Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide \(\left(\mathrm{NaN}_{3}\right)\) to decompose explosively according to the following reaction: $$2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g)$$ What mass of \(\mathrm{NaN}_{3}(s)\) must be reacted to inflate an air bag to 70.0 \(\mathrm{L}\) at STP?

To find the mass of sodium azide (NaN3) required to inflate an air bag to 70.0 L at STP, follow these steps: 1. Calculate the moles of N2 gas needed using the Ideal Gas Law: \(n(N_2) = \frac{PV}{RT} = \frac{(1\text{ atm})(70.0\text{ L})}{(0.08206\text{ L atm/mol K})(273.15\text{ K})}\) 2. Determine the moles of NaN3 required using stoichiometry: \(n(\mathrm{NaN}_3) = (n(N_2))\left(\frac{2\text{ mol NaN}_3}{3\text{ mol }N_2}\right)\) 3. Convert moles of NaN3 to mass using molar mass (65.01 g/mol): \(\text{mass}(\mathrm{NaN}_3) = n(\mathrm{NaN}_3) \times \text{molar mass}(\mathrm{NaN}_3)\) After completing these steps, you will find the mass of sodium azide needed to inflate the air bag to 70.0 L at STP.