Automobile air bags inflate following serious impacts, which...

Automobile air bags inflate following serious impacts, which trigger the chemical reaction: $$2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g)$$ If an automobile air bag has a volume of $11.8 \mathrm{L},$ what mass of $\mathrm{NaN}_{3}$ $(\mathrm{in} \mathrm{g})$ is required to fully inflate the air bag upon impact? Assume STP conditions.

Automobile air bags inflate following serious impacts, which trigger the
chemical reaction:
$$2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g)$$
If an automobile air bag has a volume of $11.8 \mathrm{L},$ what mass of $\mathrm{NaN}_{3}$ $(\mathrm{in} \mathrm{g})$ is required to fully inflate the air bag upon impact? Assume STP conditions.

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Key Concepts

Chemical Reaction Stoichiometry

This concept involves using the balanced chemical equation to determine the mole ratios between reactants and products. By understanding the stoichiometric coefficients, one can convert between the amount of a product formed and the amount of a reactant required, which is essential for calculations such as determining how much of a reactant is needed to produce a given volume of gas.

Ideal Gas Law and Molar Volume at STP

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. This relationship allows conversion of a gas volume to moles, which is vital in chemical calculations involving gaseous products. The ideal gas law itself (PV = nRT) underpins these conversions and connects the physical properties of gases with the amounts in moles.

Molar Mass and Unit Conversion

Calculating the mass of a compound from the number of moles requires using the molar mass, which is the mass per mole of a substance. This concept is key in translating the stoichiometric calculation results into a practical quantity in grams, enabling the assessment of how much of a reactant is needed for a reaction based on its molar relationships.

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