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.

Step-by-step 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* 70.6L=n* 0.0821 L atm/K mol* 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 =
`(2)/(3)* 3.14=2.09` moles of
`NaN_3`

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