The airbags that protect people in car crashes are inflated by the extremely rapid decomposition of sodium azide, which produces large volumes of nitrogen gas. 1. Write a balanced chemical equation, including physical state symbols, for the decomposition of solid sodium azide ( NaN3 ) into solid sodium and gaseous dinitrogen. 2. Suppose 43.0L of dinitrogen gas are produced by this reaction, at a temperature of 13.0°C and pressure of exactly 1atm . Calculate the mass of sodium azide that must have reacted. Round your answer to 3 significant digits.

1. Write a balanced chemical equation, including physical state symbols, for the decomposition of solid sodium azide (NaN₃) into solid sodium and gaseous dinitrogen.

NaN₃(s) → Na(s) + 1.5 N₂(g)

2. Suppose 43.0L of dinitrogen gas are produced by this reaction, at a temperature of 13.0°C and pressure of exactly 1atm. Calculate the mass of sodium azide that must have reacted. Round your answer to 3 significant digits.

First, we have to calculate the moles of N₂ from the ideal gas equation.

[tex]P.V=n.R.T\\n=\frac{P.V}{R.T} =\frac{1atm.(43.0L)}{(0.08206atm.L/mol.K).286.2K} =1.83mol[/tex]

The moles of NaN₃ are:

[tex]1.83molN_{2}.\frac{1molNaN_{3}}{1.5molN_{2}} =1.22molNaN_{3}[/tex]

The molar mass of NaN₃ is 65.01 g/mol. The mass of NaN₃ is:

[tex]1.22mol.\frac{65.01g}{mol} =79.3g[/tex]