The balanced equation is:

#0.5"N"_2 + 1.5"H"_2 rarr "NH"_3 color(white)(..................................)(1)#

The molecular mass of ammonia, #"NH"_3#, is equal to 14.01 g + 3(1.008 g), or 17.03 g.

#"Moles of ammonia" = "mass in grams"/"molecular mass" ="15.00 g"/"17.03 g/mol" = 15.00/17.03 " mol"#

Therefore, according to equation #(1)#,

#"Moles of nitrogen" = 0.5(15.00/17.03) " mol" color(white)(............) (2)#

The number of moles of nitrogen is calculated by the following equation:

#"Moles of N"_2 = ("mass of nitrogen")/ ("molar mass of nitrogen")#

Thus,

#"Mass of nitrogen" = "moles of N"_2*"molar mass of N"_2 color(white)(...) (3)#

Therefore, from equations #(2)# and #(3)#, we have:

#"Mass of nitrogen" = 0.5(15.00/17.03) " mol" xx "28.02 g/mol" = "12.34 g"#

With kind regards

Dr. Mamdouh Younes

Hamilton, Ontario, Canada