Solid sodium azide (NaN3) is used in air bags to fill them quickly upon impact. The solid NaN3 undergoes a decomposition reaction to produce Na(s) and N2(g).
a. Provide the balanced equation for the decomposition of NaN3.
b. What mass, in grams, of NaN3 is needed to fill the air bag of a vehicle to a volume of 79.0 L at 32.0 °C and 0.97 atm?
a. To provide the balanced equation for the decomposition of NaN3, we need to determine the stoichiometric coefficients of each component.
The decomposition of NaN3 is represented by the following balanced equation:
2 NaN3(s) -> 2 Na(s) + 3 N2(g)
b. To calculate the mass of NaN3 required to fill the airbag, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T = 32.0 °C + 273.15 = 305.15 K
Next, we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
Given:
P = 0.97 atm
V = 79.0 L
R = 0.0821 L.atm/mol.K
T = 305.15 K
Substituting the values into the equation, we have:
n = (0.97 atm * 79.0 L) / (0.0821 L.atm/mol.K * 305.15 K)
n ≈ 3.97 moles
Since the balanced equation shows a 2:2 ratio between NaN3 and Na(s), we can conclude that we need an equal number of moles of NaN3 to generate the desired amount of Na(s). Therefore, the number of moles of NaN3 required is also approximately 3.97 moles.
Finally, to calculate the mass of NaN3, we need to use the molar mass of NaN3, which is 65.01 g/mol:
Mass = number of moles * molar mass
Mass ≈ 3.97 moles * 65.01 g/mol
Mass ≈ 258.36 grams
Therefore, approximately 258.36 grams of NaN3 is needed to fill the airbag to a volume of 79.0 L at 32.0 °C and 0.97 atm.
2NaN3 ==> 2Na + 3N2
Use PV = nRT and solve for n = mols N2 gas at the conditions listed.
Using the coefficients in the balanced equation, convert mols N2 to mols NaN3. Then convert mols NaN3 to grams. g = mols x molar mass.