How can the density of air be measured using simple equipment?

[Alettix]

Homework Statement

Measure the density if air at normal atmospheric pressure. You can use the following equipment:

One scale with an accuracy of 0.01g
Two empty glas bottles (≈0,33 liter each)
One big bowl with water
One cork with a valve and a vacuumpump

Homework Equations

Not knowing how to solve this problem I am not sure which equations should be used, but the following could be relevant:
Density: ρ=m/V (1)
Ideal Gas equation: pV=nRT =NkT (2)
Buoyant Force: F=ρgV (3)

The Attempt at a Solution

My first thought was that the exact volume of the bottles can be measured by measuring the weight of the water which fit into them and then by knowing the density of water the volume is obtained. Then, we can meausre the weight of an empty bottel with air in it and without. From this, the mass of the air inside the bottles is obtained and the density of the air is achieved. However, I feel like this is a bit to simple. I don't have the equipment to try this at home. Do you think think this solutions works? Or do you have other ideas?

Thank you for your help! :)

 

[Orodruin]

Why do you think it is too simple?

 

[Alettix]

Why do you think it is too simple?

I thought the mass of the air was too small to be measured, but now I realized that m = 1,293*0,00033 ≈0,43 g.
So maybe this is the solution?

 

[Orodruin]

Yes, it should be enough to at least give you a quite rough estimate.

 

[Alettix]

Yes, it should be enough to at least give you a quite rough estimate.

Well, in that case the problem is solved. Thank you very much! :)