Seems to me like you might have too many unknowns to solve this, but assuming that we can use the molar volume of a gas for V then your molar mass should be 35.65249 g/mol which is pretty close to Chlorine.
The molar volume of a gas is 22.4 liters, so your equation would be:
(1.086 atm)(22.4L)/(0.0821 L*atm/mol*K)(229.9K)=n
n will be your number of moles which works out to be 1.289 mol.
you divide your given mass of 45.95 grams by the 1.29 mol to get a molar mass of 35.62 grams/mol. Chlorine (which is a gas at most temperatures) has a molar mass of 35.45 grams/mol.
But where I think this might all fall apart is that I believe that the stated temperature is just shy of Chlorine's vaporization point. So unless I'm mistaken, at that temperature and pressure, Chlorine should be a solid.
It's been like 3 years since I was in Gen Chem so you'll understand if I'm wrong here.
SLC