I've had another go at the question. If i use the formula for the entropy change of a system s = nRln(vf/vi) and use it in the case of irreversible free expansion, w = 0 -> q=0 so entropy change in the surroundings = 0. Therefor total entropy change is just given by nRln(vf/vi) it's self. So...
1 mole of an ideal gas is compressed isothermally from 1 to 10 bar at 298 K. Calculate the total entropy change associated with this process if it is carried out
1) Reversibly
2) Irreversibly
S (system) =nRln(vf/vi) for an isothermal process.
I think I am getting a bit...