The balanced chemical equation for the synthesis of sulfur trioxide from sulfur dioxide and oxygen is:
2 SO2 + O2 → 2 SO3
From the balanced equation, we can see that for every 2 moles of SO2, 2 moles of SO3 are produced. Therefore, the number of moles of SO2 required to produce 8.5 moles of SO3 is:
8.5 moles SO3 x (2 moles SO2 / 2 moles SO3) = 8.5 moles SO2
So we need 8.5 moles of SO2 to produce 8.5 moles of SO3.
To convert moles to grams, we need to use the molar mass of SO2, which is 64.06 g/mol. Therefore, the mass of SO2 required is:
8.5 moles SO2 x 64.06 g/mol = 544.31 g
So, 544.31 grams of sulfur dioxide are needed to synthesize 8.5 moles of sulfur trioxide.