What volume, in liters, at STP, is occupied by 3.30 X 10²³ molecules of oxygen gas?

Question

using dimensional analysis

Answer 1

Let's first convert 3.30x10²³ molecules to moles:

3.30x10²³ molecules x 1 mole/6.02x10²³ molecules = 0.548 moles O₂ gas

At STP, 1 mole of any ideal gas will occupy 22.4 liters

0.548 moles x 22.4 liters/mole = 12.28 liters = 12.3 liters (to 3 significant figures)

Answer 2

the dimensional analysis here will have 2 steps ... first you want to convert the given value of molecules to moles, then you can convert from moles to liters at STP

3.30 x 10^23 molecules O2 x (1 mole O2 / 6.022 x 10^23 molecules O2) x (22.4 L / 1 mole)

=3.30 x 22.4 / 6.022 L

=12.275 L

meaning that the volume here is 12.3 L