When 4.50 l of hydrogen gas react with an excess of nitrogen gas at standard temperature and pressure, how many liters of ammonia gas will be produced? n2 (g) + 3h2 (g) yields 2nh3 (g)

If the gasses participates in the reaction, and they under the same temperature and pressure,  ratio of their volumes is equal to ratio of the moles of these gasses in the reaction.                               
                                            N2 (g) + 3H2 (g)> 2NH3 (g)   
from reaction                    3 mol                               2 mol   
from the problem               4.5L                                x L

x=4.5*⅔=9/3=3 L

It shows that the experiment is designed properly.