It turns out that the Van Dar Waals constant b is equal to four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms:
a) at STP
b) at 100 atm pressure and 0 degrees Celsius
((Assume for simplicity that the idealgas equation still holds.))
Ar
a= 1.34
b = 0.0322
I'm extremely confused about this question, are they asking for the volume when they state fraction of the volume.

The units of b are liters/mole. So the actual molecules in a liter of Argon occupy b/4 or 0.008 liters.
At STP, the (mostly empty) space occupied by gas is 22.4 liters.
For the fraction, take the ratio.
Then do the same thing for the 100 atm case. The volume occupied (including space between atoms) will be 100 times less than at 1 atm STP, or 0.224 liters.

Therefore, they are asking for the volume
(a) at STP
v = 22.4 L
T = 273 K
P = 1 atm
Would I use Van der Waals equation for (a) or for (b)? I think I would have to use this equation for b
(a) V = nRT/ P
Can I use this for question a

Okay, then what equation can I use for (a)
Instead of using the idealgas equation,
can I use the molefraction
By stating "For the fraction, take the ratio. " does this apply to the molefraction

You should take the ratio of the computed volumes.
0.008/22.4 in the first case
It doesn't make sense to talk about the mole fraction of solid spheres

Okay but wait we can find the number of moles using PV = nRT? Right?
V = 22.4 L
P = 1 atm
R= 0.0831 Latm
T = 273 K