Final answer:
The mass percent of carbon in smithsonite is calculated by dividing the molar mass of carbon by the molar mass of the compound and multiplying by 100%, which is approximately 9.58%.
Step-by-step explanation:
To calculate the mass percent of carbon in the mineral smithsonite (ZnCO₃), we need to determine the molar mass of the compound and the mass of carbon in one mole of the compound. The molar mass of ZnCO₃ is the sum of the molar masses of zinc (Zn, approximately 65.38 g/mol), carbon (C, 12.01 g/mol), and three oxygen atoms (O, 16.00 g/mol each). After calculating these values, the molar mass of ZnCO₃ is about 65.38 + 12.01 + (3 × 16.00) = 125.38 g/mol. To find the mass percent of carbon, we take the mass of carbon in one mole (12.01 g) and divide it by the molar mass of the compound, then multiply by 100%. Thus, the mass percent of carbon in smithsonite is (12.01 g / 125.38 g/mol) × 100% ≈ 9.58%.