Ammonium nitrate, a common fertilizer, is used as an explosive in fireworks and by terrorists. It was the material used in the tragic explosion at the Oklahoma City federal building in 1995....

Question

How many liters of gas at 307°C and 1.00 atm are formed by the explosive decomposition of 86.6 kg of ammonium nitrate to nitrogen, oxygen, and water vapor?

Do not answer in scientific notation.

Answer 1

The balance reaction is 2NH4NO3 -------> 4N2 + O2 + 4H2O all in the gas phase.

First calculate the # of moles of NH4NO3.

Molecular mass of NH4NO3 = 80. # moles NH4NO3 = 86600 g / 80 g/mole = 1082.5 moles.

Now, calculate the # of moles of each gaseous product using the following formulas:

4N2 / 2NH4NO3 x 1082.5 moles NH4NO3 = 2165 moles N2

1 O2 / 2NH4NO3 x 1082.5 moles NH4NO3 = 541.3 moles O2

4H2O / 2NH4NO3 x 1082.5 moles NH4NO3 = 2165 moles H2O vapor

The total volume can be determined by V = nRT/P for each gas produced.

V_n2 = 2165 x 0.0821 x 580K / 1 atm = 2165 x 47.6 = 103093 L

V_O2 = 541.3 x 47.6 = 25766 L

V_H2O = 2165 x 47.6 = 103093 L

Total volume = 103093 + 25766 + 103093 = 231952 L

I used rounded numbers for atomic masses. Check calculations using more exact masses and round to the required number of significant figures.