Question

What is the maximum mass of iron, in tonnes, that can be obtained when 40 tonnes of iron(III) oxide, Fe2O3 (Molecular weight = 160), are reduced in a blast furnace according to the equation below? Fe2O3 + 3CO → 2Fe + 3CO2

Answer 1

Main Answer:

The maximum mass of iron that can be obtained is approximately 29.17 tonnes.

Step-by-step explanation:

The balanced chemical equation indicates a 1:2 ratio between iron(III) oxide (Fe2O3) and iron (Fe). This means that for every mole of Fe2O3, two moles of Fe are produced. To find the moles of iron, we use the given mass of Fe2O3 (40 tonnes) and its molar mass (160 g/mol):

`\[\text{Moles of Fe2O3} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{40 \, \text{tonnes} * 1000 \, \text{kg/tonne}}{160 \, \text{g/mol}} = 250 \, \text{moles}\]`

Since the ratio is 1:2 (Fe2O3 to Fe), the moles of iron (Fe) produced will be twice the moles of Fe2O3:

`\[\text{Moles of Fe} = 2 * \text{Moles of Fe2O3} = 2 * 250 \, \text{moles} = 500 \, \text{moles}\]`

Now, calculate the mass of iron using its molar mass (56 g/mol):

`\[\text{Mass of Fe} = \text{Moles of Fe} * \text{Molar Mass of Fe} = 500 \, \text{moles} * 56 \, \text{g/mol} = 28000 \, \text{g} = 28 \, \text{tonnes}\]`

Therefore, the maximum mass of iron that can be obtained is 28 tonnes.