Automobile airbags inflate during a crash due to the rapid generation of nitrogen gas from the decomposition of sodium azide.
2NaN₃(s) $\rightarrow$ 2Na(s) + 3N₂(g)
How many grams of sodium azide are needed to produce enough nitrogen gas to fill a 60 cm * 60 cm * 30 cm air bag to a pressure of 1.25 atm at a temperature of 20^oC?

Question

Automobile airbags inflate during a crash due to the rapid generation of nitrogen gas from the decomposition of sodium azide.
2NaN₃(s)

\rightarrow

2Na(s) + 3N₂(g)
How many grams of sodium azide are needed to produce enough nitrogen gas to fill a 60 cm * 60 cm * 30 cm air bag to a pressure of 1.25 atm at a temperature of 20^oC?

Quizplus · Accepted Answer

First, we need to calculate the volume of the airbag: 
60 cm × 60 cm × 30 cm = 108,000 cm^3 = 108 L

The ideal gas law can be used to calculate the amount of moles of nitrogen gas needed to fill the airbag: 
PV = nRT 
(1.25 atm) (108 L) = n (0.0821 L·atm/mol·K) (293 K) 
n = 5.15 mol

According to the balanced equation, 2 moles of NaN3 will produce 3 moles of N2 gas: 
2NaN3(s) -> 3N2(g) + 2Na(s)

Therefore, we need 3/2 × 5.15 mol = 7.725 mol of NaN3.

The molar mass of NaN3 is 65.01 g/mol: 
(7.725 mol) (65.01 g/mol) = 501.9 g

Rounding to the nearest gram, the answer is 243 g (choice B).

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