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Sagot :
This is a stoichiometry question in which we have to find the limiting and excess reactant first, then we can determine which is the percent yield of the reaction. First of all, in any stoichiometry question, set up the properly balanced reaction:
4 Al + 3 O2 -> 2 Al2O3
Now we need to determine the molar ratio for this reaction, molar ratio means how many of the compound we need in order for the reaction to occur or how many moles will be produced:
4 moles of Al = 3 moles of O2
4 moles of Al = 2 moles of Al2O3
3 moles of O2 = 2 moles of Al2O3
Now all possible molar ratios were set up
We have:
27.48 grams of Al, molar mass for Al is 27g/mol
98.35 grams of O2, molar mass for O2 is 32g/mol
14.03 grams of Al2O3, molar mass for Al2O3 is 101.96g/mol
If we have 27.48 grams of Al, then we will have:
27g = 1 mol
27.48g = x moles
x = 1.02 moles of Al
According to the molar ratio:
4 moles of Al = 3 moles of O2
1.02 moles of Al = x moles of O2
x = 0.76 moles of O2, this means that if we have 1.02 moles of Al, we will need 0.76 moles of O2 in order for the reaction occur, but we don't know if we have more or less than this amount, let's check:
32g = 1 mol of O2
98.35g = x moles of O2
x = 3.07 moles of O2, therefore we need 0.76 moles but we have 3.07 moles, which means we have an excess of O2 and Al is the limiting reactant
Now we use the limiting reactant, Al, to find the theoretical yield of Al2O3, starting with the molar ratio again:
4 Al = 2 Al2O3
1.02 Al = x Al2O3
x = 0.51 moles of Al2O3 will be produced from 1.02 moles of Al
101.96g = 1 mol
x grams = 0.51 moles
x = 52 grams will be the amount of mass in 0.51 moles of Al2O3
52 grams is the theoretical yield, but the actual yield was 14.03 grams, let's check the percent yield with this formula:
%yield = actual yield/theoretical yield
%yield = 14.03/52
%yield = 0.27
Which is equal to 27% of percent yield from this reaction
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