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 68 L airbag at a pressure of 242 kPa and a temperature of 29 oC.
** MAKE SURE TO HAVE THE CORRECT SIGNIFICANT DIGITS **
The amount of nitrogen required is mol
To solve this problem, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in Pascal)
V = volume (in liters)
n = amount of substance (in moles)
R = ideal gas constant (8.31 J/mol*K)
T = temperature (in Kelvin)
First, we need to convert the given pressure and temperature values to the correct units:
242 kPa = 242000 Pa
29°C = 29 + 273 = 302 K
Now we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
n = (242000 Pa)(68 L) / (8.31 J/mol*K)(302 K)
n = 16696800 / 2502.62
n ≈ 6661.04 moles
Therefore, the amount of nitrogen required to fill a 68 L airbag at a pressure of 242 kPa and a temperature of 29°C is approximately 6661.04 moles.