How can I find out the number of oxygen atoms that can fit inside a pizza box?

Answer 1

You would need to know the volume of the box, easy enough to get. Then the density of air, to find out the actual amount of air in there. Then the proportion of O2 in the air, I think it is about 18% or so. That will give you the actual mass of oxygen. The rest of it is trivial, honestly. Just do the math. Make sure that the units you use are consistent.

OK, I made a few assumptions and got a viable number. Suppose the box is 2 x 15 x 15 inches. That is 450 cubic inches.

There are 2.54 cm in an inch. So there are 2.54 cubed cm cubed in an inch cubed. 16.387 to be more exact. So there's 16.387 x 450 or 7374.18 cm cubed. This is the same as 7.37418 liters of air. 1000 cm cubed (or ml -- same thing) in a liter.

OK, air density is about 1.2 kg/meter cubed. A meter cubed is 1000 liters. Well, 7.37418 liters goes into a thousand 135.6083 times. So we want to divide 1.2 kg, which is the same as 1200 grams, by 135.6083. You get 8.85 grams of air in that box.

Let us now assume that the proportion of oxygen in there is 20%, and that it is by weight and not by volume. So then one fifth of that 8.85 grams of air is O2. 8.85 divided by 5 is 1.77.

One mole of O2 weighs 31.9988 grams. You have 1.77 grams, which is a small fraction of 31.9988. Namely 0.055315. So you have 0.055315 moles of O2. One mole is 6.02 x 10^23 and each O2 molecule contains 2 atoms.

2 x 0.055315 x 6.02 x 10^23 = 6.6598747453 x 10^22.

Roughly.

Answer 2

If this question is about the most that could fit then it is not about air. There are some possibilities to answer this based on atomic radius. I think if this question is at all practical and not pure theoretical then we should avoid atomic radii. I suggest solid oxygen as a pratical limit as to how many oxygen atoms could fit in a pizza box. The density is 1.55 g / cc.

1.55 g/cc x 6.02e23 atoms / mole x mole/16 g = 5.83 e 22 atoms per cc or 9.56 e 23 per cibic inch

Answer 3

I would go through the following methodology:

1. Decide if you are talking about pure oxygen of oxgen from the air. If it is oxygen in the air, a good approximation is that air is 21% oxygen.

2. Figure out the dimensions of the pizza box in question and find the volume.

3. Assume that the gas in question is at standard temperature and pressure (STP) conditions. Here we know that one mole of any gas occupies 22.4 Liters at STP...i.e. (22.4L / mole). Use this to find the number of moles of gas in the box.

4. Use Avagadro's number (6.02E23 atoms / mole) to convert the molar amount to the number of atoms.

5. Set up the dimensional analysis:

X L of oxygen in box*(1 mole / 22.4L)*(6.02E23 atoms / mole) = Y atoms of oxygen in box

Answer 4

Research Avogadro's number.