Concentration vs Mixing-Ratio.

Here is a reply to a colleague on the matter of "concentration" versus "mixing ratio" (as in my previous posting "Carbon in the Sky", Saturday, January 6th, 2007) which some readers might find interesting.

Dear Alexander,

I agree with your comments about the complexity of "concentrations". Chemists do indeed have various ways of expressing these things! Let's not mention "molality" versus "molarity" to describe the concentrations of solutions of various substances in liquids!

However, so as not to confuse the issue, it is probably better to refer to the amount of CO2 etc. in the atmosphere as "concentration" rather than as "mixing ratio". Yes, both terms are standard throughout the Anglo-American speaking world as far as I know.

For gas-phase species, the most commonly used units are ppm, ppb and ppt. These units express the number of molecules of pollutant found in a million, billion or trillion molecules of air. (Billion and trillion are US, not British). There is also pphm (parts per hundred million) which is sometimes used if the actual amounts of particular species make it a convenient unit. Alternatively, because numbers of molecules (or moles) are proportional to their volumes according to the ideal gas law: (PV = nRT), these units may be thought of as the number of volumes of the pollutant found in 10^6, 10^9 or 10^12 volumes of air, respectively.

This ratio of moles, molecules or volumes of the species to the number of moles, molecules or volumes of dry air is more commonly known as the "mixing ratio".

The use of mixing ratios is widespread for expressing the relative amounts of species at various altitudes throughout the atmosphere. Since the total air pressure and hence the number of molecules in a given volume decreases with altitude, a constant mixing ratio does not imply a constant concentration (i.e. as expressed in moles or molecules per unit volume).

Although not expressly stated in most cases, mixing ratios are usually referenced to dry air. If water vapour is included, the mixing ratio would vary with humidity, which could induce a variation of a few percent.

Although the term "concentration" is used frequently, if the units are ppm, ppb or ppt, it should be understood that this is really a mixing ratio. Some journals emphasize this by writing these units as ppm (v:v) etc. (i.e. to denote volumes explicitly)."

Related Reading.
"Chemistry of the Upper and Lower Atmosphere" written by Barbara J. Finlayson-Pitts and James N. Pitts, Jr. Published by Academic Press, New York, 2000, p 33, which puts the matter succinctly.