How many grams do 4.30 x 1021 molecules of UF6 weigh? Report the answer in correct number of significant figures and units.
To determine the weight of 4.30 x 10^21 molecules of UF6, you need to use the concept of molar mass and Avogadro's number.
1. Start by determining the molar mass of UF6. The molar mass is the sum of the atomic masses of all the atoms in the molecule.
The atomic mass of uranium (U) is about 238.03 g/mol, and the atomic mass of fluorine (F) is about 18.99 g/mol. Since there are 6 fluorine atoms in UF6, the molar mass of UF6 can be calculated as follows:
Molar mass of UF6 = (1 x atomic mass of uranium) + (6 x atomic mass of fluorine)
= (1 x 238.03 g/mol) + (6 x 18.99 g/mol)
= 352.02 g/mol
2. Use Avogadro's number, which is approximately 6.022 x 10^23 molecules/mol. This gives us the conversion factor to go from molecules to moles.
3. Convert the given number of molecules (4.30 x 10^21) to moles by dividing it by Avogadro's number:
Moles of UF6 = (4.30 x 10^21 molecules) / (6.022 x 10^23 molecules/mol)
4. Now, use the molar mass and the number of moles to calculate the weight:
Weight = Moles of UF6 x Molar mass of UF6
Weight = (moles of UF6) x (molar mass of UF6)
= (4.30 x 10^21 molecules) / (6.022 x 10^23 molecules/mol) x (352.02 g/mol)
5. Calculate the weight:
Weight = (4.30 x 10^21 molecules) x (352.02 g/mol) / (6.022 x 10^23 molecules/mol)
≈ 2.5 x 10^-2 g
Therefore, 4.30 x 10^21 molecules of UF6 weigh approximately 2.5 x 10^-2 grams. The answer should be reported with two significant figures, so it can be rounded to 0.025 g.