Ammonium dinitramide (AND), NH_4N(NO_2)_2, is being considered as a possible rep

Question

Ammonium dinitramide (AND), NH_4N(NO_2)_2, is being considered as a possible replacement for ammonium per chlorate as the oxidizer in the solid fuel booster rockets used to launch space shuttles. When detonated by a spark, ADN rapidly decomposes to produce a gaseous mixture of N_2, O_2, and H_2O. This is not a combustion reaction because ADN only reactant. The reaction releases a large amount of heat, so the gases are initially is the formed at a high temperature and pressure. The thrust of the rocket results mainly from the expansion of this gas mixture. Suppose a 1.6-kg sample of ADN is detonated and decomposes completely to give N_2.O_2, and H_2O. If the resulting gas mixture expands until it reaches a temperature of 100.0 degree C and a pressure of 1.00 atm, what volume will it occupy?

Explanation / Answer

NH4N(NO2)2 molar mass = 124.06 g / mol

moles of NH4N(NO2)2   = 1.6 x 10^3 / 124.06 = 12.9

NH4N(NO2)2 ----------------------> 2 N2 + 2 H2O + O2

1 mol                                             2mol      2 mol      1 mol

12.9                                              25.8        25.8       12.9

total moles of gaseous product formed = 25.8 + 25.8 + 12.9 = 64.5

n = 64.5

P   = 1 atm

T = 100 + 273 = 373 K

P V = n R T

1 x V = 64.5 x 0.0821 x 373

V = 1975 L

volume of gasesous will occupy = 1975 L

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