Question

Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide (NaN3) to decompose explosively according to the following reaction: 2NaN3 1s2 h 2Na 1s2 1 3N2 1g2 What mass of NaN3(s) must be reacted to inflate an air bag to 70.0 L at STP?

Answer 1

Answer : The mass of $NaN_3$ reacted will be, 135.395 grams.

Explanation :

The balanced decomposition reaction will be,

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

First we have to calculate the moles of $N_2$ gas.

As we know that, at STP

22.4 L volume of $N_2$ gas present in 1 mole of $N_2$ gas

So, 70.0 L volume of $N_2$ gas present in $\frac{70.0}{22.4}=3.125$ mole of $N_2$ gas

Now we have to calculate the moles of $NaN_3$.

From the balanced reaction, we conclude that

As, 3 mole of $N_2$ produced from 2 moles of $NaN_3$

So, 3.125 mole of $N_2$ produced from $\frac{2}{3}\times 3.125=2.083$ moles of $NaN_3$

Now we have to calculate the mass of $NaN_3$.

$\text{Mass of }NaN_3=\text{Moles of }NaN_3\times \text{Molar mass of }NaN_3$

Molar mass of $NaN_3$ = 23 + 3(14) = 65 g/mole

$\text{Mass of }NaN_3=2.083mole\times 65g/mole=135.395g$

Therefore, the mass of $NaN_3$ reacted will be, 135.395 grams.