Question

In the Contact Process for the manufacture of tetraoxosulfate(VI) acid, $44.8\text{ dm}^3$ of sulfur(IV) oxide ($SO_2$) gas measured at standard temperature and pressure (STP) is reacted with excess oxygen over a vanadium(V) oxide ($V_2O_5$) catalyst. If the catalytic conversion efficiency of $SO_2$ to sulfur(VI) oxide ($SO_3$) is $85\%$, and all produced $SO_3$ is subsequently absorbed in concentrated $H_2SO_4$ and hydrated to form pure $H_2SO_4$, what mass of pure $H_2SO_4$ in grams is produced? (Molar mass of $H_2SO_4 = 98\text{ g mol}^{-1}$, Molar volume of gas at STP $= 22.4\text{ dm}^3\text{ mol}^{-1}$)