When the Control Module activates the airbag assembly, an electric current is sent to the detonator, which ignites the sodium azide pellets. When it burns, it releases nitrogen gas very quickly and in large quantities. This is what inflates the airbag.
Sodium Azide is Rocket Fuel.
Sodium azide is the fuel of choice for a number of reasons. It is a solid propellant with a very high gas generation ratio. It is very stable in this application.
When Sodium azide burns, it's major product is Nitrogen gas, which makes up around 78% of the Earth's atmosphere. One of the other by-products is sodium hyxdroxide. This is commonly known as Lye, which is a caustic compound. The quantities produced are very small and present a very small risk of burns. The white powder residue seen after inflation is common corn starch, used as a lubricant for expansion of the airbag. Testing is underway with inflators that release argon gas. When I know more I'll update you.
Around 1991 TRWTM, the company that makes a large number of the airbags in vehicles in use, located one of the first 1973 Chevrolet Impalas that was made with a driver's side airbag. They reconnected the battery and stimulated the crash sensors. Lo and Behold the airbag worked perfectly. There is not a whole lot else on a car that, with no maintenance required, will last 18+ years.
As of this writing, the National Highway Traffic Safety Administration has made a ruling allowing manufacturers to put lower powered bags in vehicles. These are appearing as "Second Generation Airbags".The manufacturers are also working on smart systems to vary the power of the bags, for the weight of the occupants.