Final answer:
The mass of sodium azide needed to decompose to produce 15.367 moles of N2 is 666.9055 g, which is not one of the provided multiple-choice options. There might be an error in the given options or in understanding the question.
Step-by-step explanation:
The student's question asks how much mass of sodium azide (NaN3) is needed to decompose in order to produce 15.367 moles of nitrogen gas (N2(g)). The balanced chemical equation for the decomposition of sodium azide is:
2NaN3 (s) → 2Na (s) + 3N2 (g)
From this equation, we see that 2 moles of NaN3 produce 3 moles of N2. To find the number of moles of NaN3 needed for 15.367 moles of N2, we set up a ratio:
(2 moles NaN3 / 3 moles N2) x 15.367 moles N2 = 10.2447 moles NaN3
Now, we calculate the mass of NaN3 by using its molar mass. The molar mass of NaN3 is approximately 65 g/mol. Therefore, the required mass is:
10.2447 moles NaN3 x 65 g/mol = 666.9055 g
This answer is not present in the multiple-choice options provided, indicating a possible mistake in the student's options or a misunderstanding of the question. It's important to verify the question and provided answers for any discrepancies.