Question

A vehicle airbag uses a gas generator that contains a mixture of three compounds: NaN3, KNO3, and SiO2. A series of three reactions is used to convert the highly toxic sodium azide, NaN3, into N2 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.

1. NaN3(s)--> Na(s)+N2(g)

2. Na (s)+ KNO3(s)--> K2O(s)+N2(g)

3. K2O(s)+Na2O(s)+SiO2(s) --> K2O3Si(s)+Na2O3Si(s)

The drive-side airbag deploys when a SUV is in a head-on collision. The airbag inflates to a volume of 67.8 L and a pressure of 1.08 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.

g?

Answer 1

From ideal gas law,

PV = nRT

where,

P = pressure of the gas = 1.08 atm

V = volume of the gas = 67.8 L

T = temperature of the gas = 25 ^oC = (273 + 25) = 298 K

n = moles of the gas

R = gas constant = 0.0821 L.atm/mol.K

Now, substituting these values in the above equation to get,

1.08 x 67.8 = n x 0.0821 x 298

or, n = 3

Hence, the mol of N₂ gas produced in the reaction = 3 mol

Now,

2 NaN₃ $\rightarrow$ Na + 3 N₂

From this balanced equation, it is clear that 3 mol of N₂ is formed from 2 mol of NaN₃.

Molar mass of NaN₃ = 65 g/mol

Hence, the amount of NaN₃ that the manufacturer placed in gas generator = 2 x 65

                                                                                                                       = 130 g