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PV=kT, so V/T = k/P and is constant if P is constant. So, you want V such that
V/283 = V'/313
So, what is V'? 6.4g of SO2 is 0.1 moles, and will occupy 2.24L
V/283 = 2.24/313
Now, having V, you can see that you will have V/22.4 moles of Cl2, and each mole has a mass of 70.9 grams