Final answer:
To find how many carbon atoms are in 47.6 g of Al₂(CO₃)₃, calculate the moles of Al₂(CO₃)₃ and then use the molar ratio to find moles of carbon. Multiply the result by Avogadro's number to find the number of atoms, which is approximately 3.676 × 10²² carbon atoms.
Step-by-step explanation:
To determine how many atoms of carbon are contained in 47.6 g of Al₂(CO₃)₃, we first need to calculate how many moles of Al₂(CO₃)₃ are in 47.6 g given that its molar mass is 233.99 g/mol. Using the molar mass as a conversion factor:
47.6 g Al₂(CO₃)₃ × (1 mol Al₂(CO₃)₃ / 233.99 g Al₂(CO₃)₃) = 0.2034 mol Al₂(CO₃)₃
Since each mole of Al₂(CO₃)₃ contains 3 moles of CO₃⁻² ions, and each CO₃⁻² ion contains 1 atom of carbon, there are 3 moles of carbon atoms in 1 mole of Al₂(CO₃)₃. Multiplying the number of moles of Al₂(CO₃)₃ by the number of moles of carbon atoms gives:
0.2034 mol Al₂(CO₃)₃ × 3 mol C = 0.6102 mol C
To get the number of carbon atoms, we multiply by Avogadro's number, which is approximately 6.022 × 10²³ atoms/mol:
0.6102 mol C × (6.022 × 10²³ atoms/mol) = 3.676 × 10²² carbon atoms
Therefore, there are approximately 3.676 × 10²² carbon atoms in 47.6 g of Al₂(CO₃)₃.