answer and explanation
the first step is to balance the reaction equation
N₂ + 2O₂ > 2NO₂
now that we have balanced the equation we can calculate the number of moles of nitrogen
mols = mass / molar mass
= 62.7 g/ 14.00g/mol
= 4.48 mols
we see from the balanced equation that the mol ratio of nitrogen and nitrogen oxide is 1:2
therefor the number of mols of nitrogen oxide that will form will be
2 x 4.48 = 8.96 mol of nitrogen oxide.
now that we have the mols we can then calculate the volume using the ideal gas equation
PV =nRT
V = (nRT)/P
= (8.96 x 0.0821 x 620) / 0.72
= 633.5L