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Sagot :
Explanation:
1.8 moles of Fe2O3 will react with 2.7 moles of CO according to the following unbalanced equation.
__ Fe₂O₃ + __ CO ----> __ Fe + __ CO₂
First we have to balance this equation. We have to determine the number of atoms of each element that we have on both sides of the equation.
__ Fe₂O₃ + __ CO ----> __ Fe + __ CO₂
Fe: 2 Fe: 1
C: 1 C: 1
O: 4 O: 2
We have two atoms of Fe on the left and just one on the right side of the equation. Then we have to change the coefficient for Fe and write a 2 there.
__ Fe₂O₃ + __ CO ----> 2 Fe + __ CO₂
Fe: 2 Fe: 2
C: 1 C: 1
O: 4 O: 2
C is already balanced but O is not. We have 4 atoms of O on the left and only two on the right. So we have to change the coefficient for CO₂ and write a 2 there.
__ Fe₂O₃ + __ CO ----> 2 Fe + 2 CO₂
Fe: 2 Fe: 2
C: 1 C: 2
O: 4 O: 4
We balanced the O but unbalanced the C. Now we have to change the coefficient for CO to balance the C atoms. If we put a 2 there we will unbalance again the O atoms and will get a fraction. We can try with 3 as a coefficient for CO.
__ Fe₂O₃ + 3 CO ----> 2 Fe + 2 CO₂
Fe: 2 Fe: 2
C: 3 C: 2
O: 6 O: 4
And finally we can change again the coefficient for CO₂ and write a 3 there to balance the equation.
__ Fe₂O₃ + 3 CO ----> 2 Fe + 3 CO₂
Fe: 2 Fe: 2
C: 3 C: 3
O: 6 O: 6
The balanced equation is:
Fe₂O₃ + 3 CO ----> 2 Fe + 3 CO₂
Now we knoe that 1.8 moles of Fe₂O₃ reacted with 2.7 moles of CO. We have to find the limiting reactant. According to the equation of the reaction 1 mol of Fe₂O₃ will react with 3 moles of Co to produce 2 moles of Fe and 3 moles of CO₂. The mole ratio between Fe₂O₃ and CO is 1 to 3. We can use that relationship to find the number of moles of CO that will completely react with 1.8 moles of Fe₂O₃.
1 mol of Fe₂O₃ : 3 moles of CO mole ratio
moles of CO = 1.8 moles of Fe₂O₃ * 3 moles of CO/(1 mol of Fe₂O₃)
moles of CO = 5.4 moles
We found that 1.8 moles of Fe₂O₃ need 5.4 moles of CO to completely react, but we only had 2.7 moles of CO. So we can conclude that Fe₂O₃ is in excess and CO is limiting the reaction.
Fe₂O₃ ----> excess reactant CO ---> limiting reactant
Finally we can find the number of moles of each product that are produced when 2.7 moles of CO are completely reacted. We will use the molar ratio between it and the products.
Fe₂O₃ + 3 CO ----> 2 Fe + 3 CO₂
3 moles of CO : 2 moles of Fe molar ratio
moles of Fe = 2.7 moles of CO * 2 moles of Fe/(3 moles of CO)
moles of Fe = 1.8 moles
3 moles of CO : 3 moles of CO₂ molar ratio
moles of CO₂ = 2.7 moles of CO * 3 moles of CO₂/(3 moles of CO)
moles of CO₂ = 2.7 moles
Answer: d) 1.8 moles of Fe and 2.7 moles of CO₂.
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