If a sample containing 3.00 ml of nitroglycerin (density=1.592g/ml) is detonated, how many total moles of gas are produced?

To determine the number of moles of gas produced from the detonation, we need to know the reaction that happens. For the detonation of nitrogycerin, the reaction is expressed as:

4C3H5NO9 = 12CO2 + 6N2 + O2 + 10H2O

All of the products from the reaction are gases. So, we need to calculate how much of each product is formed. We do as follows:

Moles C3H5NO9 = 3 mL (1.592 g/mL) (1 mol / 227.09 g) = 0.021 g C3H5NO9

moles CO2 = 0.021 g C3H5NO9 (12 mol CO2 / 4 mol C3H5NO9) = 0.063

moles N2 = 0.021 g C3H5NO9 (6 mol N2 / 4 mol C3H5NO9) = 0.032

moles O2 = 0.021 g C3H5NO9 (1 mol O2 / 4 mol C3H5NO9) = 0.0053

moles H2O = 0.021 g C3H5NO9 (10 mol H2O / 4 mol C3H5NO9) = 0.053

total moles of product = 0.153 moles