Automotive air bags inflate when sodium azide, NaN3, rapidly decomposes to its component elements: 2 NaN31s2¡2 Na1s2 + 3 N21g2 (c) How many grams of NaN3 are required to produce 10.0 ft3 of nitrogen gas, about the size of an automotive air bag, if the gas has a density of 1.25 g/L?

Verified step by step guidance

1. Convert the volume of nitrogen gas from cubic feet to liters using the conversion factor: 1 ft³ = 28.3168 L.
2. Calculate the mass of nitrogen gas using the density formula: \( \text{mass} = \text{density} \times \text{volume} \).
3. Use the molar mass of nitrogen gas (N₂) to convert the mass of nitrogen gas to moles.
4. Use the stoichiometry of the balanced chemical equation to find the moles of NaN₃ required. The equation shows that 2 moles of NaN₃ produce 3 moles of N₂.
5. Convert the moles of NaN₃ to grams using its molar mass.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this case, understanding the stoichiometric coefficients from the decomposition of sodium azide is essential to relate the amount of NaN3 needed to produce a specific volume of nitrogen gas.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. The ideal gas law (PV=nRT) can be used to relate the volume of gas produced to the number of moles and the conditions of the gas. In this question, knowing how to apply the ideal gas law will help convert the volume of nitrogen gas into moles, which can then be used to find the mass of sodium azide required.

Density and Volume Relationships

Density is defined as mass per unit volume and is a critical concept for converting between mass and volume. In this scenario, the density of nitrogen gas is given, allowing for the calculation of the mass of nitrogen produced from the specified volume. This mass can then be used in conjunction with stoichiometry to determine the required mass of sodium azide.