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
Use the coefficients in the the balanced equation.
mols C needed = 0.45 mol Al x (3 mols C/4 mols Al) = ?
Then you know that 1 mol C contains 6.02E23 atoms.
To determine the number of atoms of carbon needed to produce 0.45 mol of Al, we need to use the balanced chemical equation provided:
3C + 2Al2O3 → 4Al + 3CO2
From the balanced equation, we can see that the ratio of C to Al is 3:4. This means that for every 3 moles of carbon, we will produce 4 moles of aluminum.
Given that we have 0.45 mol of aluminum, we can set up the following proportion:
(3 moles of C / 4 moles of Al) = (x moles of C / 0.45 moles of Al)
Cross multiplying, we have:
4 moles of Al * x moles of C = 3 moles of C * 0.45 moles of Al
4x = 1.35
Simplifying, we find:
x = 1.35 / 4
x = 0.3375 mol of C
To convert this to the number of atoms, we can use Avogadro's number, which states that 1 mole of any substance contains approximately 6.022 × 10^23 particles (atoms, molecules, etc.).
So, the number of atoms of carbon needed can be calculated as:
0.3375 mol of C * 6.022 × 10^23 atoms/mol = 2.030186875 × 10^23 atoms
Rounded to the appropriate number of significant figures, the answer is:
D. 2.0 × 10^23 atoms
To determine how many atoms of carbon are needed to produce 0.45 mol Al, we need to use the balanced chemical equation provided. The equation shows that 3 moles of carbon react with 2 moles of Al2O3 to produce 4 moles of Al and 3 moles of CO2.
First, we need to calculate the number of moles of carbon required:
0.45 mol Al × (3 mol C / 4 mol Al) = 0.3375 mol C
Next, we can use Avogadro's Number (6.022 × 10^23) to convert the number of moles of carbon to atoms of carbon:
0.3375 mol C × (6.022 × 10^23 atoms / 1 mol C) = 2.03 × 10^23 atoms C
Therefore, the correct answer is D. 2.0 × 10^23 atoms.