Answer :
To determine the mass of cerussite [tex](\text{PbCO}_3)[/tex] that contains 35.0 grams of lead (Pb), we need to understand the composition and molar masses involved.
Step 1: Calculate the molar mass of lead [tex](\text{Pb})[/tex].
- The atomic mass of Pb (lead) is approximately 207.2 g/mol.
Step 2: Calculate the molar mass of cerussite [tex](\text{PbCO}_3)[/tex].
- Molar mass of [tex]\text{PbCO}_3 = \text{Pb} + \text{C} + 3(\text{O})[/tex].
- Molar mass of C (carbon) is approximately 12.01 g/mol.
- Molar mass of O (oxygen) is approximately 16.00 g/mol.
- Therefore, molar mass of [tex]\text{PbCO}_3 = 207.2 + 12.01 + 3 \times 16.00 = 267.21[/tex] g/mol.
Step 3: Determine the mass of [tex]\text{PbCO}_3[/tex] that contains 35.0 grams of Pb.
- Using a proportion:
[tex]\frac{\text{mass of Pb}}{\text{molar mass of Pb}} = \frac{\text{mass of PbCO}_3}{\text{molar mass of PbCO}_3}[/tex] - Plug in the values:
[tex]\frac{35.0}{207.2} = \frac{x}{267.21}[/tex] - Solving for [tex]x[/tex]:
[tex]x = \frac{35.0 \times 267.21}{207.2} \approx 45.1 \text{ grams}[/tex]
Step 4: Choose the correct option.
- The mass of [tex]\text{PbCO}_3[/tex] that contains 35.0 grams of lead is approximately 45.1 grams. Therefore, the correct answer is B) 45.1 g.
