Final answer:
To calculate the number of molecules in 12 grams of UF₆, first determine its molar mass, then divide the mass by the molar mass to get the number of moles, and finally multiply the number of moles by Avogadro's number to find the molecules. The approximate answer with two significant figures is 2.1 × 10^22 molecules.
Step-by-step explanation:
To find the number of molecules in 12 grams of UF₆, we first need to calculate its molar mass. The molar mass of UF₆ can be determined by adding the atomic masses of uranium (either ^235U or ^238U) and six times the atomic mass of fluorine. For ^238U, the molar mass of UF₆ is 238.05 + (6 × 18.998) = 352.04 g/mol. With this molar mass, we use Avogadro's number, which is 6.022 × 10^23 molecules/mol, to calculate the number of molecules in 12 grams of UF₆.
First, we find the number of moles:
Number of moles = Mass (g) / Molar Mass (g/mol)
Number of moles of UF₆ = 12 g / 352.04 g/mol ≈ 0.0341 mol
Now, we multiply the number of moles by Avogadro's number to find the molecules:
Number of molecules = Number of moles × Avogadro's number
Number of molecules in 12 grams of UF₆ ≈ 0.0341 mol × 6.022 × 10^23 molecules/mol ≈ 2.05 × 10^22 molecules