Question

Ammonium nitrate decomposes explosively upon heating according to the following balanced equation: 2NH4NO3(s)→2N2(g)+O2(g)+4H2O(g)

a.) Calculate the total volume of gas (at 121 ∘C and 767 mmHg ) produced by the complete decomposition of 1.62 kg of ammonium nitrate.

Answer 1

Molar mass of NH4NO3,

MM = 2*MM(N) + 4*MM(H) + 3*MM(O)

= 2*14.01 + 4*1.008 + 3*16.0

= 80.052 g/mol

mass of NH4NO3 = 1.62 Kg = 1.62*10^3 g

mol of NH4NO3 = (mass)/(molar mass)

= 1.62*10^3/80.05

= 20.24 mol

According to balanced equation

mol of gas formed = (7/2)* moles of NH4NO3

= (7/2)*20.24

= 70.83 mol

Given:

P = 767.0 mm Hg

= (767.0/760) atm

= 1.0092 atm

n = 70.83 mol

T = 121.0 oC

= (121.0+273) K

= 394 K

use:

P * V = n*R*T

1.0092 atm * V = 70.83 mol* 0.08206 atm.L/mol.K * 394 K

V = 2269.15 L

Answer: 2.23*10^3 L