Question

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

Answer 1

`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.