# Homework Help: Converting mg/hr to ppb

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1. Feb 23, 2017

### greengirl

Editor Note: Moved from a technical forum and therefore no template.

Hi! I'm terrible at this sort of thing so came to this forum for help. I'm trying to figure out how much ozone an air purifier will throw into my indoor air. The unit produces 360 mg/hr. My space is 2500 square feet. Ceilings are 10 feet high.

The threshold for ozone safety is 50 ppb.

Can anyone help me figure out how long I can run the unit before I reach the 50 ppb threshold?

Last edited by a moderator: Feb 23, 2017
2. Feb 23, 2017

### RUber

ppb is parts per billion, right?
I can walk through the process, but I cannot vouch for how accurate the approximations are.

According to Wikipedia, air at 20 degrees Celsius is about 1.2 kg per m^3.
And molar mass of dry air is 0.0289644 kg/mol. This means that
$\frac{1.2}{0.0289644}$ should approximate the number of molecules (in moles) in a cubic meter.
Using the rough conversion of 3m $\approx$ 10ft, your space is about 15mx15mx3m $\approx$ 675 cubic meters.
As a rough estimate, I would use
$675 \frac{1.2}{0.0289644} = 27965 \approx 28000$
moles of air particles in your home.

Next, we will convert 360mg/hour into particles per hour.
Ozone is O_3, which has molar mass of 16*3 = 48g/mol. If you are outputting 360 mg per hour, then that is
$\frac{360 mg }{48000mg} = .0075$ moles per hour.

dividing the moles of ozone by the moles of air, you get
$\frac{7.5 x 10^{-3} }{ 2.8 x 10^4 } = 2.7 x 10^{-7}$
Converting to parts per billion, you want the exponent to be -9, so multiply by 100 to get about 270 ppb.

Lastly, you should consider how much ozone will dissipate and/or convert by natural processes back to oxygen. This rate of change will work against the buildup of ozone in your home.

Finally, as I was looking for additional conversions, I found a link to California's recent action on ozone-producing air purifiers. It looks like there is good information at their web page
https://www.arb.ca.gov/research/indoor/aircleaners/consumers.htm

3. Feb 23, 2017

### greengirl

Wow! I'm glad I came here for help. Thank you RUber!

So, it would produce 270 ppb in an hour?

4. Feb 24, 2017

### RUber

That's what I get based on the conversions and approximations I used.
It seems high, but I think that is why recently many consumer groups have advocated against ozone-producing air purifiers -- because they replace one type of pollutant with another.
Ozone does naturally dissipate, so if you use it continuously for 100 hours, you would have significantly less than 27000ppb in your home.
That is the extent of my knowledge on the matter, though. I am simply a mathematician, not an environmental (air quality) scientist.