Can you guys check my math?

important maths... how many bubbles in a beer! https://www.acs.org/content/acs/en/pressroom/presspacs/2021/acs-presspac-april-21-2021/cracking-open-the-mystery-of-how-many-bubbles-are-in-a-glass-of-beer.html

Scott Traynor

When dealing with giant numbers, I would suggest using Wolfram Alpha for quick calculations.

I once had a few breaths into an oxygen sensor and found that I was breathing out 15% oxygen compared to the normal reading of 21% I was interested from a sub aqua point of view when giving mouth to mouth resuscitation. The human body is quite a machine. Filling diving cylinders needs clean air and how dangerous a little contamination when using compressed air and diving to a depth of 30m+ and the effect of partial pressures [see link below]. Off topic again sorry. Waffle - as to why I was doing this. 1984 I was tuning 15+ gas burners for a bright brazing furnace with an oxygen sensor to get the air mixture within spec so that they did not burn lean and deform the INCONEL radiant burner tube that radiated heat in to the conveyor that brazed domestic water heat exchanges. The inert atmosphere of the brazing chamber was supplied by an exothermic generator. https://photos.app.goo.gl/d95gTFigonR3tYat8 this was the heat exchanger https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=ktn&LN=FR&NM=457 Just in case you interested Furnace Brazing https://www.msdmanuals.com/en-gb/home/injuries-and-poisoning/diving-and-compressed-air-injuries/gas-toxicity-during-diving And how Oxygen can be TOXIC

John Harrison

Just checked, the one built into windows seems to handle 32 digits. Which is enough, but I want to just be able to enter (Big Clives air molecules #) by just pressing 10 then the Trillion button twice.

Paul Malloy

First of all, there's an equation for that, the ideal gas law pV=NRT. (Read up on wiki) according to my use of that equation, and checked on line at standard termperature and pressure (room temp at sea level, basically) there are about 2.44x10^25 (NASA says "about 1x10^25" ) molecules of gas in 1 cubic meter, Now we can just use the volume of lungs directly, 6 litres of air is 6*10^-3 M^3, gets 1.47x10^23 gas molecules in a pair of full lungs for 10 parts per billion we subtract 8 orders of and get 1.47x10^15 ozone molecules in a full set of lungs 1.47 peta ozone molecules. Above you have written down a 1 with 25 zeros for NASAS number, accepted as "about" , 8 zeros less which would be 1x10^17 for the Ozone in a cubic meter, correct and three magnitudes less, but 6x for the amount in a lung (6 with 14 zeros) all jivving with NASAS estimate of 10 trillion trillion or a 10 with 2x12 zeros after it.

OOO,OOO,OOO,OO fancy that!

Ymir the Frost Giant

Check out vintage ones from the 70s - you could get up to 16 digits easily. I have an old Sanyo ICC-82 which has 8 digits but works internally up to 16, with a button to press so you can swap between the two halves of you answer. Many others did this too. I also have a 1990s Russian one with 16 digits that can process 31 digits internally. I hope to make a 31-digit nixie display for it. Admittedly not hundred,s but getting there!

Ymir the Frost Giant

100,000,000,000,000 I seem to have lost 000 somewhere?

Ian James

I'm still looking for a calculator with million, billion, trillion, buttons on it.

Paul Malloy

Yep, the first thing that came into my mind was Avodagro hypothesis, this is one of the things that stuck in my head from school 40 years ago... 1 mole of gas at 20C is 24 litres (22.4 litres at 0C), and always contains 6.02 x 10^23 molecules. Why would I remember this... Clive's question is literally the first time this was useful.

Paul Slootman

I'm with Steve Perry - this is only really a ratio between two big numbers, so I would boil both of them down to digestible size whilst keeping the ratio as is. But I still have a feeling that your math could have 5 added to it. Or a lower case 's' - either would do.

Ymir the Frost Giant

... people on the planet...

Ymir the Frost Giant

Yeah, but they sound great.

Big Clive

Your math is correct. Numbers do get very silly indeed when you start looking at small objects - cells in the body, molecules in a gram, etc.

Charles

https://opentextbc.ca/biology/chapter/20-2-gas-exchange-across-respiratory-surfaces/

Just chiming in here. When you breathe, there is not a 100% exchange, so that has to be factored in. I found this site...but Canadians...sorry I am Canadian...

The "Kink Packulator" would be a good name for a Bad Dragon product.

Get rid of all those extra zeros, divide all the numbers by 1000,000, or 1000 until you get something sensible to work with :)

My guesses at least had about the same number of zeros (and yeah I'd much rather work in powers of ten than illions)

adrian

Clive, except for the fact that the number of air molecules in a cubic meter of air varies enormously depending on temperature, air pressure and humidity, your numbers look right to me plus or minus an order of magnitude. I came up with 2.77*10^25 molecules of air at 20C and standard atmospheric pressure and 0% humidity. So within a factor of 3 of the number you started with. So maybe more like 1,662 trillion molecules of ozone. But of course, humidity will lower that number. So perhaps your 600 trillion is close after all.

Seat Warmer

Nope. 10^25 is 10 followed by 24 zeroes. 10 parts per billion is 1 part per 100 million or 1x10^-8. 6 liters is 6x10^-3. 10^25 * 10^-8 * 6*10^-3 = 6*10^14 or 600,000,000,000,000. 600 trillion.

Seat Warmer

The cink palculator does have the splendid ability to work with ten digits instead of the usual 8. Very hand for things like capacitive reactance computations.

Big Clive

Isn't it funny - the world we live in isn't really analogue at all, but made of things you could count given enough time? Photo multiplier tubes are a good way to experience this.

Mike Page

Checks out. I'd avoid the higher -illions though, they are ambiguous.

Mike Page

While scientific notation is perfectly cromulent, many of us prefer engineering notation. 600e12 is what the pink calculator would say if it were a properly configured vintage Hewlett-Packard RPN model.

Checking your math the long way around: 10 trillion trillion = 10*1E12*1E12 = 10E24 = 1E25 10 parts per billion = 10E-9 = 1E-8 Multiply them together and you get 1E17, or 100,000,000,000,000,000

fluffy

To date I've not found an ozone meter that seems to give a realistic indication. It seems like you have to go for regularly calibrated lab grade equipment to get viable results.

Big Clive

I won't be comparing it to swimming pools. I just want to have a realistic figure for the scaremongers who imply that ANY level of ozone is bad news.

Big Clive

You can smell ozone at 0.1ppm, which is way too much.

Big Clive

average Volume of human adult breath is given as 1200 ml/breath so 1.2 L (physiopedia) so roughly 325 trillion molecules of Ozone per breath at 10 ppb Ozone (edit: trillion)

If my math is correct, 26,884,557,000,000,000,000,000,000 molecules per m^3. Avagadro's constant (6.022x10^23 molecules/mole) / (22.4L/mole) * (1000 L/m^3). Assuming the 10ppb is correct, that would be 26,884,557,000,000,000 Ozone molecules / m^3. Or 161,307,342,000,000 molecules per (very large) breath.

Andy Clements

1 ppb Ozone is given as 2,15 µg/m³, so 10 ppb would be 21,5 µg/m³, which would be 0,448 *10^-6 mol of O3 per cubic metre (48g/mol weight of O3), which would be equivalent to 2.7 *10^17 molecules per cubic metre or 2.7*10^14 molecules per litre

Clive, 10 septillion is the same as 10^25. 10 followed by 25 zeros. 10 parts per billion is equal to 1 X 10^-10, or one part in 10 billion. Multiply the two by simply adding the exponents, e.i. 25-10=15 So that give you 10^15 or 1,000,000,000,000,000,000 ozone molecules per cubic meter. 6 liters is equal to .006 cubic meter or 6 X 10^3 Multiply 6 X 10^-3 times 10 ^15 give us 6 X 10^12, oe 6,000,000,000,000 molecules of ozone, 6 trillion ozone moleules ber breath. I think I got it right. Dennis Smith

Dennis Smith

Don't use these stupid terms like billion, trillion etc. They mean different things in different languages, and writing long sequences of digits is also confusing and inefficient. Much better just to use powers of ten. Not hard to learn and you won't get lost any more.

Jonas Otter

The point I’d add (as some others have eluded to ) is the lung volume isn’t a breath - realistically it’s the ‘tidal volume’ is the ‘breath’ you take - typically < C20 % of the total volume

RDM

My calculations agree with yours

I've just been sniffing the ion wind directly from my ozone generator - how many molecules is that :p

Raven Luni

You're definitely not an American... :P

Scott Miller

Air at 20 °C and 1 atm contains 0.04158 mol of various particles per litre (https://en.wikipedia.org/wiki/Number_density) 1 mol = 6.022*10^23 => 1 L of air contains about 2.50 * 10^22 particles (6.022*10^23 * 0.04158) One cubic metre of air therefore contains 2.50 * 10^25 particles. If the number of 10 ppb is correct, one litre of air would contain 2.50 * 10^25 * 10^-8 = 2.50 * 10^17 or two hundred fifty quadrillion molecules of ozone That means that 6 L of air contains 1.5 * 10^22 particles of which 1.5 * 10^14 or one hundred and fifty trillion are ozone molecules. “Fun” facts: The long-term maximum allowed concentration according to EU standards is 55 ppb. At concentrations above 90 ppb the general public has to be informed immediately. At 100ppb over one hour symptoms like teary eyes, irritation of mucous membranes, headaches, coughing and reduced respiratory function are to be expected. At about 180ppb over one hour medium to severe health risks even for healthy individuals are to be expected. This took me much longer than I'd like to admit. :-) edit: calculation error

I understand part of the appeal here is to manipulate ridiculously huge numbers (and especially writing them _not_ in scientific notation to have even more impact), however back on the topic, isn't it more customary to define the amount in moles per L at STP? Ah nevermind, I forget this a YT wide audience. Defining the concept of mole or avagadro constant would bore the audience and not yield any impressive numbers. Better do like news outlets and compare everything to number of swimming pools or stadiums! ("if each ozone molecule were one person, they would fill X million stadiums"... roll eyes)

Raphaël

It's an American organization... Whichever scale they use is likely the wrong one. :P

Scott Miller

Do you have a link (or keywords in case Patreon blocks the link) to NASA's count of molecules per cubic metre?

Big Clive

Yeah. When I started computing this it was a total mind bender. But the results are staggering.

Big Clive

Technically speaking you also inhale some of Queen Cleopatra's farts too.

Big Clive

Many good answers. Better bin my mediocre one.

Hagen

Yeah, my biggest worry was missing and adding zeros. It makes a huge difference.

Big Clive

Avogadro would say: 6.022 E23 ;) Absolutely agree with the rest. I guess that the ozone that would reach the lungs would be < <10%.

Hub Rijcks

I'll stick to the Warm White vs. Cool White arguments!

Roughly correct with a lot of assumptions. Did you know that with every breath you take, you inhale some molecules of the last breath of Julius Cesar? That was one of the exam questions in my former days.

Hub Rijcks

Numbers look good to me, but as a biologist my maths isn’t up to engineering standards! I can say that as correctly pointed out above, you’re not going to get close to 6 litres of breath even during strenuous exercise. Much more like 0.5-1 litre under resting conditions.

NASA says 10^23 molecules per cubic metre, which is 1 with 23 zeroes after it. Knock off 8 zeroes for 10 parts per billion. A cubic metre is 1,000 litres, so knock off 3 more zeroes for that and you have 1,000,000,000,000 molecules of ozone per litre. 6 litres is total volume. Max breath ("vital") volume might be 5 litres if you really try, and the average breath might be 1 litre, or a bit less. So I reckon you're oit by a factor of maybe 600. Close enough for jazz :-)

Pedantic chemist here. 24.8L is the volume at 25oC and 1 bar pressure. 22.4L is the volume at 0oC and 1 atm pressure. This gives 2.4E25 molecules / m^3 (close enough to Clive's figure of 1E25 ).

Thomas R Burkholder

The maths looks good to me unless I check it again and miss a zero then add an extra zero lol but yes the top number is 10 trillion trillion and the rest works from there lol

Looks right to me. One mole of a gas at standard temperature and pressure takes up 22.414 litres. One mole is 6.02X10^23 molecules or 602 followed by 21 zeros. Treating air as if it were all nitrogen (or oxygen or whatever) a cubic metre contains 1000 litres. So it contains 44.61 moles or 2.68 followed by 25 zeros molecules. With one part ozone in every 10^8 we get 2.68x10^17 ozone molecules per cubic metre. However, the stuff is violently reactive and most of it won't get as far as your lungs as O3 has a desperate wish to become 1.5xO2 and will react with just about anything on the way into your lungs.

Donald Meston

Yep, the math/maths checks out. And it makes sense in the context that an average breath (which wouldn't be the lung's full capacity) is supposed to be on the order of 25 sextillion. Which is around half of the 60 sextillion you'd get for the full capacity by this math. So that sounds about right

Shuken Flash

In the UK, the O3 levels are often higher than 10ppb, often 20-40 ppb. http://www.apis.ac.uk/overview/pollutants/overview_o3.htm

KinkPaculator throwing a fit ?

Peter Stevens

I find those numbers really hard to read (scientific notation is simpler than counting zeroes). But I think it's in the ballpark. The first number should be of the order 1e25, which it is. Ten parts per billion is 1e-8, so eight zeroes less, seems ok. But with gases, what "ppm" means depends whether it's mass fraction (mass of ozone / mass of everything) or mole fraction (number of ozone molecules / total number of molecules), but the difference between those is only a factor of 5 or so, so in that scale it doesn't matter much. The math is ok for the third one too, and in general, given the error in the original value of 1e25 air molecules per cubic metre, it's probably correct within a factor of 10 or so, which, for a physicist, in an estimate like this, is close enough.

1 mole of (ideal) gas occupies 22.4 L 1 cubic metre is 44.64 * 22.4 L 1 cubic metre of gas (air) is therefore ~ 44.64 mol 1 mol is ~ 1E23 atoms 44.64 mol is threrefor ~ 1E25 atoms (same as Clive) 10 parts per billion = 10E-9 = 1E-8 So 10ppb of 1E25 is 1E17 (same as Clive) If the lung is 6 litres then yes 0.006 of 1E17 of ozone is in a breath: = 6E14 (same as Clive) One thing to note it's approx 500ml of air exchanged per breath though (Wikipedia) Which would be 0.0005 * 1E17 or 50000000000000 (50 trillion) ozones per breath

I used Avogadro's number: there are 6.02*10^23 molecules in 22.4 litres of air. Back-calculating from that, I get 1,612*10^12 molecules of ozone in 6l of air.

Stephen King

Looks good to me. (1E25 * 1E-8 = 1E17, 1E17 * 6E-3 = 6E14, where 1En= 1x10^n)

The sources seem suspect but I don't know.

Gordon Chin

Looks correct, and I'll give a shoutout for Wolfram Alpha for this kind of thing: https://www.wolframalpha.com/input/?i=10+trillion+trillion+*+.01+ppm

PPB parts per billion in a gas is conventionally on the basis of mass / weight. Not sure you can apply that to number of molecules , or later, in lung volume without doing some extra conversions

Bloody hell, how about using exponents? ;) 10 * 10^17

Frank

Yup. Your maths is spot on.

Does NASA use the short or long scale for these numbers? because depending on what they use that might be correct or off by quite some. See https://en.wikipedia.org/wiki/Long_and_short_scales

CH23

Yes a bit of a head thrash but I agree that your figures are correct.

Dr Andy Hill

The arithmetic is valid.

Correct except it's maths not math. 🙂

I'm sorry man. I suck at math. I suck that I need to build machines to do math for me...and ones talk too LOL!! I know I'm exhaling more ozone as I'm being treated by ionization radiation and the air molecules are being broken by the beams...and there is the Cherenkov radiation making my eye into a nuclear reactor. GOOD TIMES! BADASS!

Michael Thompson

Assuming the numbers are correct, the math seems to check out.

Jason Brinkerhoff

I get the same result at 100,000,000,000,000,000‬ at ground level Edit: my maths (10,000,000,000,000,000,000,000,000/1,000,000)*0.01

GL_1_Code1_1A

Yup, it's good!

Jon

WolframAlpha gives you 2.652×10^25 molecules for "the number of air molecules in one cubic metre". Edit: their description of air: molar mass | 28.96 g/mol phase | gas (at STP) boiling point | -194.5 °C density | 0.001275 g/cm^3 (at 0 °C) I'm not sure how much they consider the composition of "air"

MrTridac

Correct

Pieter Gosselink