Stoichiometric relationship between liters and grams

[ptownbro]

My daughter stump me on a question related to liters and grams in stoichiometry. Wondering if someone could help explain.

First we know that 1 mole always eqauls 22.4 liters at STP. And 1 mole also always equals the selected element's atomic mass in grams on the periodic table.

So...

Let's say you're dealing with Oxygen which has an atomic mass of 16 grams.

Therefore:
1 mole of O is 16g
1 mole of O₂ is 32g
1 mole of O₃ is 48g

You multiple the periodic table atomic mass be the number of atoms you have in the given molecule.

Here's the question: Why don't you do that on the liters side too?

Why isn't:
1 mole of O = 22.4 L
1 mole of O₂ = 44.8LL
1 mole of O₂ = 67.2L

If you have more mass wouldn't you have more volume?

 

[Bystander]

First we know that 1 mole of an ideal gas always eqauls 22.4 liters at STP.

1 mole of O = 22.4 L
1 mole of O2 = 44.8LL
1 mole of O2 = 67.2L

You've written formulae for monatomic oxygen, oxygen (diatomic, what we breathe), and ozone. One mole of monatomic oxygen weighs 16 g, and would occupy 22.4 L if it were stable. One mole of diatomic oxygen weighs 32 g, and occupies 22.4 L. One mole of ozone weighs 48 g, and might occupy 22.4 L for a measureable length of time before it decomposes.

 

[ptownbro]

Yes I know that 1 mole of each (O, O₂, and O₃) will all eqaul 22.4L. But why? Why wouldn't their be higher volumes respectively given that their masses are higher?

 

[Bystander]

The volume of an ideal gas depends only on the number of molecules.

 

[Borek]

In ideal gas volume of the molecules is infinitely small - their "own" volume is zero. Because of that observed volume of the gas is not sum of the volumes of the molecules, but depends only on how they bounce of each other, and on the strength with which they push away tank walls (which depends on the number of molecules and their kinetic energy/momentum, which in turn depend only on the temperature).

For real gases volumes of the molecules are no longer negligible, but at STP gases are reasonably close to being almost ideal - volume occupied by the molecules itself is orders of magnitude lower than the volume occupied by the gas. That means the same number of molecules of every gas occupies the same total volume, as it is not the "own" volume of the molecules that matters, but their number and energies.

This approximation - that the same number of moles of every gas occupies the same volume - fails when the conditions are such that the gas can be no longer treated as ideal - that means very low temperatures and high pressures.

 

[ptownbro]

Ok. Thanks all for your responses. I think I've got it.

 

[Heliosphan]

The size of gas molecules are negligible when dealing with ideal gas laws. Unless it's super cold, or at a really low pressure when there isn't a lot of energy, they just take up the volume of their system. Or at least that's what I understood from my class.

 

[Borek]

or at a really low pressure

High pressure.