## Chapter 5

## Q. 5.12

## Q. 5.12

Sodium azide (NaN_{3}) is used in some automobile air bags. The impact of a collision triggers the decomposition of NaN_{3} as follows:

2NaN_{3}(s) → 2Na(s) + 3N_{2}(g)The nitrogen gas produced quickly inflates the bag between the driver and the windshield and dashboard. Calculate the volume of N2 generated at 80°C and 823 mmHg by the decomposition of 60.0 g of NaN_{3}.

Strategy From the balanced equation, we see that 2 mol NaN_{3} \bumpeq 3 mol N_{2} so the conversion factor between NaN_{3} and N_{2} is

\frac{3 mol N_{2}}{2 mol NaN_{3}}Because the mass of NaN_{3} is given, we can calculate the number of moles of NaN_{3} and hence the number of moles of N_{2} produced. Finally, we can calculate the volume of N_{2} using the ideal gas equation.

## Step-by-Step

## Verified Solution

First, we calculate the number of moles of N_{2} produced by 60.0 g NaN_{3} using the following sequence of conversions

grams of NaN_{3} → moles of NaN_{3} → moles of N_{2}

so that

moles of N_{2}=60.0 \cancel{g NaN_{3}}\times \frac{1 \cancel{mol NaN_{3}}}{65.02 \cancel{g NaN_{3}}} \times \frac{3 mol N_{2}}{2 \cancel{mol NaN_{3}}}

=1.38 mol N_{2}

The volume of 1.38 moles of N_{2} can be obtained by using the ideal gas equation

V=\frac{nRT}{P}=\frac{(1.38 mol)(0.0821 L . atm/K . mol)(80+273 K)}{(823/760) atm}=36.9 L