A sample of hematite Fe2O3 has the mass 4.83 x 10 3 kg. a. how much iron (kg) can be extracted from this sample of hematite?
b. what is the percentage of iron in this ore?
To find the amount of iron (Fe) that can be extracted from the sample of hematite (Fe2O3), we need to consider the stoichiometry of the reaction between hematite and iron.
The balanced chemical equation for this reaction is:
2 Fe2O3 + 3 C → 4 Fe + 3 CO2
From this equation, we can see that each mole of Fe2O3 reacts with 4 moles of Fe. To find the amount of iron that can be extracted, we need to convert the mass of hematite into moles, then use the ratio of moles between Fe2O3 and Fe.
a. Calculating the mass of iron (Fe) that can be extracted:
1. Determine the molar mass of Fe2O3 and Fe.
- Molar mass of Fe2O3: (2 x atomic mass of Fe) + (3 x atomic mass of O)
- Fe: 55.845 g/mol
- O: 15.999 g/mol
- Molar mass of Fe2O3 = (2 x 55.845) + (3 x 15.999) = 159.69 g/mol
- Molar mass of Fe: 55.845 g/mol
2. Convert the mass of hematite (Fe2O3) to moles by dividing the given mass by the molar mass of Fe2O3.
- moles of Fe2O3 = mass of Fe2O3 / molar mass of Fe2O3
- moles of Fe2O3 = 4.83 x 10^3 kg / 159.69 g/mol
- Convert kg to g: 4.83 x 10^3 kg = 4.83 x 10^6 g
- moles of Fe2O3 = 4.83 x 10^6 g / 159.69 g/mol
3. Use the stoichiometric ratio between Fe2O3 and Fe to find the moles of Fe.
- moles of Fe = moles of Fe2O3 x (4 moles of Fe / 2 moles of Fe2O3)
- moles of Fe = (4.83 x 10^6 g / 159.69 g/mol) x (4 mol / 2 mol)
- moles of Fe = 60,401.3 mol
4. Convert the moles of Fe to kilograms by multiplying by the molar mass of Fe and dividing by 1000.
- mass of Fe = moles of Fe x molar mass of Fe / 1000
- mass of Fe = 60,401.3 mol x 55.845 g/mol / 1000
- mass of Fe = 3,372.3 kg
b. Calculating the percentage of iron in the ore:
To calculate the percentage of iron in the ore, we need to divide the mass of iron extracted by the initial mass of the hematite sample, then multiply by 100%.
1. Calculate the percentage of iron:
- Percentage of iron = (mass of Fe / mass of hematite) x 100%
- Percentage of iron = (3,372.3 kg / 4.83 x 10^3 kg) x 100%
Thus, the amount of iron that can be extracted from the sample of hematite is 3,372.3 kg, and the percentage of iron in the ore is calculated using the formula above.