Final answer:
To find the mass of nitrogen produced from 100 grams of sodium azide, calculate the number of moles of sodium azide and use the stoichiometry of the reaction (2 NaN3 → 3 N2) to find the moles of nitrogen, which is then converted to mass (64.6 grams).
Step-by-step explanation:
To determine the mass of nitrogen produced from the decomposition of sodium azide, we can use stoichiometry based on the balanced chemical equation:
2 NaN3 (s) → 2 Na (s) + 3 N2 (g)
First, the molar mass of sodium azide, NaN3, is calculated by adding the atomic masses of sodium (Na) and azide (N3). Sodium has an atomic mass of approximately 23 g/mol, and nitrogen has an atomic mass of approximately 14 g/mol. Therefore, the molar mass of sodium azide is 65 g/mol (23 g/mol + (3 × 14) g/mol).
Given 100 grams of sodium azide, the amount in moles is found by dividing the mass by the molar mass:
- Mass of sodium azide = 100 g
- Molar mass of sodium azide = 65 g/mol
- Number of moles of sodium azide = Mass / Molar mass = 100 g / 65 g/mol = 1.538 moles
Using the stoichiometry of the reaction, we know that 2 moles of sodium azide produce 3 moles of nitrogen gas. Therefore, for every 2 moles of NaN3, 3 moles of N2 are produced.
Number of moles of nitrogen gas = (3 moles N2 / 2 moles NaN3) × 1.538 moles NaN3 = 2.307 moles N2
Finally, to find the mass of nitrogen gas, multiply the number of moles by the molar mass of nitrogen gas (N2), which is 28 g/mol (2 × 14 g/mol).
Mass of nitrogen gas = Number of moles × Molar mass = 2.307 moles × 28 g/mol = 64.6 g
Therefore, the mass of nitrogen produced from the decomposition of 100 grams of sodium azide is approximately 64.6 grams.