If a sample containing 2.00 ml of nitroglycerin (density=1.592g/ml) is detonated, how many total moles of gas are produced?

The overall balanced chemical reaction for this is:

Detonation of Nirtoglycerin 
4 C3H5N3O9 --> 12 CO2 + 6 N2 + O2 + 10 H2O 

Therefore:

2.00 mL x 1.592 g/mL = 3.184 g 
3.184 g / 227.1 /mol = 0.0140 mol nitroglycerin 
4 moles --> 12 + 6 + 1 + 10 = 29 moles of gas 
0.0140 mol x (29/4) = 0.1017 moles of gases or (0.102 mol)