Question

The air bags in automobiles were once inflated by nitrogen gas generated by the rapid decomposition of

sodium azide, NaN3.

2 NaNz (s) 2 Na (s) + 3 N2 (g)

If an air bag has a volume of 53.4 L and is to be filled with nitrogen gas at a pressure of 1.07 atm and a
temperature of 23.7°C, how many moles of NaNz must decompose? You may assume the Ny behaves as
an ideal gas.

Answer 1

1.57 mol NaN₃

Step-by-step explanation:

• 2 NaN₃ (s) → 2 Na (s) + 3 N₂ (g)

First we use PV=nRT to calculate the number of N₂ moles that need to be produced:

• P = 1.07 atm

• V = 53.4 L

• n = ?

• R = 0.082 atm·L·mol⁻¹·K⁻¹

• T = 23.7 °C ⇒ 23.7 + 273.16 = 296.86 K

Inputing the data:

• 1.07 atm * 53.4 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 296.86

And solving for n:

• n = 2.35 mol N₂

Finally we convert N₂ moles into NaN₃ moles, using the stoichiometric coefficients of the balanced reaction:

• 2.35 mol N₂ *
  `(2molNaN_3)/(3molN_2)` = 1.57 mol NaN₃