Question

The drive-side airbag deploys when a sports car is in a head-on collision. The airbag inflates to a volume of 67.8 L and a pressure of 1.68 atm at 25.0 °C. Calculate the amount of NaN3, in grams, that the manufacturer of the vehicle placed into the gas generator to produce this amount of nitrogen gas. Assume the nitrogen gas behaves as an ideal gas and the only source of the nitrogen gas is the first reaction shown above. A list of physical constants can be found here.

Answer 1

Balanced equation:
2 NaN₃ ====> 2 Na + 3 N₂
Reaction type: decomposition

PV= nRT

P = Pressure in atm = 1.68 atm V= Volume in Liter = 67.8 L

n = no of moles = ? R = 0.0821 L atm K-1 Mol-1

T = Temperature in Kelvin = 273 +25 = 298 K

n = PV/RT = 1.68 x 67.8 / 0.0821 x 298 = 4.655 Moles

Moles of Nitrogen = 4.655 Moles

Moles of NaN3 reacted =  3.103

Mass of NaN3 reacted = 3.103 x 65 = 201.74 gm

Hence 201.74 gm of NaN3 reacted to produce N2 volume of 67.8 L and a pressure of 1.68 atm at 25.0 °C.