Sodium azide is used in air bags for automobiles.The gas produced from the decomposition of sodium azide is nitrogen. 2NaN₃(s) → 2Na(s) + 3N₂(g)
What mass of NaN₃ is required to inflate a bag with a volume of 45 L at a pressure of 1.0 atm and a temperature of 305 K? The gas law constant is 0.0821 L⋅atm/mol⋅K and the molar mass of NaN₃ is 65.0 g/mol.

Question

Quizplus · Accepted Answer

First, use the ideal gas law equation PV = nRT to find the moles of nitrogen gas (N₂) produced. Given P = 1.0 atm, V = 45 L, R = 0.0821 L⋅atm/mol⋅K, and T = 305 K, solving for n gives n = PV/RT = (1.0 atm * 45 L) / (0.0821 L⋅atm/mol⋅K * 305 K) ≈ 1.8 mol of N₂. Since the reaction produces 3 moles of N₂ for every 2 moles of NaN₃ decomposed, the moles of NaN₃ required are (1.8 mol N₂) * (2 mol NaN₃ / 3 mol N₂) = 1.2 mol NaN₃. The mass of NaN₃ needed is then mass = moles * molar mass = 1.2 mol * 65.0 g/mol = 78 g, or 7.8 × 10¹¹ g.

Sodium Azide Is Used in Air Bags for Automobiles