I find the diffusion of the smell of flatulence to be a better comparison, because it invokes a visceral reaction ("eww", "yuck", etc.). Imagining a device which does this seems easier. I have a worse idea of what "1/4 of a human exhalation" means.
If we're willing to get closer than a mile (questionable in the above scenario), we can apply an inverse law for gas diffusion [4] (I was surprised it wasn't inverse square!) and find that the apparatus can can detect a single average fart at a distance of around 30 feet -- easily covering most elementary school classrooms and automating away the "whom smelt it dealt it" dilemma.
[1] https://www.chemistryworld.com/news/explainer-the-chemistry-... [2] https://en.wikipedia.org/wiki/Tidal_volume [3] https://en.wikipedia.org/wiki/Flatulence [4] https://physics.stackexchange.com/questions/290059/inverse-s...
https://www.ncbi.nlm.nih.gov/pubmed/10410929
It turns out that humans exhale all kinds of things.
I guess a can of soda is something comparable that people are considerably more aware of.
1/4HEM