Automobile air bags employ a chemical reaction involving the rapid decomposition of sodium azide
(NaN3) into sodium metal and nitrogen gas to inflate in a collision. How much sodium azide is required
to decompose to inflate a 20.0 L air bag? Assume that the gas is at standard temperature and pressure, and
thus occupies 22.4 L per mole.
a. 76.3 g
b. 42.8 g
c. 38.7 g
d. 62.7 g
=38.7 g (c)
Steps
20/22.4= 0.89 mols of NaN3
Balanced Equation
2(NaN3) --> 2(Na) + 3(N2)
Looking for mols of n2
So 2(0.89)/3= mols of n2 =0.59 mol
Then molar mass of NaN3 = 65
0.59x65= 38.7 g
See the post on limestone. All of these stoichiometry problems are worked the same way.
To calculate the amount of sodium azide required to inflate a 20.0 L airbag, we need to determine the number of moles of nitrogen gas required based on the ideal gas law.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure (assume standard pressure = 1 atm)
V = volume (20.0 L)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (assume standard temperature = 298 K)
Rearranging the equation to solve for n, we have:
n = PV / RT
Substituting the given values, we have:
n = (1 atm) x (20.0 L) / (0.0821 L·atm/mol·K x 298 K)
n = 0.678 moles of nitrogen gas
Now we need to find the molar ratio between sodium azide (NaN3) and nitrogen gas (N2). The balanced equation for the decomposition of sodium azide is:
2 NaN3 → 2 Na + 3 N2
From the balanced equation, we can see that 2 moles of NaN3 decompose to produce 3 moles of N2.
Therefore, the amount of sodium azide required is:
(0.678 moles of N2) x (2 moles of NaN3 / 3 moles of N2) = 0.452 moles of NaN3
Finally, we can calculate the mass of sodium azide required using its molar mass. The molar mass of NaN3 is:
(23.0 g/mol x 1) + (14.0 g/mol x 1) + (3 x 16.0 g/mol) = 65.0 g/mol
Thus, the mass of sodium azide required is:
0.452 moles x 65.0 g/mol = 29.4 g.
None of the provided answer choices match 29.4 g.
To determine the amount of sodium azide (NaN3) required to inflate a 20.0 L airbag, we need to use the given information about the gas at standard temperature and pressure (STP).
First, let's convert the volume of the airbag from liters to moles. At STP, one mole of gas occupies 22.4 L. Therefore, we can calculate the number of moles of gas in the airbag as follows:
Number of moles = Volume of airbag / Volume per mole
Number of moles = 20.0 L / 22.4 L/mol
Now, we need to consider the balanced chemical equation for the decomposition of sodium azide:
2NaN3 → 2Na + 3N2
From the balanced equation, we can see that 2 moles of sodium azide produce 3 moles of nitrogen gas. Therefore, the ratio of sodium azide to nitrogen gas is 2:3.
Since the number of moles of nitrogen gas is equal to the number of moles of sodium azide, we can use the calculated number of moles of gas in the airbag to find the number of moles of sodium azide required.
Number of moles of sodium azide = Number of moles of nitrogen gas
Now, we can use the molar mass of sodium azide (65.01 g/mol) to convert the number of moles of sodium azide to grams.
Mass = Number of moles × Molar mass
Mass = Number of moles of sodium azide × (65.01 g/mol)
We can substitute the calculated number of moles of sodium azide (from earlier) into the equation to get the mass required.
Finally, we can compare the calculated mass to the given options of 76.3 g, 42.8 g, 38.7 g, and 62.7 g to determine the correct answer.