A couple of customers have recently asked about standard concentrations and converting from ppm_{v }to mg/m³. Honestly, I have no clue how I have never blogged about this subject, especially considering how fundamental and critical this topic is. So here we go:

Air concentrations at ppm are parts per million by volume and should therefore be expressed as ppm_{v}. Although sometimes people forget the “v” at the end, it is implied. Unless of course they meant parts per million by mole, which is sometimes used for air as well; and just so happens to be conveniently identical for an ideal gas and practically identical for most compounds in air at standard temperature and pressure (STP).

But for the most part it should go as follows:

Which you may then conceptualize as:

Now… I have encountered some confusion as to the fact that ppm_{v} may be directly interpreted as mg/m^{3}. **Please do not make this mistake**! The water and soil folks have the luxury of jumping from ppm to mg/L. But that is because they are not dealing with the density of gases, which are temperature and pressure dependent.

So how do we go from ppm_{v} to mg/m^{3} (this is exactly the same for ppb_{v} to µg/m³)… here is how:

Where T = temperature in K = 273.15 + °C and 0.08205 is the Universal gas constant in L atm K^{-1} mol^{-1}, which you may find on the good ole interweb.

Or you could stick to the short version of the aforementioned, which only requires you to remember an ideal gas will occupy 24.45 L/mol at 1 atm and 25 °C. Yes, not the 22.4 L/mol you see littered all over the internet. Unless of course your STP includes 0 °C. Therefore, the above equation simply reduces to the following:

Remember, use the exact same equation for ppb_{v} to µg/m³.

Thanks for the post. I do have one question. What I am trying to do is convert a volume of gas std (22 components) to the mass of one of the components. I am using the ideal gas ratio of 24.45L/mol to do this. For example: a gas std that has a mole percent of 0.995 for carbon monoxide. If I start with 100uL of gas, the result would be 13.9ug of CO. My goal is to have a calibration curve that plots instrument response -vs- ug CO, using various volumes of gas std to generate the different component mass. Is this an appropriate use of the 24.45l/mol relationship?

If the results are in mass such as ug/sample or ug/filter or ug/xad sample, can you convert to ug/m3 by just applying the volume of air to that sample??

Short answer: yes.

If for example you get your TO-11A results as formaldehyde at 2 µg/cartridge, you would then just do the appropriate math to swap in the volume of air sampled to get µg/m³. Keeping with the same example, if you had sampled 0.5 m³, then your final formaldehyde concentration would be 4 µg/m³. Then refer back to the blog to go from µg/m³ to ppbv.