Question

12. Liquid nitroglycerin is a shock sensitive compound that produces gases in an exothermic (heat releasing) reaction shown below.

4C₃H₅(NO₃)₃ (l) → 6N₂(g) + 10H₂O (g) + 12CO₂ (g) + O₂ (g)

If 16 ounces (454 g) of nitroglycerin is detonated in a 0.500 L container and the temperature of all the gases produced is 175 oC, what is the total pressure in the container?

(a) 417 atm

(b) 805 atm

(c) 1070 atm

(d) 208 atm

Answer 1

molar mass of nitroglycerin = 227 gm/mol then 454 gm of nitroglycerin = 454/227 = 2 mole

Accordding to reaction 4 mole of nitroglycerin produce 6 mole of N₂ then 2 mole of nitroglycerin produce 3 mole of N₂

Accordding to reaction 4 mole of nitroglycerin produce 10 mole of H₂O then 2 mole of nitroglycerin produce 5 mole of H₂O

Accordding to reaction 4 mole of nitroglycerin produce 12 mole of CO₂ then 2 mole of nitroglycerin produce 6 mole of CO₂

Accordding to reaction 4 mole of nitroglycerin produce 1 mole of O₂ then 2 mole of nitroglycerin produce 0.5 mole of O₂

total mole of the gas produced = 3 mole of N₂ + 5 mole of H₂O +  6 mole of CO₂ +  0.5 mole of O₂ = 14.5 mole of gas

use ideal gas equation to calculate pressure

Ideal gas equation

PV = nRT             where, P = atm pressure= ?

V = volume in Liter = 0.5 L

n = number of mole = 14.5 mol

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 175⁰C = 273.15+ 175 = 448.15 K

We can write ideal gas equation

P = nRT/V

Substitute value in above equation

P = 14.50.08205448.15 / 0.5 = 1066.35atm

total pressure in container is 1066.35 atm