what mass of sodium azide is needed to fill a 2.50-L air bag with nitrogen gas at a pressure of 1140 torr and 25C?

Question

In air bags used in automobiles, the gas that fills the bags is produced from the reaction of sodium azide, NaN3: what mass of sodium azide is needed to fill a 2.50-L air bag with nitrogen gas at a pressure of 1140 torr and 25C?

Answer 1

There are two things needed to start this problem - 1. The realization that you will need to use the ideal gas equation PV=nRT and solve for n and 2. A balanced chemical equation.

 

The general approach will be to determine the number of moles of nitrogen, N2, in 2.50L of nitrogen gas at 1140 torr and 25C. Once this is obtained then use the number of moles of gas and the balanced chemical equation and solve a stoichiometry problem to determine the mass of NaN3 needed.

 

1.  Ideal Gas Equatioin

 

n = PV/RT = ((1140 torr/760 torr/1 atm)(2.50 L))/((0.082058 L•atm/mol•K)(298K)) = 0.153 mol N2

 

2.  Balanced equation

 

2 NaN3(s) –> 2 Na(s) + 3 N2(g)

 

3. Stoichiometry problem

 

0.153 mol N2 x (2 mole NaN3/3 mole N2) x (65.0 g NaN3/1 mol NaN3) = 6.63 g NaN3