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??
To solve this problem, we need to use stoichiometry.
First, let's determine the number of moles of nitrogen gas (N2) needed to fill the airbag.
From the balanced chemical equation, we know that 2 moles of NaN3 produce 3 moles of N2.
Now, we need to convert the volume to moles using the ideal gas law equation:
PV = nRT
Where:
P = pressure (1.00 atm)
V = volume (70.0 L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (0°C = 273 K)
Now let's rearrange the equation to solve for n:
n = PV / RT
Substituting the values:
n = (1.00 atm) * (70.0 L) / (0.0821 L·atm/(mol·K)) * (273 K)
n = 3.11 moles of N2
Since we know that 2 moles of NaN3 produce 3 moles of N2, we can then calculate the number of moles of NaN3:
2 mol NaN3 produce 3 mol N2
x mol NaN3 produce 3.11 mol N2
Using a proportion:
x = (2 mol NaN3 * 3.11 mol N2) / 3 mol N2
x = 2.07 moles of NaN3
Now we can calculate the mass of NaN3:
The molar mass of NaN3 is:
Na = 22.99 g/mol
N = 14.01 g/mol
Molar mass of NaN3 = (22.99 g/mol) + (3 * 14.01 g/mol)
Molar mass of NaN3 = 65.00 g/mol
Finally, we can determine the mass of NaN3 by multiplying the moles of NaN3 by its molar mass:
Mass of NaN3 = 2.07 mol * 65.00 g/mol
Mass of NaN3 = 134.55 g
Therefore, approximately 134.55 grams of NaN3 must be reacted to inflate an airbag to 70.0 L at 0°C and 1.00 atm.