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# Question: Is there a predictive relationship between the number of PM 2.5 and smaller airborne particulates compared to the mass of the same ug per cubic meter?

Tomp is asking a question about air-quality

by Tomp |

Today's cost effective particle counters measure PM 2.5 and PM 10. PM 2.5 and smaller are the greatest health risk. Is there a way to take the measurement of the mass of PM 2.5 in micrograms per cubic meter and extrapolate an approximate number of total airborne particles at PM 2.5 and smaller? For example, could we know that a 2.0 ug per m3 has approximately 20M PM 2.5 and below particles and 1 ug per m3 would then have 10M?

@Tomp, I'm not sure I understand your question but "particle counters" are basically counting particles and converting the counts to densities. The ones I know about allow you to get the output as either densities, such as µg per cubic meter, or counts, such as particles per dl. Hope this helps.

Hi @Tomp, and thank you for replying @jeffalk. Chiming in with a link to additional documentation that @jiteovien provided on another question: https://publiclab.org/questions/Ag8n/08-18-2018/pharmaceutical-class-100000-particulate-as-compared-to-pm2-5#c20449

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Short answer ... No. Long answer ... Absolutely no!

I'll try to explain why, even though it sounds possible, the uncertainties are so large that the assumptions you'll need to make will make the answer meaningless.

The first thing to understand is that the particles in the air are NOT of the same size and that the range of sizes is very large (see here for some examples). The next thing is to remember that the mass of a particle is related to its volume which is a function of the size cubed so let's work a little example.

Let's assume that all particles are spheres and that have a density of 1g/m3 so that one particle of a given size will weigh:

10 μm : 0.0005 μg

2.5 μm : 0.000008 μg

1 μm : 0.0000005 μg

0.1 μm : 0.0000000005 μg

So, one particle of 1 μm weights 1000 times less than a particle of 10 μm which means that if you measure a concentration of PM10 of let's say 100 μg/m3, the number of particles in that population can be anywhere between 200 thousand and 200 million per cubic meter and without any other information you can't make the estimate any narrower.

So ... don't go down that path as you'll end up with essentially made up numbers.

Thanks for this! I guess you're also implying that the mass distribution also doesn't follow any simple or predictable trends? Like, is there no general rule for the spread of particle masses in a generic air sample? I guess I imagine there wouldn't be, but I'm just curious. Thanks again!

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The particle size distribution (mass, volume or number) is very variable and even though "on average" it's fairly stable, the day-to-day variability is very large and quite unpredictable.

There are hundreds of scientific publications that deal with characterising the size distribution in different environments.

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