Question

Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This action causes sodium azide (NaN3) to decompose explosively according to the following reaction. 2 NaN3(s) → 2 Na(s) + 3 N2(g) What mass of NaN3(s) must be reacted to inflate an air bag to 70.6 L at STP?

Answer 1

Answer: 136 g of  $NaN_3$ must be reacted to inflate an air bag to 70.6 L at STP.

Explanation:

Using ideal gas equation:

$PV=nRT$

P= pressure of nitrogen gas = 1 atm (at STP)

V =volume of nitrogen gas = 70.6 L

n = number of moles of nitrogen gas = 1 atm (at STP)

R = gas constant = 0.0821 Latm/Kmol

T = temperature of nitrogen gas = 273 K (at STP)

$1atm\times 70.6L=n\times 0.0821 L atm/K mol\times 273$

$n=3.14$

For the balanced chemical reaction:

$2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)$

3 moles of nitrogen are produced by = 2 moles of $NaN_3$

3.14 moles of nitrogen are produced by =$\frac{2}{3}\times 3.14=2.09$ moles of $NaN_3$

Mass of $NaN_3$ = Moles × Molar mass = 2.09 mole × 65 g/mol = 136 g