At standard conditions, one liter of air, 0.21 L of oxygen gas, contains 0.0094 moles of $\rm O_2$. What is the total quantity of oxygen gas molecules in the atmosphere?

  • $\begingroup$ more about accuracy. I have provided an answer to the best accuracy I had, but, likely possible to make much more educated guesses. $\endgroup$
    – ElnorCat
    Jun 26 '20 at 16:04
  • $\begingroup$ Need to be careful here... I don't think your question is really asking about how much gas is in the entire world's atmosphere (which the others answer), but the amount in the atmosphere you are looking at in the 1st sentence (it sounds like a homework question, yes?). If so, what they're really wanting you to do is convert the moles to molecules. You should have learned a conversion ratio value for that... may have a "special" name for a scientist. $\endgroup$ Nov 23 '20 at 23:02
  • $\begingroup$ If it is a hw question, and they are really asking about the entire world's atmosphere, there should be another value for the world's atmosphere given in the assignment that you'll then use. If this is what you're working on, we can try to guide you more... chat may be a good place to get more input. We don't generally just tell you the answer, but want to help you work through it by guiding. $\endgroup$ Nov 23 '20 at 23:05

It is easier to calculate:

  1. The pressure of air on the ocean level is $\approx 100 \rm {kPa}$.
  2. Thus, its weight is $\approx$ 100000N over $1 \rm m^2$.
  3. Considering that the overwhelming majority of the atmosphere is below some km over the surface of the Earth, we can ignore the decrease of the gravity with height.

Now calculate the mass of the air above a square meter (ten tons). And multiple it with the surface of the Earth (in square meters). Then, divide it with the mean molar mass of air and multiple with the partial pressure of $\ce{O2}$ in it ($\approx$ 29%).

  • 1
    $\begingroup$ Change "above" to "below". $\endgroup$
    – Spencer
    Nov 25 '20 at 23:04
  • $\begingroup$ @Spencer Thanks! $\endgroup$
    – peterh
    Nov 26 '20 at 7:29
  • $\begingroup$ “neglige” isn’t a word, but it should definitely be 👍 $\endgroup$
    – Gimelist
    Dec 28 '20 at 8:42
  • $\begingroup$ @Gimelist Yeah :-) But I fixed my English extension. :-) Thanks! $\endgroup$
    – peterh
    Dec 28 '20 at 8:46
  • $\begingroup$ The only problem is that this assumes the same molecular composition throughout the air column. $\endgroup$
    – Spencer
    Dec 28 '20 at 13:05

https://www.newscientist.com/article/mg15020308-500-the-last-word/ says the atmosphere weighs 5 × 10^21 grams. The molar weight of oxygen gas is 32 gram per mole. Based on that estimate for the weight of atmosphere, the total quantity of O2 in atmosphere is around 5*10^21/32 = 1.5625e+20 mole.

  • 1
    $\begingroup$ you forgot to account for the fact oxygen only makes up ~23% of the atmosphere by mass. $\endgroup$
    – John
    Nov 24 '20 at 3:55

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