Answer:
a) The limiting reagent in this reaction is SiO₂ .
b) The theoretical yield of Si from this reaction = 72,494.85 g = 72.5 kg
c) The percent yield of Si from this reaction = 91%
Explanation:
a) The limiting reagent is the reagent whose amount at the start of the reaction is in shortage according to the stoichiometric balance. It is is the reactant that determines how much of other reactants will react and how much products will be formed. It is theoretically, completely used up in the reaction.
The non-limiting reagent is usually in excess according to the stoichiometric balance.
154.9 kg of SiO2 is allowed to react with 78.0 kg of carbon to produce 66.0 kg of silicon.
The balanced equation for the reaction is
SiO₂ + 2C -------> Si + 2CO
1 mole of SiO₂ reacts with 2 moles of C according to the stoichiometric balance
To obtain which reactant is in excess and which one is the limiting reagent, we have to find the number of moles of reactant present at the start of the reaction.
Number of moles = (mass)/(molar mass)
For SiO₂, mass = 154.9 kg = 154,900 g, Molar mass = 60.02 g/mol
Number of moles = (154900/60.02)
Number of moles = 2580.81 moles
For Carbon, mass = 78.0 kg = 78,000 g, Molar mass = 12.011 g/mol
Number of moles = (78000/12)
Number of moles = 6494.05 moles
Recall, 1 mole of SiO₂ reacts with 2 moles of C
If Carbon was the limiting reagent,
6494.05 moles of Carbon would require (6494.05/2) moles of SiO₂ to react; 3247.025 moles of SiO₂. Which is more than the available number of moles of SiO₂ at the start of the reaction. Hence, Carbon isn't the limiting reagent.
SiO₂ as the limiting reagent,
1 mole of SiO₂ reacts with 2 moles of Carbon,
2580.81 moles of SiO₂ would react with (2×2580.81) moles of Carbon; 5161.62 moles of Carbon. Which is in the limit of available number of moles of Carbon at the start of the reaction. Hence, SiO₂ is the limiting reagent which determines which amount of other reactants react and the amount of products formed.
b) Theoretical yield of Si in the reaction.
SiO₂ + 2C -------> Si + 2CO
SiO₂ being the limiting reagent.
1 mole of SiO₂ gives 1 mole of Si,
2580.81 moles of SiO₂ will give 2580.81 moles of Si.
Mass produced = (number of moles produced) × (Molar mass)
Number of moles of Si produced = 2580.81 moles
Molar mass of Si = 28.09 g/mol
Theoretical mass of Si produced = (2580.81) × (28.09) = 72494.85 g = 72.5 kg
c) Percemt yield of Si
Percent yield = 100% × (Actual yield)/(Theoretical yield)
Actual yield of Si = 66 kg
Theoretical yield of Si = 72.49485 kg
Percent yield = 100% × (66/72.49485)
Percent yield = 91.04% = 91%
Hope this Helps!!!
