Answer to Question #169409 in General Chemistry for Dawson

Question

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. How many liters of gas at 307°C and 1.00 atm are formed by the explosive decomposition of 80.3 kg of ammonium nitrate to nitrogen, oxygen, and water vapor? Do not answer in scientific notation.

Answer 1

2NH₄NO₃ → 2N₂ + O₂ + 4H₂O

M(ammonium nitrate) = 80.04 g/mol

$n = \frac{m}{M}$

n(ammonium nitrate) $= \frac{80.3 \times 10^3}{80.04} = 1003.25 \;mol$

n(nitrogen) = n(ammonium nitrate) = 1003.25 mol

n(oxygen) = $\frac{1}{2}$ n(ammonium nitrate) = 501.62 mol

n(water vapor) = 2n(ammonium nitrate) = 2006.5 mol

n(total) = 1003.25 + 501.62 + 2006.5 = 3511.37 mol

Ideal gas law:

pV = nRT

T = 307 + 273 = 580 K

p = 1 atm

R = 0.08206 L×atm/mol×K

$V = \frac{nRT}{p} \\ = \frac{3511.37 \times 0.08206 \times 580}{1} = 167122.95 \;L$

Answer: 167,122.95 L