Atmospheric Science: What is a Mole of Air?

What is a Mole of Air

Aficionados of the countryside are aware that it’s beneficial to differentiate between molehills and cowpats whilst traversing a field.

Similarly, aficionados of science should realise that it’s beneficial to differentiate between moles and cowpats whilst traversing the field of Atmospheric Science.

Understanding the difference begins with the arcane concept of a mole.

A mole defines a “quantity that measures the size of an ensemble of elementary entities”.

Therefore, before a mole can be defined it’s necessary to define the ensemble and then agree upon the elementary entities that are contained within the ensemble.

This is where the fun begins because ensembles and their elementary entities are defined by human beings.

Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles.
It is a macroscopic property and it is sometimes referred to as chemical amount.
The International System of Units (SI) defines the amount of substance to be proportional to the number of elementary entities present.
The SI unit for amount of substance is the mole.
It has the unit symbol mol.

Two ensembles that are frequently used in Atmospheric Science are Air and Atmosphere.

Both of these ensembles are very difficult to define because their associated elementary entities are extremely diverse and variable.

Air is the stuff humans breathe as they walk across a field.

Sometimes the air is hot and sometimes it’s cold [temperature].
Sometimes the air is sticky and sometimes it’s dry [humidity].
Sometimes the air is heavy and sometimes it’s light [barometric pressure].
Sometimes the air is calm and sometimes it’s blowing a gale [wind speed].
Sometimes the air contains frozen water [snow and hail].
Sometimes the air contains liquid water [rain and fog].
Sometimes the air contains soot from a nearby bonfire [particulate matter].
Sometimes the air contains dust from the Sahara desert [particles].
Sometimes the air contains smelly marsh gas [trace gases].
Sometimes the air crackles with static electricity [charge].
Etc etc etc…

Atmosphere is the stuff humans walk through as they cross a field.

Sometimes the atmosphere contains arcing electricity.
Sometimes the atmosphere is thin in mountain pastures.
Sometimes the atmosphere contains clouds.
Sometimes the atmosphere displays mirages.
Sometimes the atmosphere displays rainbows.
Sometimes the atmosphere displays auroras.
Sometimes the atmosphere displays fireballs and meteors.
Sometimes the atmosphere displays sunlight.
Sometimes the atmosphere displays moonlight.
Sometimes the atmosphere contains insufficient air to breathe.
Sometimes the atmosphere contains air that is poisonous to breathe.
Sometimes the atmosphere seems to stretch out to the stars.
Etc etc etc…

Clearly, the real world is difficult to encapsulate with crisp, clean concepts.

However, in the laboratory, it is possible to create the ideal conditions for encapsulation.

Furthermore, when ideal laboratory conditions become agreed standards then they help ensure experimental results are comparable and can be replicated.

Accordingly, scientists who can control their experimental [and operating] environments have embraced standards with gay abandon.

Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data.

The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards.

Other organizations have established a variety of alternative definitions for their standard reference conditions.

In chemistry, IUPAC established standard temperature and pressure (informally abbreviated as STP) as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of 100 kPa (14.504 psi, 0.987 atm, 1 bar).

An unofficial, but commonly used standard is standard ambient temperature and pressure (SATP) as a temperature of 298.15 K (25 °C, 77 °F) and an absolute pressure of 100 kPa (14.504 psi, 0.987 atm). The STP and the SATP should not be confused with the standard state commonly used in thermodynamic evaluations of the Gibbs energy of a reaction.

NIST uses a temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 101.325 kPa (14.696 psi, 1 atm). The International Standard Metric Conditions for natural gas and similar fluids are 288.15 K (59.00 °F; 15.00 °C) and 101.325 kPa.

The successful application of these standards have [for example] enabled scientists to collectively advance their knowledge regarding the Thermodynamics of Dry Air.

Thermodynamics of Dry Air
The thermodynamic equilibrium state of a quantity of dry air is defined by the volume V and pressure P of the air.

Example: At 25°C 1.0kg of dry air has volume 0.847m3 and pressure 101kPa.

In fact, the application of standards has been so successful [in the laboratory] that the scientists have even standardised the definition of a mole.

The mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 12g of the isotope carbon-12.

This number is called Avogadro’s number and has the value 6.02214129(30) × 1023.

It is the numerical value of the Avogadro constant which has the unit 1/mol, and relates the molar mass of an amount of substance to its mass.

This very curious standard simply dictates than a mole of any ensemble must contain 6.02214129(30) × 1023 elementary entities.

Apparently, the mole has been successful in chemistry.

The mole is widely used in chemistry instead of units of mass or volume as a convenient way to express amounts of reactants or of products of chemical reactions.

For example, the chemical equation 2 H2 + O2 → 2 H2O implies that 2 mol of dihydrogen (H2) and 1 mol of dioxygen (O2) react to form 2 mol of water (H2O).

In honour of the unit, some chemists celebrate October 23 (a reference to the 1023 part of Avogadro’s number) as “Mole Day”.

It starts at 6:02 a.m. and ends at 6:02

In chemistry, the molar mass M is a physical property.
It is defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance.
The base SI unit for molar mass is kg/mol.
However, for historical reasons, molar masses are almost always expressed in g/mol.

Molar masses are almost never measured directly.
They may be calculated from standard atomic masses, and are often listed in chemical catalogues and on material safety data sheets (MSDS).

The atomic mass (ma) is the mass of an atomic particle, sub-atomic particle, or molecule.
It may be expressed in unified atomic mass units; by international agreement, 1 atomic mass unit is defined as 1/12 of the mass of a single carbon-12 atom (at rest).

Obviously, the selection of elementary entities becomes a very important topic.

The mole may also be used to express the number of atoms, ions, or other elementary entities in a given sample of any substance.

The concentration of a solution is commonly expressed by its molarity, defined as the number of moles of the dissolved substance per litre of solution.

The number of molecules in a mole (known as Avogadro’s constant) is defined such that the mass of one mole of a substance, expressed in grams, is exactly equal to the substance’s mean molecular mass.

For example, the mean molecular mass of natural water is about 18.015, so one mole of water is about 18.015 grams.

Making use of this equation considerably simplifies many chemical and physical computations.

In particle physics they use “elementary particles” as their elementary entities.

In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles.

Known elementary particles include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are “matter particles” and “antimatter particles”, as well as the fundamental bosons (gauge bosons and Higgs boson), which generally are “force particles” that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

Everyday matter is composed of atoms, once presumed to be matter’s elementary particles – atom meaning “indivisible” in Greek – although the atom’s existence remained controversial until about 1910, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy.

A particle’s mass is quantified in units of energy versus the electron’s (electronvolts).

Through conversion of energy into mass, any particle can be produced through collision of other particles at high energy, although the output particle might not contain the input particles, for instance matter creation from colliding photons.

In thermodynamic they use particles that “cannot be broken into smaller pieces” as their elementary entities.

The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter N, is the number of constituent particles in that system.

The particle number is a fundamental parameter in thermodynamics which is conjugate to the chemical potential.

Unlike most physical quantities, particle number is a dimensionless quantity.

It is an extensive parameter, as it is directly proportional to the size of the system under consideration, and thus meaningful only for closed systems.

A constituent particle is one that cannot be broken into smaller pieces at the scale of energy k•T involved in the process (where k is the Boltzmann constant and T is the temperature).

For example, for a thermodynamic system consisting of a piston containing water vapour, the particle number is the number of water molecules in the system.

The meaning of constituent particle, and thereby of particle number, is thus temperature-dependent.

The concept of particle number has a main role in theoretical considerations.

In situations where the actual particle number of a given thermodynamical system needs to be determined, mainly in chemistry, it is not practically possible to measure it directly by counting the particles.

If the material is homogeneous and has a known amount of substance n expressed in moles, the particle number N can be found by the relation N = nNA, where NA is the Avogadro constant.

In Atmospheric Science they chose molecules as their elementary entities.

The most abundant is molecular nitrogen (N2) with a mixing ratio CN2 = 0.78 mol/mol; N2 accounts for 78% of all molecules in the atmosphere.

Next in abundance are molecular oxygen (O2) with CO2 = 0.21 mol/mo

Introduction to Atmospheric Chemistry – D J Jacob – Princeton University Press – 1999
Measures of Atmospheric Composition

This is a very convenient decision because Atmospheric Science can now borrow all the ideal science developed in the laboratory.

The mixing ratio CX of a gas X (equivalently called the mole fraction) is defined as the number of moles of X per mole of air.

It is given in units of mol/mol (abbreviation for moles per mole), or equivalently in units of v/v (volume of gas per volume of air) since the volume occupied by an ideal gas is proportional to the number of molecules.

Pressures in the atmosphere are sufficiently low that the ideal gas law is always obeyed to within 1%.

Introduction to Atmospheric Chemistry – D J Jacob – Princeton University Press – 1999
Measures of Atmospheric Composition

The air density is a property used in many branches of science as aeronautics; gravimetric analysis; the air-conditioning industry; atmospheric research and meteorology; the agricultural engineering in their modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models; and the engineering community that deals with compressed air from industry utility, heating, dry and cooling process in industry like a cooling towers, vacuum and deep vacuum processes, high pressure processes, the gas and light oil combustion processes that power our turbines airplanes, gas turbine-powered generators and heating furnaces, and air conditioning from deep mines to space capsules.

The density of humid air may be calculated as a mixture of ideal gases.


However, Atmospheric Science had to make a few compromises when it reached this decision because the real world doesn’t emulate ideal laboratory conditions.

Standard Dry Air — an agreed-upon gas composition for air from which all water vapour has been removed.

There are various standards bodies which publish documents that define a dry air gas composition.

Each standard provides a list of constituent concentrations, a gas density at standard conditions and a molar mass.

It is extremely unlikely that the actual composition of any specific sample of air will completely agree with any definition for standard dry air.

Firstly, Atmospheric Science compromised by pretending that nothing in the atmosphere is larger than a molecule.


In meteorology, a cloud is a visible mass of liquid droplets or frozen crystals made of water or various chemicals suspended in the atmosphere above the surface of a planetary body.

Hail is a form of solid precipitation.
It is distinct from sleet, though the two are often confused for one another.
It consists of balls or irregular lumps of ice, each of which is called a hailstone.

Unlike graupel, which is made of rime, and ice pellets, which are smaller and translucent, hailstones consist mostly of water ice and measure between 5 millimetres (0.2 in) and 15 centimetres (6 in) in diameter.


Night clouds or noctilucent clouds are tenuous cloud-like phenomena that are the “ragged edge” of a much brighter and pervasive polar cloud layer called polar mesospheric clouds in the upper atmosphere, visible in a deep twilight.
They are made of crystals of water ice.


Atmospheric particulate matter – also known as particulates or particulate matter (PM) – are tiny pieces of solid or liquid matter associated with the Earth’s atmosphere.
They are suspended in the atmosphere as atmospheric aerosol, a term which refers to the particulate/air mixture, as opposed to the particulate matter alone.
However, it is common to use the term aerosol to refer to the particulate component alone. Sources of particulate matter can be manmade or natural.
They can adversely affect human health and also have impacts on climate and precipitation.

Mount Cleveland

Volcanic ash consists of fragments of pulverized rock, minerals and volcanic glass, created during volcanic eruptions, less than 2 mm (0.079 inches) in diameter.
The term volcanic ash is also often loosely used to refer to all explosive eruption products (correctly referred to as tephra), including particles larger than 2mm.


Sources of Solar System dust include comet dust, asteroidal dust, dust from the Kuiper belt, and interstellar dust passing through the Solar System.
The terminology has no specific application for describing materials found on the planet Earth except for dust that has demonstrably fallen to Earth.
By one estimate, as much as 40,000 tons of cosmic dust reaches the Earth’s surface every year.

Secondly, Atmospheric Science compromised by pretending the atmosphere is a well mixed, homogenous ideal dry gas mixed with a variable amount of water vapour which is also deemed to be an ideal gas.

CO2 sources and sinks


The real history of carbon dioxide gas analysis – Ernst-Georg Beck

Mixing Ratios

Methane and Carbon Monoxide in the Troposphere
Atmospheric Physics Group, University of Toronto

In meteorology, a cloud is a visible mass of liquid droplets or frozen crystals made of water or various chemicals suspended in the atmosphere above the surface of a planetary body.

Other forms appear as non-convective layered sheets like low stratus, and as limited-convective rolls or ripples as with stratocumulus. Both of these layered forms have middle- and high-étage variants identified respectively by the prefixes alto- and cirro-.

Thirdly, Atmospheric Science compromised by pretending their elementary entities [molecules and atoms] form a stable ideal gas mixture which never brakes down into smaller pieces nor aggregates into other entities.

Cosmogenic nuclides (or cosmogenic isotopes) are rare isotopes created when a high-energy cosmic ray interacts with the nucleus of an in situ solar system atom, causing cosmic ray spallation.

These isotopes are produced within earth materials such as rocks or soil, in Earth’s atmosphere, and in extraterrestrial items such as meteorites.


Photodissociation, photolysis, or photodecomposition is a chemical reaction in which a chemical compound is broken down by photons.
It is defined as the interaction of one or more photons with one target molecule. Photodissociation is not limited to visible light.
Any photon with sufficient energy can affect the chemical bonds of a chemical compound.
Since a photon’s energy is inversely proportional to its wavelength, electromagnetic waves with the energy of visible light or higher, such as ultraviolet light, x-rays and gamma rays are usually involved in such reactions.


Photochemistry of Important Atmospheric Species – Prof. Jose-Luis Jimenez – 2005
Cooperative Institute for Research in Environmental Sciences
University of Colorado at Boulder

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons to form ions, often in conjunction with other chemical changes.

Ionization can result from the loss of an electron after collisions with sub atomic particles, collisions with other atoms, molecules and ions, or through the interaction with light.

Plasma recombination is a process by which positive ions of a plasma capture a free (energetic) electron and combine with electrons or negative ions to form new neutral atoms.

Dissociation in chemistry and biochemistry is a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into smaller particles such as atoms, ions or radicals, usually in a reversible manner.

Dissociation is the opposite of association and recombination.

Rain is liquid water in the form of droplets that have condensed from atmospheric water vapor and then precipitated—that is, become heavy enough to fall under gravity.

Fourthly, Atmospheric Science compromised by pretending their defined elementary entities [molecules and atoms] are electrically neutral.


Volta, over a century ago, discovered with some degree of exactitude that the proportions of the ordinates of the curve or gradient of electric potential increased as the distance from the earth increases, and, more recently, Engel has provided data to calculate the increase.

It appears that the electric density increases 88 volts with each metre of altitude above the earth, or, in feet equivalents, 1-19 volts per foot of altitude.

Journal of the Royal Horticultural Society – Volume 33 – 1908

Of late years, additional interest has attached to the possibility of the connection, owing to Elster and Geitel’s discovery that air drawn from the soil is ionized, and their consequent suggestion that change of barometric pressure may influence potential gradient, by modifying the rate at which this ionized air escapes into the atmosphere.

Atmospheric Electric Potential Results at Kew –Dr. C. Chree
Philosophical Transactions of the Royal Society – 1906

The profiles of the total positive ion number density, n+, (red curve) and of the total negative number ion density, n-, (blue dashed curve) are shown here together with typical profiles of the number densities of the various positive ion types.

In the lower atmosphere, where negative ions do exist, ne=n+-n- , the ledge designated as the D-region is largely due to the selective ionisation of NO by solar Lyman- radiation.

There are no free electrons in the stratosphere and the troposphere (where n+=n- in an ion-ion plasma).

Ionic composition

Ion chemistry of the terrestrial atmosphere – Prof. Dr. Patrik Španěl
J. Heyrovsky Institute of Physical Chemistry – Prague – Czech Republic

Daytime ionospheric and atmospheric composition

Earth’s Atmosphere – School of Physics, University of Sydney

Obviously, after making so many compromises Atmospheric Science was also willing to pretend that the ideal [laboratory] laws of physics can be applied in the real world.

A thermodynamic system is a precisely specified macroscopic region of the universe, defined by boundaries or walls of particular natures, together with the physical surroundings of that region, which determine processes that are allowed to affect the interior of the region, studied using the principles of thermodynamics.

An isolated system is an idealized system that has no interaction with its surroundings.

It is not customary to ask how is its state detected empirically.

Ideally it is in its own internal thermodynamic equilibrium when its state does not change with time.

A system that is not isolated can be in thermodynamic equilibrium with its surroundings, according to the characters of the separating walls. Or it can be in a state constant or precisely cyclically changing in time – a steady state – that is far from equilibrium. Or it can be in a changing state that is not in thermodynamic equilibrium.

Classical thermodynamics considers only states of thermodynamic equilibrium or states constant or precisely cycling in time.

An interaction of system and surroundings can be by contact, for example allowing conduction of heat, or by long-range forces, such as an electric field established and maintained by the surroundings.

However, having compromised upon the thorny issue of elementary entities, the boffins in Atmospheric Science were then confronted by the challenge of having to define their all embracing ensemble [the atmosphere] which “in principle” stretches halfway to the Moon.

In principle, the exosphere covers all distances where particles are still gravitationally bound to Earth,
i.e. particles still have ballistic orbits that will take them back towards Earth.

The upper boundary of the exosphere can be defined as the distance at which the influence of solar radiation pressure on atomic hydrogen exceeds that of the Earth’s gravitational pull.

This happens at half the distance to the Moon (190,000 kilometres (120,000 mi)).


Atomic spectra – Institut für Theoretische Physik, Universität Hannover

Evidently, Atmospheric Science thought 190,000 kilometres was far too complicated for them to even contemplate and, besides, they didn’t want reality to interfere with their short and sweet list of molecular elementary entities they had so skilfully crafted.

Only the other hand, the natural limit of their ideal gas laboratory theories is at the very miserly altitude associated with the first Isopycnic Level of about 8 kilometres.

Atmospheric Science required another compromise solution and settled upon a nice round figure of 100 kilometres.

Temperatur und mittlere molare Masse

However, Atmospheric Science occasionally mumbles something about 85 kilometres because they forgot all about something [or other] like the D Layer in the Ionosphere [which they are now trying to write out of the plot].

Therefore, when an aficionado of science is asked “What is a Mole of Air?” they can politely reply “A convenient fiction” or, if they wish to be more direct, they can simply state it’s “A cowpat”.

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6 Responses to Atmospheric Science: What is a Mole of Air?

  1. Jim Coyle says:

    Go to Rodentator .c0m to see how to handle moles

  2. George says:

    Really interesting coverage. “A convenient fiction”, indeed, if “air” is being assumed to be one homogenous lump of sky-stuff! Moles are very handy in chemistry because they let you deal with proportions of particular chemicals relative to each other for particular interactions, but that doesn’t really extent do the whole ecosystem of course…

    It would be interesting to know what effect these assumptions/compromises have on predictions or models. I would hope that the actual models make some effort to be more sophisticated than just assuming the whole atmosphere is just one big extent of ideal dry air, but I don’t know. Do you have any info/ideas on that?

    • malagabay says:

      I have no specifics on the “models”.

      Similarly, I would hope they make some effort.
      I guess not too much effort when it comes to “climate models”…
      but some of the meteorological models seem to be looking good well beyond the usual “two or three day window” usually associated with weather forecasts.

      That opinion is based upon watching some of Joe Bastardi’s “Saturday Summaries” over at

      • George says:

        Thanks for the link.

        It occurred to me that I’ve never actually read the IPCC stuff on models, so I jumped over there and they have quite a readable-looking chapter on “Climate Models and their Evaluation”, including sections such as “What explains the spread in model’s… estimates?” and “How reliable are the models used…?”, which might be interesting.

        Link, but takes a while to load, ‘cos it’s fairly big:

        Sample content:

        8.8 Representing the Global System with Simpler Models

        8.8.1 WhyLowerComplexity?

        An important concept in climate system modelling is that of a spectrum of models of differing levels of complexity, each being optimum for answering specific questions. It is not meaningful to judge one level as being better or worse than another independently of the context of analysis. What is important is that each model be asked questions appropriate for its level of complexity and quality of its simulation.

        If you’re on the lookout for other areas to kick into, it might be worth a look, grist for your mill and all that.

  3. Pingback: Atmospheric Science: The Second Level | MalagaBay

  4. Pingback: US Standard Atmosphere Supplements 1966 | MalagaBay

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