Sodium azide (NaN3) yields N2 gas when heated to 300 °C, a reaction used in automobile air bags. If 1.00 mol of N2 has a volume of 47.0 L under the reaction conditions, how many liters of gas can be formed by heating 38.5 g of NaN3? The reaction is

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Write the balanced chemical equation for the decomposition of sodium azide: 2 NaN_3 \rightarrow 2 Na + 3 N_2.

Calculate the molar mass of NaN_3 by adding the atomic masses of sodium (Na) and nitrogen (N).

Determine the number of moles of NaN_3 in 38.5 g by dividing the mass by the molar mass of NaN_3.

Use the stoichiometry of the balanced equation to find the moles of N_2 produced from the moles of NaN_3. According to the equation, 2 moles of NaN_3 produce 3 moles of N_2.

Calculate the volume of N_2 gas produced using the given volume of 1.00 mol of N_2 (47.0 L) and the moles of N_2 obtained from the stoichiometry.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 of sodium azide and nitrogen gas will help in calculating how much N2 can be produced from a given mass of NaN3.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For sodium azide (NaN3), calculating its molar mass is essential to convert the mass of NaN3 (38.5 g) into moles. This conversion is necessary to apply stoichiometry and determine the volume of nitrogen gas produced from the decomposition of sodium azide.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law allows us to calculate the volume of gas produced under specific conditions. In this scenario, knowing that 1.00 mol of N2 occupies 47.0 L at the given temperature enables us to find the volume of nitrogen gas generated from the moles of NaN3 decomposed.

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