Automobile airbags

Question

Automobile airbags contain solid sodium azide, NaN 3 , that reacts to produce nitrogen gas when heated, thus inflating the bag. 2 NaN 3 ( s ) ⟶ 2 Na ( s ) + 3 N 2 ( g ) Calculate the value of work, w , for the system if 22.0 g NaN 3 reacts completely at 1.00 atm and 22 ∘ C.

Answer 1

2NaN₃(s) ==> 2Na(s) + 3N₂(g) .. balanced equation

w = -P∆V

w = work = ?

P = pressure = 1.00 atm

∆V = change in volume (see calculation below)

In order to find the change in volume, we will use the ideal gas law PV = nRT, but before we do that, we will need to determine the moles of N₂ gas formed in the above reaction.

molar mass NaN₃ = 65.0 g / mol

moles NaN₃ reacted = 22.0 g x 1 mol / 65.0 g = 0.338 mols NaN₃

moles N₂ produced = 0.338 mols NaN₃ x 3 mols N₂ / 2 mol NaN₃ = 0.508 mols N₂ formed

PV = nRT

Volume N₂ = V = nRT/P = (0.508 mol)(0.0821 Latm/Kmol)(295K)/1.00 atm

Volume N₂ = 12.3 L

Now, back to our work equation

w = -P∆V

w = -(1.00 atm)(12.3 L)

w = - 12.3 Latm

We can convert this value to joules using the factor that 1 Latm = 101.325 joules

w = -12.3 Latm x 101.325 J / L atm

w = - 1246 J (negative because the system is doing work on the surroundings).