4 C3HsN309 (1) 12 CO2 (g) + 6 N2 (g) +10 H20 (g) + 02(g) What volume is occupied by all of the gases produced when 1.00 kg of nitroglycerin explodes? The total pressure is 1.54 atm at 423°C

1 Answer
Mar 5, 2018

#1184.98"L"# of gas is produced.

Explanation:

We know that the reaction is:

#4"C"_3"H"_5"N"_3"O"_9rarr12"CO"_2+6"N"_2+10"H"_2"O"+"O"_2#

The molar mass of nitroglycerin is #227.09"g/mol"#, and we have #1000"g"# of it. Converting to moles:

#n=1000/227.09=4.404"mol"#

We see that on the reactants side, #4# moles of reactant exist, and on the products side, #12+6+10+1=29# moles of product is formed.

So the ratio between the two is #4:29#. Say #x# moles of product are produced. Then:

#4/29=4.404/x#

#x=(29*4.404)/4#

#x=31.929"mol"# of product is formed.

According to the Ideal Gas Law:

#PV=nRT#

Here, #P=1.54"atm"#, #n=31.929"mol"#, #T=696.15"K"# and #R=0.0821"L atm K"^-1"mol"^-1#

Rearranging to solve for #V#:

#V=(nRT)/P# and inputting:

#V=(31.929*0.0821*626.15)/1.54#

#V=1184.98"L"# of gas is produced.