Answer
(a) 1.33 mol
(b) 4.8 mol
(c) 0.107 mol
(d) 27.5 mol
Work Step by Step
(a) Calculating how much product can be made based on the amount of each reactant, we have
$2\,mol\,Mn\times\frac{2\,mol\,MnO_{3}}{2\,mol\,Mn}=2\,mol\,MnO_{3}$
$2\,mol\,O_{2}\times\frac{2\,mol\,MnO_{3}}{3\,mol\,O_{2}}=1.33\,mol\,MnO_{3}$
Since $2\,mol\,O_{2}$ makes the least amount of product, it is the limiting reactant.
Theoretical yield is the maximum amount of product that can be made in a reaction based on the amount of limiting reactant.
Therefore, theoretical yield= $1.33\,mol$.
(b) Calculating how much product can be made based on the amount of each reactant, we have
$4.8\,mol\,Mn\times\frac{2\,mol\,MnO_{3}}{2\,mol\,Mn}=4.8\,mol\,MnO_{3}$
$8.5\,mol\,O_{2}\times\frac{2\,mol\,MnO_{3}}{3\,mol\,O_{2}}=5.67\,mol\,MnO_{3}$
Since $4.8\,mol\,Mn$ makes the least amount of product, it is the limiting reactant.
Theoretical yield= $4.8\,mol$
(c) Calculating how much product can be made based on the amount of each reactant, we have
$0.114\,mol\,Mn\times\frac{2\,mol\,MnO_{3}}{2\,mol\,Mn}=0.114\,mol\,MnO_{3}$
$0.161\,mol\,O_{2}\times\frac{2\,mol\,MnO_{3}}{3\,mol\,O_{2}}=0.107\,mol\,MnO_{3}$
Since $0.161\,mol\,O_{2}$ makes the least amount of product, it is the limiting reactant.
Theoretical yield= $0.107\,mol$
(d) Calculating how much product can be made based on the amount of each reactant, we have
$27.5\,mol\,Mn\times\frac{2\,mol\,MnO_{3}}{2\,mol\,Mn}=27.5\,mol\,MnO_{3}$
$43.8\,mol\,O_{2}\times\frac{2\,mol\,MnO_{3}}{3\,mol\,O_{2}}=29.2\,mol\,MnO_{3}$
Since $27.5\,mol\,Mn$ makes the least amount of product, it is the limiting reactant.
Theoretical yield= $27.5\,mol$
