The balanced chemical equation is:
\[
2 \mathrm{NO} + 5 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3} + 2 \mathrm{H}_{2} \mathrm{O}
\]
From the equation, 2 moles of \(\mathrm{NO}\) produce 2 moles of \(\mathrm{NH}_{3}\). Therefore, the conversion factor is:
\[
\frac{2 \text{ moles } \mathrm{NH}_{3}}{2 \text{ moles } \mathrm{NO}}
\]
Calculate the moles of \(\mathrm{NH}_{3}\) from 28 moles of \(\mathrm{NO}\):
\[
28 \text{ moles } \mathrm{NO} \times \frac{2 \text{ moles } \mathrm{NH}_{3}}{2 \text{ moles } \mathrm{NO}} = 28 \text{ moles } \mathrm{NH}_{3}
\]
From the equation, 5 moles of \(\mathrm{H}_{2}\) produce 2 moles of \(\mathrm{NH}_{3}\). Therefore, the conversion factor is:
\[
\frac{2 \text{ moles } \mathrm{NH}_{3}}{5 \text{ moles } \mathrm{H}_{2}}
\]
Calculate the moles of \(\mathrm{NH}_{3}\) from 45 moles of \(\mathrm{H}_{2}\):
\[
45 \text{ moles } \mathrm{H}_{2} \times \frac{2 \text{ moles } \mathrm{NH}_{3}}{5 \text{ moles } \mathrm{H}_{2}} = 18 \text{ moles } \mathrm{NH}_{3}
\]
The limiting reagent is the reactant that produces the lesser amount of product. From the calculations:
- \(\mathrm{NO}\) can produce 28 moles of \(\mathrm{NH}_{3}\).
- \(\mathrm{H}_{2}\) can produce 18 moles of \(\mathrm{NH}_{3}\).
Thus, \(\mathrm{H}_{2}\) is the limiting reagent because it produces fewer moles of \(\mathrm{NH}_{3}\).
- The number of moles of \(\mathrm{NH}_{3}\) that can form is \(\boxed{18 \text{ moles}}\).
- The limiting reagent is \(\boxed{\mathrm{H}_{2}}\).