Given:

mass, m = 14g

Molar mass of N\(_2\) = 14 X 2 = 28g/mol

number of moles, n = ?

But n = \(\frac{m}{M}\) = \(\frac{14}{28}\) 

 n = 0.5 mole

Also, recall that Number of moles = \(\frac{Number of Molecules}{Avogadro number}\)

  n  = \(\frac{N}{L}\)

  N = n x L

 = 0.5 x 6.02 x  10\(^{23}\)

 = 3.01 x 10\(^{23}\) molecules