I hope you paid attention in math and chemistry:
Inside the airbag is a gas generator containing a mixture of NaN3, KNO3, and SiO2. When the car undergoes a head-on collision, a series of three chemical reactions inside the gas generator produce gas (N2) to fill the airbag and convert NaN3, which is highly toxic (The maximum concentration of NaN3 allowed in the workplace is 0.2 mg/m3 air.), to harmless glass (Table 1). Sodium azide (NaN3) can decompose at 300oC to produce sodium metal (Na) and nitrogen gas (N2). The signal from the deceleration sensor ignites the gas-generator mixture by an electrical impulse, creating the high-temperature condition necessary for NaN3 to decompose. The nitrogen gas that is generated then fills the airbag. The purpose of the KNO3 and SiO2 is to remove the sodium metal (which is highly reactive and potentially explosive, as you recall from the Periodic Properties Experiment) by converting it to a harmless material. First, the sodium reacts with potassium nitrate (KNO3) to produce potassium oxide (K2O), sodium oxide (Na2O), and additional N2 gas. The N2 generated in this second reaction also fills the airbag, and the metal oxides react with silicon dioxide (SiO2) in a final reaction to produce silicate glass, which is harmless and stable. (First-period metal oxides, such as Na2O and K2O, are highly reactive, so it would be unsafe to allow them to be the end product of the airbag detonation.)
The airbag's acceleration (a) can be computed from the velocities and distance moved (d) by the following formula encountered in any basic physics text:
vf2 - vi2 = 2ad.
Substituting in the values above,
(89.4 m/s)2 - (0.00 m/s)2 = (2)(a)(0.300 m)
a = 1.33x104 m/s2.
The force exerted on an object is equal to the mass of the object times its acceleration (F = ma) ; therefore, we can find the force with which the gas molecules push a 2.50-kg airbag forward to inflate it so rapidly. 2.5 kg is a fairly heavy bag, but if you consider how much force the bag has to withstand (see Figure 5), it becomes apparent that a lightweight-fabric bag would not be strong enough. Note: In the calculation below, we are assuming that the airbag is supported in the back (i.e., all the expansion is forward), and that the mass of the airbag is all contained in the front face of the airbag.
F = ma
F = (2.50 kg)(1.33x104 m/s2)
F = 3.33x104 kg·m/s2 = 3.33x104 N.
Pressure is defined as the force exerted by a gas per unit area (A) on the walls of the container (P = F/A), so the pressure (in Pascals) in the airbag immediately after inflation can easily be determined using the force calculated above and the area of the front face of the airbag (the part of the airbag that is pushed forward by this force). Note: The pressure calculated is gauge pressure.
The amount of gas needed to fill the airbag at this pressure is then computed by the ideal-gas law. Note: the pressure used in the ideal gas equation is absolute pressure. Gauge pressure + atmospheric pressure = absolute pressure.