The basic unit conversion from number of molecules to a weight-per-volume unit is straight-forward since a molecule of a certain type always has the same weight, the “molecular mass”, taking natural atomic isotope variations into account.
Effectively, you of course never count the number of molecules but just scale (calibrate) the reading of an instrument to for example micrograms-per-cubic-metre, matching the expected concentration where the measurements take place.
Volume, Temperature, and Pressure
However, there is a catch with concentrations in weight-per-volume. The volume depends on the temperature and pressure at the point of the measurements. Alternatively expressed, the same number of molecules (weight) takes up different volumes at different temperatures and pressures.
It is not an issue in an in-situ monitoring device where the measurements are made in the natural habitat of the molecules. The issue occurs in sampling devices where the measurements typically are made in a closed measurement cell separated from the actual sampling point. Most likely, the cell has a different temperature and/or a different pressure than the gas mixture at the sampling point.
Normalization Standards
In the fundamental conversion to a weight-per-volume unit, the volume in question is the actual volume in the measurement cell, with the temperature and pressure it happens to have. This is probably not representative for the conditions at the sampling point. To avoid confusion, it is therefore practice to normalize the volume to a specific standard condition.
In the industry, the standard is almost always 0 °C and 1 atm (one atmosphere = 101.325 kPa). In air quality applications, the temperature standard can vary. Countries within the European Union and countries otherwise following EU standards apply a temperature of 20 °C, while the United States and countries following U.S. standards apply a temperature of 25 °C. In either case, the volume we arrive to is often referred to as the normalized volume or the standardized volume – both expressions are in use and mean the same.
Weight-per-volume Units
Depending on type of molecule, the weight-per-volume unit is often mg/m3 or g/m3 in industrial contexts, and µg/m3 or in a few cases ng/m3 or mg/m3 in ambient air applications. The volume part of a weight-per-normalized-volume unit is sometimes expressed as m3N where N indicates the normalization. However, the N is sometimes omitted, and it can in any event mean different temperature standards. It is therefore important to check what type of normalization, if any, a set of data actually represents.
In-situ instruments often give the concentrations in units of weight-per-normalized-volume even if there is no difference between the “sampling point” and the point of measurements. It can often be a legislative requirement, but it is usually also required to provide abilities to calibrate the instruments against known gas concentrations provided in volume-per-volume units.
Volume-per-volume Units
Once the weight-per-normalized volume is established, it is also possible to convert the concentration to a volume-per-volume unit, being an alternative standard for expressing concentrations. This is also a matter of natural constants, only depending on the type of molecule. The molecular mass come in play again, but also the “molar volume” which also is a natural constant, ideally 22.414 m3/kmol at 0 °C and 1 atm.
Going from weight-per-normalized-volume to volume-per-volume is just a matter of multiplying with a constant factor, although a different factor for each type of molecule and each normalization standard. The factor can be calculated from the molar volume and the mass of the individual atomic elements of the molecule, but all factors are fixed so they are usually just picked from a table.
The volume-per-volume unit used in industrial contexts is typically ppm (volumetric parts per million) or in some cases % (volumetric percent), while the corresponding unit in air quality applications often is ppb (volumetric parts per billion) or in a few cases ppm.
Other Normalizations
In the industry, normalization can also be made to dry gas and/or a fixed oxygen level. The “dry gas” expression has its background in the water content of the flue gas often being notable (percentage levels) and sampling instruments requiring the gas mixture to be conditioned by drying before it is led into a cell where the concentration measurements can be made. Such instruments often have no option but to express the concentration in “dry gas” since there is no parallel measurement of how much humidity (water molecules) has been removed from the gas mixture. As a result, this has become an optional normalization standard.
Also instruments capable of measuring concentrations in wet gas (i.e. a gas mixture including water vapour) may have an option to mathematically subtract the water content and present a dry concentration. A condition for this is of course that the absolute water concentration also is measured, in parallel with the gas or gases to be presented in “dry” units.
Oxygen Normalization and Emission Limits
Normalization to a fixed oxygen level is a way to allow emission limits to be expressed as concentrations, automatically scaled with the size of the furnace, without need to also measure gas flow and then express the emissions in weight-per-time units. The oxygen level at the tail of a combustion process is a measurement of how much excess air slips through the combustion process (“lean combustion”) and follows the combustion products out through the stack. The higher oxygen level, the more excess air in the flue gas, and the more dilution (in terms of lower concentration) of the pollutants being emitted to the ambient air. However, by normalization to a fixed oxygen level, the concentrations can be expressed independently of how lean the combustion process runs, and fixed emission limits can then be set in terms of concentrations.
About the Author
Bengt Löfstedt
Operative Support, OPSIS AB