Ammonium nitrate a common fertilizer was used by terrorists in the trgic explosion in oklahoma city in 1995.how many litres of gas at 307oc and 1.00atm are formed by the explosive decomposition of 15kg of ammonium nitrate to nitrogen, oxygen and water vapour
Solution
2NH4NO3=2N2 + O2 + 4H2O
mols NH4NO3 = grams/molar mass = ? This is approx 180 but that's just an estimate. You need a more accurate answer.
Then mols N2 formed = 180 x (2 mols N2/2 mols NH4NO3) = approx 180.
mols O2 formed = 180 x (1 mol O2/2 mols NH4NO3) = approx 180/2 = approx 90
mols H2O (gas) formed = 180 x (4 mols H2O/2 mols NH4NO3) = 180 x 2 = approx 360.
Now add mols N2 gas to mols O2 gas to mols H2O gas to find total mols gas. Then use PV = nRT at the conditions listed to find total volume in liters.
To find the number of liters of gas formed by the explosive decomposition of ammonium nitrate, we need to use the given balanced equation:
2NH4NO3 = 2N2 + O2 + 4H2O
First, let's calculate the moles of ammonium nitrate (NH4NO3) using its molar mass, which is 80.043 amu (grams per mole):
Molar mass of NH4NO3 = (1 x molar mass of N) + (4 x molar mass of H) + (3 x molar mass of O)
= (1 x 14.007 amu) + (4 x 1.008 amu) + (3 x 16.00 amu)
= 80.043 amu
Given mass of ammonium nitrate = 15 kg = 15000 grams
Moles of NH4NO3 = Mass of NH4NO3 / Molar mass of NH4NO3
= 15000 g / 80.043 g/mol
= 187.45 mol
According to the balanced equation, 2 moles of NH4NO3 decompose to form 1 mole of O2 gas. Therefore, the number of moles of O2 gas produced is:
Moles of O2 = (Moles of NH4NO3 / 2)
= 187.45 mol / 2
= 93.73 mol
Using the ideal gas law, we can calculate the volume of gas at given conditions:
PV = nRT
Where:
P = pressure of gas (1.00 atm)
V = volume of gas (to be calculated)
n = number of moles of gas (93.73 mol)
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature of gas in Kelvin (307°C = 307 + 273.15 = 580.15 K)
Rearranging the equation, we have:
V = nRT / P
= (93.73 mol) * (0.0821 L.atm/mol.K) * (580.15 K) / (1.00 atm)
= 4770.55 L
Therefore, approximately 4770.55 liters of gas at 307°C and 1.00 atm are formed by the explosive decomposition of 15 kg of ammonium nitrate to nitrogen, oxygen, and water vapor.