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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.

Respuesta :

maacastrobr

Answer:

1.57 mol NaN₃

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 * [tex]\frac{2molNaN_3}{3molN_2}[/tex] = 1.57 mol NaN₃

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