Certainly! Let's start by identifying the given information and the required steps to find the mass of [tex]\( 8.2 \times 10^{22} \)[/tex] molecules of [tex]\( CHCl_3 \)[/tex].
1. Given:
- The number of molecules of [tex]\( CHCl_3 \)[/tex] is [tex]\( 8.2 \times 10^{22} \)[/tex].
- Avogadro's number, which is [tex]\( 6.022 \times 10^{23} \)[/tex] molecules/mol.
- The molar mass of [tex]\( CHCl_3 \)[/tex]:
- Carbon ([tex]\(C\)[/tex]) has an atomic mass of 12 g/mol.
- Hydrogen ([tex]\(H\)[/tex]) has an atomic mass of 1 g/mol.
- Chlorine ([tex]\(Cl\)[/tex]) has an atomic mass of 35.5 g/mol.
- There are three chlorine atoms in [tex]\( CHCl_3 \)[/tex].
2. Calculate the molar mass of [tex]\( CHCl_3 \)[/tex]:
[tex]\[
\text{Molar mass of } CHCl_3 = 12 \, \text{g/mol} \, (\text{for C}) + 1 \, \text{g/mol} \, (\text{for H}) + 3 \times 35.5 \, \text{g/mol} \, (\text{for Cl})
\][/tex]
[tex]\[
\text{Molar mass of } CHCl_3 = 12 + 1 + 3 \times 35.5 = 12 + 1 + 106.5 = 119.5 \, \text{g/mol}
\][/tex]
3. Calculate the number of moles of [tex]\( CHCl_3 \)[/tex]:
- The number of moles is found by dividing the number of molecules by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{8.2 \times 10^{22} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mol}}
\][/tex]
[tex]\[
\text{Number of moles} \approx 0.13616738625041513 \, \text{mol}
\][/tex]
4. Calculate the mass in grams:
- The mass is found by multiplying the number of moles by the molar mass:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}
\][/tex]
[tex]\[
\text{Mass} = 0.13616738625041513 \, \text{mol} \times 119.5 \, \text{g/mol}
\][/tex]
[tex]\[
\text{Mass} \approx 16.27200265692461 \, \text{g}
\][/tex]
So, the mass of [tex]\( 8.2 \times 10^{22} \)[/tex] molecules of [tex]\( CHCl_3 \)[/tex] is approximately [tex]\( 16.27 \, \text{grams} \)[/tex].
