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 determine the mass of NaN3 required to inflate an airbag, you need to use the ideal gas law and the balanced chemical equation.
First, we need to calculate the number of moles of N2 gas required to fill the airbag at the given conditions. We can use 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 in Kelvin (0°C = 273 K)
Rearranging the equation to solve for n:
n = PV / RT
Substituting the given values:
n = (1.00 atm) * (70.0 L) / (0.0821 L·atm/(mol·K) * 273 K)
Simplifying and calculating:
n ≈ 2.45 moles
From the balanced chemical equation, we know that 2 moles of NaN3 react to form 3 moles of N2 gas. Therefore, we need to find the amount of NaN3 required to produce 2.45 moles of N2 gas.
Using the ratio of moles between NaN3 and N2, we set up the following conversion:
2 moles NaN3 → 3 moles N2
x moles NaN3 → 2.45 moles N2
Using a proportion:
(2 moles NaN3) / (3 moles N2) = (x moles NaN3) / (2.45 moles N2)
Solving for x:
x ≈ (2 moles NaN3 * 2.45 moles N2) / 3 moles N2
x ≈ 1.633 moles NaN3
Finally, we can calculate the mass of NaN3 using the molar mass of NaN3:
Mass = moles * molar mass
Molar mass of NaN3 = (23 g/mol Na + 14 g/mol N + (3 * 16 g/mol N)) = 65 g/mol
Mass = 1.633 moles * 65 g/mol
Mass ≈ 106 g
Therefore, approximately 106 grams of NaN3 must be reacted to inflate the airbag to 70.0 L at 0°C and 1.00 atm.