One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is below.
Fe2O3 + 3 CO 2 Fe + 3 CO2
Suppose that 1.86 103 kg of Fe are obtained from a 5.98 103 kg sample of Fe2O3. Assuming that the reaction goes to completion, what is the percent purity of Fe2O3 in the original sample?
This is exactly the same process as in your previous problem. The only difference is that instead of given a reactant and you calculate the product, in this case you are given the product and you must calculate the reactant. By the way you need to find your arrow key. --> or ==> or >>>
To find the percent purity of Fe2O3 in the original sample, we need to compare the amount of Fe2O3 that reacted with the amount of Fe that was obtained.
First, let's calculate the molar mass of Fe2O3:
Fe2 = 2 × atomic mass of Fe = 2 × 55.847 g/mol = 111.694 g/mol
O3 = 3 × atomic mass of O = 3 × 16.00 g/mol = 48.00 g/mol
Molar mass of Fe2O3 = 111.694 g/mol + 48.00 g/mol = 159.694 g/mol
Now, let's calculate the moles of Fe obtained:
Moles of Fe = Mass of Fe / Molar mass of Fe = (1.86 × 10^3 kg) / (55.847 g/mol) = 33.33 × 10^3 mol
According to the balanced equation, 1 mole of Fe2O3 reacts with 2 moles of Fe. So, the moles of Fe2O3 in the original sample can be calculated as follows:
Moles of Fe2O3 = 0.5 × Moles of Fe = 0.5 × (33.33 × 10^3 mol) = 16.67 × 10^3 mol
Now, let's calculate the mass of Fe2O3 in the original sample in grams:
Mass of Fe2O3 = Moles of Fe2O3 × Molar mass of Fe2O3 = (16.67 × 10^3 mol) × (159.694 g/mol) = 2.66 × 10^6 g
Finally, let's calculate the percent purity:
Percent purity = (Mass of Fe2O3 / Mass of original sample) × 100
Percent purity = (2.66 × 10^6 g / (5.98 × 10^3 kg)) × 100 = 44.5%
Therefore, the percent purity of Fe2O3 in the original sample is approximately 44.5%.