Nitric acid, $\mathrm{HNO}_{3}$, is manufactured by the Ostwald process, in which nitrogen dioxide, $\mathrm{NO}_{2}$, reacts with water.
$$
3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)
$$
How many grams of nitrogen dioxide are required in this reaction to produce $7.50 \mathrm{~g} \mathrm{HNO}_{3} ?$