Answer :

To find out how many grams [tex]\(4.3 \times 10^{21}\)[/tex] molecules of [tex]\(UF_6\)[/tex] weigh, we need to follow a few steps:

1. Calculate the Molar Mass of [tex]\(UF_6\)[/tex]:
- First, find the molar mass of uranium (U). Uranium has a molar mass of approximately 238.02891 g/mol.
- Next, find the molar mass of fluorine (F). Fluorine has a molar mass of approximately 18.9984032 g/mol.
- Since there are six fluorine atoms in each [tex]\(UF_6\)[/tex] molecule, multiply the molar mass of fluorine by 6.

[tex]\[
\text{Molar mass of } UF_6 = 238.02891 \, \text{g/mol} + 6 \times 18.9984032 \, \text{g/mol}
\][/tex]
[tex]\[
\text{Molar mass of } UF_6 = 352.0193292 \, \text{g/mol}
\][/tex]

2. Use Avogadro's Number to Find the Moles of [tex]\(UF_6\)[/tex]:
- Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many molecules are in one mole of any substance.
- To find the number of moles from the given number of molecules, divide the number of molecules by Avogadro's number.

[tex]\[
\text{Moles of } UF_6 = \frac{4.3 \times 10^{21} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mol}}
\][/tex]

3. Calculate the Mass of [tex]\(UF_6\)[/tex]:
- Once the number of moles is known, multiply it by the molar mass of [tex]\(UF_6\)[/tex] to find the mass in grams.

[tex]\[
\text{Mass of } UF_6 = \left(\frac{4.3 \times 10^{21}}{6.022 \times 10^{23}}\right) \times 352.0193292 \, \text{g/mol}
\][/tex]

The calculated mass of [tex]\(UF_6\)[/tex] is approximately 2.51 grams. Thus, [tex]\(4.3 \times 10^{21}\)[/tex] molecules of [tex]\(UF_6\)[/tex] weigh about 2.51 grams.

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Rewritten by : Barada