ammonia is produced by the reaction of hydrogen and nitrogen according to this balanced equation:?

The molecular weight of nitrogen is 14.0 so the molecular weight of nitrogen gas (N2) is 28.0.

13.4 grams / 28.0 grams per mol = 0.478 mols of N2.

Here's 1/2 mole on N2 per mole of NH3 so 0.478*2 = 0.957 moles of NH3

The molecular weight of NH3 is 17.0 so 0.957 * 17.0 = 16.3 grams.

I'm guessing that they provided a number on the grams of nitrogen because this reaction occurred in an excess of hydrogen.  If there wasn't any hydrogen present, then the reaction wouldn't take place, obviously.  Since we are given the amount of limiting reactant, we can simply find the number of moles of the limiting reactant ( 13.4/28.02=.478mol N2).  Then, we use mole ratios to go from reactant to product.  (2 mol NH3/1 mol N2 =.9568mol NH3).  This is the moles of ammonia produced.  Then, convert this into grams: (.9568mol NH3 * (17.02g/mol))=16.29g NH3

N = 14 g/mol
N2 = 28 g/mol
NH3 = 17 g/mol
From the equation you can see for every mole of N2 it makes two moles of NH3

If you have 13.4 g of N2 ,

13.4g / 28 g/mol = 0.48 mole of N2 gas

Since every mole of N2 makes 2 moles of NH3:
0.48 mole * 2 = 0.96 mole of ammonia are made

0.96 mole NH3 * 17 g/mol NH3  = 16.27 grams of NH3 produced