Sodium azide (NaN3) is used in some automobile air bags. The impact of a collision triggers the decomposition of NaN3 as follows:2NaN3(s) → 2Na(s) + 3N2(g) The nitrogen gas produced quickly inflates the bag between the driver and the windshield and dashboard. Calculate the volume of N2 generated at

Question

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

[latex]2NaN_{3}(s) → 2Na(s) + 3N_{2}(g)[/latex]

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 [latex]NaN_{3}[/latex].

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

[latex]\frac{3 mol N_{2}}{2 mol NaN_{3}} [/latex]

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

Accepted Answer

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

grams of [latex]NaN_{3}[/latex] → moles of [latex]NaN_{3}[/latex] → moles of [latex]N_{2}[/latex]

so that

moles of [latex]N_{2}=60.0 \cancel{g NaN_{3}} imes \frac{1 \cancel{mol NaN_{3}}}{65.02 \cancel{g NaN_{3}}} imes \frac{3 mol N_{2}}{2 \cancel{mol NaN_{3}}} [/latex]

=1.38 mol [latex]N_{2}[/latex]

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

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

=36.9 L

Question 5.12: Sodium azide (NaN3) is used in some automobile air bags. The...

Related Answered Questions

Verified Answer:

Verified Answer:

Verified Answer:

Calculate the root-mean-square speeds of helium atoms and nitrogen molecules in m/s at 25°C. Strategy To calculate the root-mean-square speed we need Equation (5.16). What units should we use for R and ℳ so that urms will be expressed in m/s? ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

The combustion of acetylene with pure oxygen produces a very high-temperature flame used for welding and cutting metals. Calculate the volume of O2 (in liters) required for the complete combustion of 7.64 L of acetylene (C2H2) measured at the same temperature and pressure. ...

Verified Answer:

Verified Answer: