Question

The air bags in your vehicle work using the following sets of reactions:

2NaN₃ → 2Na +3N₂

10Na + 2KNO₃ → K₂O + 5Na₂O + N₂

When your vehicle detects a collision, the sodium azide (NaN₃) is activated (heated up) to start the decomposition reaction. This produces nitrogen gas and sodium metal. The sodium metal produced in the first reaction is then used in the second reaction to produce more nitrogen gas to inflate your airbag in your vehicle.

Say a typical airbag contains 130 g of NaN₃ and the temperatures inside your airbag are around 40°C with a normal air pressure of 1.0 atm.

What volume of N₂ gas is produced when your air bag is deployed (you must consider both reactions as they both produce nitrogen)?

Answer 1

Given ,

Mass of Sodiumazide = 130g

Molecular weight of NaN3 = 65

Moles of NaN3 = mass / molecular weight

= 130 / 65

= 2 moles

From 1st reaction, stoichiometry says , 2 moles of NaN3 produces 2 moles of sodium and 3 moles of N2.

And reaction-2 says, 10 moles of Na produces 1 mole of N2, But we have only 2 moles of Na, so we get (1/10)*2=0.2 moles of N2.

So we will be having 3.4 moles of N2. ( 3 moles from reaction-1 and 0.2 moles from reaction-2)

Therefore, Amount of Nitrogen = 3.2 moles of Nitrogen.

At the given temperature and pressure assume, Nitrogen behaves ideally,

That implies 1 mole N2 occupies, 22.4 L

So, 3.2 moles of N2 occupies = 3.2*22.4 = 71.68 L

Answer = 71.68 Liters.