28.0134 grams.
One mole of any element is the atomic weight of that element. And since a nitrogen molecule has 2 nitrogen atoms, then you have 2 moles of nitrogen atoms in a mole of nitrogen molecules. So, since the atomic weight of nitrogen is 14.0067 g/mol, the mass of a mole of nitrogen molecules is 2 mol * 14.0067 g/mol = 28.0134 g.