Airbags contain a mixture of sodium azide, potassium nitrate, and silicon dioxide. A sensor detects a head on collision that cause the sodium azide to be ignited and to decompose forming sodium and nitrogen gas. This gas fills a nylon or polyamide bag such that the front face of the bag travels at a velocity of 150 to 250 miles per hour. This process, from the initial impact of the crash to full inflation of the airbag, takes only about 40 milliseconds. Sodium is very dangerous so the sodium reacts with potassium nitrate present to produce potassium oxide (K2O), sodium oxide (Na2O), and additional N2 gas. The N2 generated in this second reaction also fills the airbag. The metal oxides react with silicon dioxide (SiO2) in a final reaction to produce silicate(glass), which is harmless and stable.
a. Write a balanced chemical equation for the first reaction in the airbag gas generator (the decomposition of NaN3).
b. Write a balanced equation for the net gas-generating reactions (the combination of the first and second reactions).
c. If a car has an airbag that has a volume of 60.0L and the bag requires a pressure of 2.37 atm at 25.00C, calculate the grams of sodium azide needed to inflate the bag.