Please see the attached file.

How would I figure out the work performed by a piston assembly that changes the volume of 5 grams of nitrogen from Vi=0.03 cubic meters to Vf=0.75 cubic meters isothermally at room temperature? I know that nitrogen is a diatomic molecule.
I have tried the equation:
w=nRT lnVf/Vi but am not coming up with any of the possible answers. Am I missing something in the equation?

You are almost there.
For a isothermal process,
(a)
The work done is
(b)
Substitute (a) into (b)

(c)
Now we need to find n, R, T
The molecular weight of N2 is 28 grams/mole.
So the moles of 5 grams N2 is

The room temperature
The gas constant is
Vi = 0.03 m3, Vf = 0.75 m3
Plug the above values into (c)

So the work done is 1400.25 J.