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.

1.57 mol NaN₃

Explanation:

First we use PV=nRT to calculate the number of N₂ moles that need to be produced:

Inputing the data:

And solving for n:

Finally we convert N₂ moles into NaN₃ moles, using the stoichiometric coefficients of the balanced reaction:

a sequence is a function whose domain is the set of natural numbers.

natural numbers are all the negative and positive integers