Question

A vehicle airbag uses a gas generator that contains a mixture of three compounds: NaN3NaN3 , KNO3KNO3 , and SiO2SiO2 . A series of three reactions is used to convert the highly toxic sodium azide, NaN3NaN3 , into N2N2 gas and harmless silicate glass. The nitrogen gas fills up the airbag, causing it to rapidly expand in a head‑on collision.

Balance the reactions involved in the deployment of an airbag by inserting the appropriate coefficients.

reaction 1:

NaN3(s)−→ΔNa(s)+N2(g)NaN3(s)→ΔNa(s)+N2(g)

reaction 2:

Na(s)+KNO3(s)⟶K2O(s)+Na2O(s)+N2(g)Na(s)+KNO3(s)⟶K2O(s)+Na2O(s)+N2(g)

reaction 3:

K2O(s)+Na2O(s)+SiO2(s)⟶K2O3Si(s)+Na2O3Si(s)

The driver‑side airbag deploys when a sports car is in a head‑on collision. The airbag inflates to a volume of 62.3 L and a pressure of 1.57 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 that the nitrogen gas behaves as an ideal gas and the only source of the nitrogen gas is the first reaction shown. A list of physical constants may be helpful.

Answer 1

Given condition, the only source of nitrogen is the first reaction shown,

Given data,

V = 62.3 L

P = 1.57 atm

T = 25.0 + 273 = 298 K

R = 0.0821 L.atm / K.mol

n = ?

Ideal gas equation,

P V = n R T
n = P V / ( R T )

n = 1.57 x 62.3 / ( 0.0821 x 298 )

n = 4.00 mol

Given balanced equation (1)

2 NaN3 (s) --------------> 2 Na (s) + 3 N2 (g)

From the above balanced equation,

3 mol of N2 is produced from 2 mol of NaN3

Then,

4.00 mol of N2 is produced from 4.00 x 2 / 3 = 2.67 mol of NaN3

So,

Moles of NaN3 = 2.67 mol

Molar mass of NaN3 = 23 + 3 ( 14 ) = 23 + 42 = 67.0 g / mol

Mass of NaN3 = Moles x molar mass = 2.67 x 67.0 = 179. g.

Therefore,

Mass of NaN3 = 179. g.