Anthony T. answered • 02/28/21

Patient Math & Science Tutor

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.