To calculate the theoretical yield and percent yield, we need to understand a few concepts and use some formulas.
1. Balanced Equation: The given balanced equation is 4Al + 3O2 -> 2Al2O3. This tells us that for every 4 moles of aluminum (Al) reacting with 3 moles of oxygen (O2), we get 2 moles of aluminum oxide (Al2O3).
2. Molar Mass: The molar mass of aluminum (Al) is 26.98 g/mol, and the molar mass of aluminum oxide (Al2O3) is 101.96 g/mol.
Now let's calculate the theoretical yield:
Step 1: Convert the mass of aluminum (Al) to moles.
The molar mass of Al is 26.98 g/mol.
Number of moles of Al = Mass of Al / Molar mass of Al
Number of moles of Al = 160 g / 26.98 g/mol
Number of moles of Al = 5.93 mol (rounded to two decimal places)
Step 2: Calculate the moles of aluminum oxide (Al2O3) using the mole ratio from the balanced equation.
From the balanced equation, we know that 4 moles of Al will produce 2 moles of Al2O3.
Moles of Al2O3 = (Number of moles of Al / 4) * 2
Moles of Al2O3 = (5.93 mol / 4) * 2
Moles of Al2O3 = 2.96 mol (rounded to two decimal places)
Step 3: Convert the moles of aluminum oxide (Al2O3) to the mass.
Mass of Al2O3 = Moles of Al2O3 * Molar mass of Al2O3
Mass of Al2O3 = 2.96 mol * 101.96 g/mol
Mass of Al2O3 = 301.88 g (rounded to two decimal places)
The theoretical yield of aluminum oxide (Al2O3) is 301.88 g.
Now let's calculate the percent yield:
The percent yield is calculated by dividing the actual yield by the theoretical yield and multiplying by 100%.
Percent yield = (Actual yield / Theoretical yield) * 100%
In this case, the actual yield is given as 260 g, and the theoretical yield is calculated as 301.88 g.
Percent yield = (260 g / 301.88 g) * 100%
Percent yield = 86.00% (rounded to two decimal places)
The percent yield of the reaction is 86.00%.