Final answer:
Using Avogadro's number, we calculate the moles of CH4 and then use the molar mass to find the mass of the given number of molecules. The mass of CH4 for 9.90 × 10²⁴ molecules is approximately 26.3072 grams, which does not match any of the provided answers.
Step-by-step explanation:
The question asks to find the mass of 9.90 × 10²⁴ molecules of methane (CH₄). To answer this question, we'll first need to relate the number of molecules to moles using Avogadro's number, which is 6.022 × 10² molecules per mole. Considering that CH₄ has a molar mass of approximately 16 g/mol (12 g/mol for carbon and 1 g/mol for each of the four hydrogens), we can now calculate the mass.
First, we find the number of moles by dividing the given number of molecules by Avogadro's number:
Number of moles of CH₄ = (9.90 × 10²⁴ molecules) / (6.022 × 10² molecules/mol) ≈ 1.6442 moles
Next, we use the molar mass to find the mass:
Mass of CH₄ = (1.6442 moles) × (16 g/mol) ≈ 26.3072 grams
However, since the provided answer choices don't include this exact value, we must consider that there might have been a mistake in the options provided or in the calculations and should revisit the numbers given or seek clarification. But based purely on the calculation, none of the options a) 6 grams, b) 12 grams, c) 18 grams, or d) 24 grams are correct.