When an airbag is activated in a collision, sodium azide rapidly decomposes to produce nitrogen gas. Chemical engineers carefully choose the quantity of sodium azide to produce the required chemical amount of nitrogen gas.
Use the ideal gas law to predict the chemical amount of nitrogen gas required to fill a 44 L airbag at a pressure of 219 kPa and a temperature of 33 oC.
First, we need to determine the number of moles of nitrogen gas required to fill the airbag using the ideal gas law equation:
PV = nRT
where:
- P is the pressure (219 kPa)
- V is the volume (44 L)
- n is the number of moles of gas
- R is the ideal gas constant (8.31 L·kPa/mol·K)
- T is the temperature (33°C + 273 = 306 K)
Rearranging the equation to solve for n:
n = PV / RT
n = (219 kPa * 44 L) / (8.31 L·kPa/mol·K * 306 K)
n = 1.09 mol
Therefore, approximately 1.09 moles of nitrogen gas are required to fill the 44 L airbag at a pressure of 219 kPa and a temperature of 33°C.