Air bags are actived when a servere impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide (NaN3) to decompose explosively according to the following reaction:
2NaN3=2Na(s)+3N2(g)
what mass of NaN3(s) must be reacted to inflate an air bag to 70.0L at 0C and 1.00atm??
Use PV = nRT to calculate n = number of moles N2 needed, then use this example of a stoichiometry problem I've posted to go through the remainder of the problem. You can dispense with step 1, writing the equation.
http://www.jiskha.com/science/chemistry/stoichiometry.html
To determine the mass of NaN3 required to inflate an airbag, you'll need to use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = the ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
To solve this problem, you'll need to follow these steps:
Step 1: Convert the given temperature to Kelvin.
0°C + 273 = 273K
Step 2: Rearrange the ideal gas law equation to solve for moles.
n = PV / RT
Step 3: Calculate the moles of N2 gas.
n(N2) = (1.00 atm) * (70.0L) / (0.0821 L·atm/mol·K * 273K)
Step 4: Determine the stoichiometry of the reaction.
From the balanced equation: 2 NaN3 = 2 Na + 3 N2
The molar ratio of NaN3 to N2 is 2:3. That means for every 3 moles of N2 produced, 2 moles of NaN3 are required.
Step 5: Calculate the moles of NaN3 required.
n(NaN3) = (2/3) * n(N2)
Step 6: Convert moles of NaN3 to mass using the molar mass.
The molar mass of NaN3 is calculated by adding the atomic masses of each element:
Molar mass of Na = 22.99 g/mol
Molar mass of N = 14.01 g/mol
Molar mass of NaN3 = (22.99 g/mol) + 3(14.01 g/mol)
Step 7: Calculate the mass of NaN3 required.
mass(NaN3) = n(NaN3) * molar mass(NaN3)
By following these steps, you can now calculate the mass of NaN3 required to inflate the airbag to the given volume, pressure, and temperature.