The air bags in cars are inflated when a collision triggers the explosive, highly exothermic decomposition of sodium azide (NaN3): 2NaN3(s) → 2Na(s) + 3N2(g) The passenger-side air bag in a typical car must fill a space approximately four times as large as the driver-side bag to be effective. Calculate the mass of sodium azide required to fill a 113-L air bag. Assume the pressure in the car is 1.00 atm and the temperature of N2 produced is 85°C.

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Alleei Alleei · Answer 1 · 2020-03-13T09:10:02+01:00

Answer : The mass of [tex]NaN_3[/tex] required is, 166.4 grams.

Explanation :

First we have to calculate the moles of nitrogen gas.

Using ideal gas equation:

[tex]PV=nRT[/tex]

where,

P = Pressure of [tex]N_2[/tex] gas = 1.00 atm

V = Volume of [tex]N_2[/tex] gas = 113 L

n = number of moles [tex]N_2[/tex] = ?

R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]

T = Temperature of [tex]N_2[/tex] gas = [tex]85^oC=273+85=358K[/tex]

Putting values in above equation, we get:

[tex]1.00atm\times 113L=n\times (0.0821L.atm/mol.K)\times 358K[/tex]

[tex]n=3.84mol[/tex]

Now we have to calculate the moles of sodium azide.

The balanced chemical reaction is,

[tex]2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)[/tex]

From the balanced reaction we conclude that

As, 3 mole of [tex]N_2[/tex] produced from 2 mole of [tex]NaN_3[/tex]

So, 3.84 moles of [tex]N_2[/tex] produced from [tex]\frac{2}{3}\times 3.84=2.56[/tex] moles of [tex]NaN_3[/tex]

Now we have to calculate the mass of [tex]NaN_3[/tex]

[tex]\text{ Mass of }NaN_3=\text{ Moles of }NaN_3\times \text{ Molar mass of }NaN_3[/tex]

Molar mass of [tex]NaN_3[/tex] = 65 g/mole

[tex]\text{ Mass of }NaN_3=(2.56moles)\times (65g/mole)=166.4g[/tex]

Therefore, the mass of [tex]NaN_3[/tex] required is, 166.4 grams.