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Chapter 5

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.

 

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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