 781 1 × 10²⁵ m⁻³. Using the ideal gas law p = n k_B T, amagat values translate to pressure through p = f n₀ k_B T. Alternatively, using molar quantities, f equals the ratio of molar volume at STP (22.414 L·mol⁻¹) to the actual molar volume.

Specifying reference conditions across disciplines

While amgat notation predates modern SI conventions, ISO 80000 recognises its continued use in aeronomy and gas discharge physics. Some fields adopt modified reference conditions—such as 288.15 K and 101.325 kPa for atmospheric science—so practitioners must specify the standard used when quoting amg values.

Historical Background and Persistence in Modern Practice

Émile Amagat’s experiments and adoption

Émile Amagat investigated gas compressibility in the late 19th century, devising the amagat scale to compare real gas behaviour with ideal predictions. His work predated widespread adoption of the pascal and the mole, yet the convenience of expressing densities as multiples of a reference persisted. Early aeronomy papers, glow discharge studies, and spectroscopy research all employed amg to normalise results across laboratories.

Persistence across aeronomy and plasma physics

Even after the 1971 SI adoption of the mole and subsequent updates, the amagat remained entrenched in fields where number density directly influences phenomena. Plasma physicists describe collisional frequencies using amg, while atmospheric chemists express constituent densities and airglow intensities in the same unit to simplify modelling equations.

Conceptual Foundations: Mixtures, Partial Amagat Values, and Non-Ideal Corrections

Partial amagat bookkeeping for mixtures

Gas mixtures allocate amg values proportionally to mole fractions. If dry air registers 1.00 amg at STP, nitrogen contributes about 0.78 amg and oxygen 0.21 amg. Adding trace gases or adjusting humidity simply modifies partial amg contributions, enabling straightforward bookkeeping in atmospheric models and laboratory setups.

Accounting for non-ideal behaviour with compressibility

Non-ideal behaviour introduces deviations captured by virial equations of state or compressibility factors Z. The effective amg becomes f_eff = p/(Z p₀) × (T₀/T), where subscript 0 indicates reference conditions. High-pressure gas lasers and shock tube experiments routinely correct amg values using measured or tabulated Z factors to maintain accuracy.

Measurement Techniques and Calibration

Pressure–temperature measurements for amg

Number density can be inferred from pressure and temperature measurements using calibrated transducers and platinum resistance thermometers. For low-density regimes, optical methods such as interferometry, Rayleigh scattering, or cavity ring-down spectroscopy determine amg values by correlating refractive index changes with number density. Mass spectrometers and residual gas analysers provide composition data that, combined with total density, yield partial amg values.

Optical diagnostics and composition analysis

Calibration traceability stems from SI pressure and temperature standards. Gas-handling systems use piston gauges, capacitance diaphragm gauges, or quartz crystal resonators to validate pressure, while standard thermometers confirm temperature. Uncertainty budgets consider sensor drift, gas purity, and thermal gradients. The molar volume calculator assists in propagating uncertainties between molar quantities and amg.

Applications: Aeronomy, Plasma Physics, and Spectroscopy

Atmospheric science and aeronomy workflows

Atmospheric scientists use amg to describe constituent profiles in the upper atmosphere, where densities vary across orders of magnitude. Airglow intensity equations and photochemical models incorporate amg to relate reaction rates, aligning with the rayleigh unit for emission brightness.

Plasma engineering and spectroscopy calibration

Plasma engineers specify gas fills for discharge tubes and tokamak neutral beams in amg to ensure reproducible particle densities. Laser spectroscopy experiments quote buffer gas densities in amg to standardise collisional broadening data. In gas metrology, amg-based comparisons help reconcile laboratory reference cells before transferring results into SI molar density units.

Importance for Communication, Modelling, and Standards

Communicating gas density with a common scale

The amgat simplifies communication between disciplines by providing an intuitive scale anchored to familiar atmospheric conditions. Researchers can exchange data without recalculating absolute densities, reducing transcription errors and ensuring compatibility across modelling software.

Standards and mission requirements anchored to amg

Standards organisations recognise the amg’s role in documentation. NASA and ESA mission requirements frequently specify atmospheric densities in amg for entry, descent, and landing analyses. Industrial gas suppliers reference amg when certifying specialty gas mixtures, ensuring customers can predict equipment performance over a range of temperatures and pressures.