How many atoms of carbon are needed to produce 0.45 mol Al?
3C + 2Al2O3 4Al + 3CO2
A. 2.6 × 1026 atoms
B. 9.7 × 1024 atoms
C. 3.0 × 1022 atoms
D. 2.0 × 1023 atoms
You will need 3/4 of .45 mole of C.
AvagradrosNumber*.45*.75
To determine the number of atoms of carbon needed to produce 0.45 mol Al, we need to use the given balanced chemical equation:
3C + 2Al2O3 → 4Al + 3CO2
First, we need to determine the molar ratio between carbon and aluminum. From the balanced equation, we can see that 3 moles of carbon are required to produce 4 moles of aluminum.
Therefore, the correct molar ratio is 3 moles of carbon: 4 moles of aluminum.
Now, we can set up a proportion using the molar ratio:
(0.45 mol Al) / (4 mol Al) = (x mol C) / (3 mol C)
To solve for x, we can cross-multiply and divide:
x = (0.45 mol Al) * (3 mol C) / (4 mol Al)
x = 0.3375 mol C
To convert from moles to atoms, we need to use Avogadro's number, which states that 1 mole of any substance contains 6.022 × 10^23 particles (atoms, molecules, ions, etc.).
Therefore, to find the number of atoms of carbon, we can multiply the number of moles of carbon by Avogadro's number:
Number of atoms of carbon = (0.3375 mol C) * (6.022 × 10^23 atoms/mol)
Number of atoms of carbon = 2.03 × 10^23 atoms
Therefore, the correct answer is D. 2.0 × 10^23 atoms.