Fe2O3(s)+3CO(g)→2Fe(s)+3CO2(g)
The reaction mixture initially contains 22.55 g Fe2O3 and 14.78 g CO. Determine the limiting reactant and the theoretical yield of Iron.
how many moles of each reactant?
Each mole of Fe2O3 takes 3 moles of CO2
which will be used up first?
the Fe yield will be twice the moles of Fe2O3 consumed.
Convert that to grams
To determine the limiting reactant and the theoretical yield of iron, we need to compare the amount of product each reactant can produce. We will follow these steps:
Step 1: Convert the given masses of Fe2O3 and CO to the number of moles.
First, let's calculate the number of moles of Fe2O3:
The molar mass of Fe2O3 (iron(III) oxide) is:
Fe: 55.85 g/mol
O: 16.00 g/mol (3 atoms = 48.00 g/mol)
Therefore, the molar mass of Fe2O3 is 55.85 g/mol + 48.00 g/mol = 103.85 g/mol.
Number of moles of Fe2O3 = mass / molar mass
Number of moles of Fe2O3 = 22.55 g / 103.85 g/mol
Calculate the number of moles of CO:
The molar mass of CO (carbon monoxide) is:
C: 12.01 g/mol
O: 16.00 g/mol
Therefore, the molar mass of CO is 12.01 g/mol + 16.00 g/mol = 28.01 g/mol.
Number of moles of CO = mass / molar mass
Number of moles of CO = 14.78 g / 28.01 g/mol
Step 2: Use the balanced equation and stoichiometry to determine the number of moles of Fe that can be produced.
From the balanced equation:
Fe2O3:CO = 1:3 (the ratio is 1:3)
Based on the stoichiometry, the reaction requires 1 mole of Fe2O3 to react with 3 moles of CO to produce 2 moles of Fe.
Using this ratio, we can compare the number of moles calculated in step 1 and determine the limiting reactant.
Step 3: Calculate the moles of Fe that can be produced from each reactant.
Moles of Fe produced from Fe2O3 = number of moles of Fe2O3 × (2 moles of Fe / 1 mole of Fe2O3)
Moles of Fe produced from CO = number of moles of CO × (2 moles of Fe / 3 moles of CO)
Step 4: Determine the limiting reactant.
The limiting reactant is the reactant that produces the least number of moles of Fe. The reactant with fewer moles of Fe produced is the limiting reactant.
Step 5: Calculate the theoretical yield of Fe.
The theoretical yield of Fe is the maximum amount of Fe that can be produced based on the limiting reactant.
The theoretical yield of Fe is calculated by multiplying the number of moles of Fe produced from the limiting reactant by the molar mass of Fe:
The molar mass of Fe (iron) is 55.85 g/mol.
Theoretical yield of Fe = moles of Fe produced (limiting reactant) × molar mass of Fe
To summarize, follow these steps to determine the limiting reactant and theoretical yield of Fe:
1. Calculate the number of moles of Fe2O3 and CO.
2. Use the balanced equation to determine the moles of Fe produced from each reactant.
3. Identify the limiting reactant based on the smallest mole value.
4. Calculate the theoretical yield of Fe using the limiting reactant's moles of Fe and the molar mass of Fe.
By following these steps, you can determine the limiting reactant and the theoretical yield of iron in the given reaction mixture.