If a sample containing 2.50 ml of nitroglycerin (density=1.592g/ml) is detonated, how many total moles of gas are produced?

Density = mass / volume
mass of nitroglycerin  = density x volume = 1.592 x 2.5 = 3.98 grams
molar mass of nitroglycerin = 3(12) + 5(1) + 3(14) + 9(16) = 227 grams
number of moles reacting = mass / molar mass = 3.98/227 = 0.017 moles

The balanced chemical equation for this reaction is as follows:
4C3H5N3O9 > 12CO2(g) + 6N2(g) + O2(g) + 10H2O(g)

From the balanced equation:
4 moles of nitroglycerin produces a total of 12 + 6 + 1 + 10 = 29 moles of gas.
Therefore:
0.017 moles of nitroglycerin produces a total of:
(0.017 x 29) / 4 = 0.12325 moles of gases