Problem: Ammonium nitrate decomposes explosively upon heating according to the following balanced equation: 2 NH4NO3(s) → 2 N2(g) + O2(g) + 4 H2O(g). Calculate the total volume of gas (at 126˚C and 751 mmHg) produced by the complete decomposition of 1.56 kg of ammonium nitrate.

FREE Expert Solution

Recall the Ideal Gas Law equation:

$\overline{){\mathbf{PV}}{\mathbf{=}}{\mathbf{nRT}}}$

Step 1. mol reactant

molar mass of NH4NO3 = 80.043 g/mol

16.2 mol

Step 2. volume of each product

$\mathbf{PV}\mathbf{=}\mathbf{nRT}\phantom{\rule{0ex}{0ex}}\frac{\overline{)\mathbf{P}}\mathbf{V}}{\overline{)\mathbf{P}}}\mathbf{=}\frac{\mathbf{nRT}}{\mathbf{P}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{nRT}}{\mathbf{P}}}$

P = 751 mmHg = 0.988 atm
T = 126˚C + 273.15 = 399.15 K
R = 0.08206 (L·atm)/(mol·K)

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Problem Details

Ammonium nitrate decomposes explosively upon heating according to the following balanced equation: 2 NH4NO3(s) → 2 N2(g) + O2(g) + 4 H2O(g). Calculate the total volume of gas (at 126˚C and 751 mmHg) produced by the complete decomposition of 1.56 kg of ammonium nitrate.