Final answer:
To calculate the required mass of nitrogen to yield 6.022×1024 molecules, we divide the number of molecules by Avogadro's number to get moles and then multiply by the molar mass of nitrogen. The result is 280.2 grams, which does not match the given options, suggesting a possible typo in the question.
Step-by-step explanation:
To determine the mass of nitrogen (N2) needed to produce 6.022×1024 molecules of nitrogen, we need to calculate the moles of nitrogen this number of molecules represents and then convert it to grams using the molar mass of nitrogen.
One mole of any substance contains Avogadro's number of molecules, which is approximately 6.022×1023. Therefore, 6.022×1024 molecules of nitrogen would be equivalent to 10 moles of nitrogen (since 6.022×1024 molecules divided by 6.022×1023 molecules per mole equals 10 moles).
The molar mass of nitrogen (N2) is 28.02 g/mol (from the periodic table: 2 x 14.01 g/mol). Using the molar mass, we can calculate the mass of 10 moles of nitrogen:
10 moles × 28.02 g/mol = 280.2 grams
This value is not matched by any of the options provided in the question, which likely means there was either a mistake in the question or in understanding the given options. However, using the closest numerical option, it appears that option c) 28.64 grams is a typo, and it should reflect the mass of 1 mole of nitrogen, which would be 28.02 grams, not 10 moles. Thus, the correct amount required by the stoichiometry for 10 moles (representative of 6.022×1024 molecules) would be 280.2 grams.