Sodium azide, NaN3, the explosive compound found in automobile air bags, decomposes according to the following equation: 2NaN3(s)right arrow 2Na(s) + 3N2(g) What mass of NaN3 is required to provide the nitrogen needed to inflate an 80.0-L bag to a pressure of 1.3 atm at 27 degree C? What is the density of the gas under these conditions?

1.9 × 10² g NaN₃

1.5 g/L

Explanation:

Step 1: Write the balanced decomposition equation

2 NaN₃(s) ⇒ 2 Na(s) + 3 N₂(g)

Step 2: Calculate the moles of N₂ formed

N₂ occupies a 80.0 L bag at 1.3 atm and 27 °C (300 K). We will calculate the moles of N₂ using the ideal gas equation.

P × V = n × R × T

n = P × V / R × T

n = 1.3 atm × 80.0 L / (0.0821 atm.L/mol.K) × 300 K = 4.2 mol

We can also calculate the mass of nitrogen using the molar mass (M) 28.01 g/mol.

4.2 mol × 28.01 g/mol = 1.2 × 10² g

Step 3: Calculate the mass of NaN₃ needed to form 1.2 × 10² g of N₂

The mass ratio of NaN₃ to N₂ is 130.02:84.03.

1.2 × 10² g N₂ × 130.02 g NaN₃/84.03 g N₂ = 1.9 × 10² g NaN₃

Step 4: Calculate the density of N₂

We will use the following expression.

ρ = P × M / R × T

ρ = 1.3 atm × 28.01 g/mol / (0.0821 atm.L/mol.K) × 300 K = 1.5 g/L