(C) The balanced chemical equation for the reaction is:
$4 NH_{3(g)} + 5 O_{2(g)} \rightarrow 4 NO_{(g)} + 6 H_{2}O_{(g)}$
From the stoichiometry:
$4 \times 17 \, g$ of $NH_{3}$ $(68 \, g)$ reacts with $5 \times 32 \, g$ of $O_{2}$ $(160 \, g)$ to produce $4 \times 30 \, g$ of $NO$ $(120 \, g)$.
Calculate the limiting reagent:
For $10.00 \, g$ of $NH_{3}$,the required $O_{2} = \frac{160 \, g \, O_{2}}{68 \, g \, NH_{3}} \times 10.00 \, g \, NH_{3} \approx 23.53 \, g \, O_{2}$.
Since only $20.00 \, g$ of $O_{2}$ is available,$O_{2}$ is the limiting reagent.
Calculate the yield of $NO$ based on the limiting reagent $(O_{2})$:
$160 \, g$ of $O_{2}$ produces $120 \, g$ of $NO$.
Therefore,$20.00 \, g$ of $O_{2}$ produces $\frac{120 \, g \, NO}{160 \, g \, O_{2}} \times 20.00 \, g \, O_{2} = 15.00 \, g$ of $NO$.