Iron metal is formed during the reduction of iron(III) oxide:
Fe2O3 + 3CO 2Fe + 3CO2
When 29.7 kg of Fe2O3 react with 17.8 kg of CO and 4.5 kg of Fe are recovered, what is the percent yield for the reaction?
To find the percent yield for the reaction, we need to compare the actual yield to the theoretical yield.
Step 1: Calculate the molar masses of Fe2O3, CO, and Fe.
- Molar mass of Fe2O3 = 2 * Atomic mass of Fe + 3 * Atomic mass of O
- Molar mass of Fe2O3 = (2 * 55.845 g/mol) + (3 * 16.00 g/mol) = 159.69 g/mol
- Molar mass of CO = Atomic mass of C + Atomic mass of O
- Molar mass of CO = 12.01 g/mol + 16.00 g/mol = 28.01 g/mol
- Molar mass of Fe = 55.845 g/mol
Step 2: Convert the given masses of Fe2O3, CO, and Fe to moles.
- Moles of Fe2O3 = Mass of Fe2O3 / Molar mass of Fe2O3
- Moles of Fe2O3 = 29.7 kg * (1000 g/kg) / 159.69 g/mol = 185.96 mol
- Moles of CO = Mass of CO / Molar mass of CO
- Moles of CO = 17.8 kg * (1000 g/kg) / 28.01 g/mol = 635.13 mol
Step 3: Use the balanced equation to determine the theoretical yield of Fe.
From the balanced equation: 1 mol Fe2O3 produces 2 mol Fe.
- Moles of Fe = (Moles of Fe2O3) * (2 mol Fe / 1 mol Fe2O3)
- Moles of Fe = 185.96 mol * (2 mol Fe / 1 mol Fe2O3) = 371.92 mol
Step 4: Calculate the theoretical mass of Fe.
- Mass of Fe = Moles of Fe * Molar mass of Fe
- Mass of Fe = 371.92 mol * 55.845 g/mol = 20,764.81 g
Step 5: Calculate the percent yield.
- Percent Yield = (Actual yield / Theoretical yield) * 100
- Actual yield = 4.5 kg * (1000 g/kg) = 4500 g
- Percent Yield = (4500 g / 20,764.81 g) * 100 = 21.68%
The percent yield for the reaction is approximately 21.68%.
To calculate the percent yield for a reaction, you need to compare the actual yield (the amount of product obtained) to the theoretical yield (the maximum amount of product that could be obtained according to the balanced chemical equation).
In this case, the balanced chemical equation is:
Fe2O3 + 3CO -> 2Fe + 3CO2
From the balanced equation, we can see that the molar ratio between Fe2O3 and Fe is 1:2. This means that for every 1 mole of Fe2O3 reacted, 2 moles of Fe will be produced.
First, let's convert the masses of Fe2O3, CO, and Fe to moles:
- Moles of Fe2O3: 29.7 kg of Fe2O3 * (1 mol Fe2O3 / molar mass of Fe2O3)
- Moles of CO: 17.8 kg of CO * (1 mol CO / molar mass of CO)
- Moles of Fe: 4.5 kg of Fe * (1 mol Fe / molar mass of Fe)
Next, we can determine the theoretical yield of Fe by using the mole ratio from the balanced equation. Since the molar ratio is 1:2 between Fe2O3 and Fe, we can calculate the moles of Fe that would be produced if all the Fe2O3 reacted.
- Moles of Fe (theoretical yield): Moles of Fe2O3 * (2 mol Fe / 1 mol Fe2O3)
Now, calculate the actual yield of Fe by using the given mass of Fe:
- Moles of Fe (actual yield): 4.5 kg of Fe * (1 mol Fe / molar mass of Fe)
Finally, to find the percent yield, divide the actual yield by the theoretical yield and multiply by 100:
- Percent yield: (Moles of Fe [actual yield] / Moles of Fe [theoretical yield]) * 100
Plug in the calculated values into the equation above to find the percent yield.