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4. Calculate the atom economy for the production of iron from iron(III) oxide in the blast furnace. Fe_(2)O_(3)+3COarrow 2Fe+3CO_(2)

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SophieProfessional · Tutor for 6 years

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45.8%

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## Step 1: First, we need to understand what atom economy is. Atom economy is a measure of the amount of starting materials that become useful products. In other words, it is the theoretical yield of the desired product divided by the total yield of all products, multiplied by 100%. ### The formula for atom economy is: **\[ \text{Atom Economy} = \frac{\text{Molar mass of desired product}}{\text{Total molar mass of all reactants}} \times 100\% \]** ## Step 2: In this reaction, the desired product is iron (Fe). So, we need to calculate the molar mass of iron and the total molar mass of all reactants. ### The molar mass of iron (Fe) is: **\[ \text{Molar mass of Fe} = 2 \times \text{atomic mass of Fe} = 2 \times 55.85 \text{g/mol} = 111.7 \text{g/mol} \]** ### The total molar mass of all reactants is: **\[ \text{Total molar mass of reactants} = \text{molar mass of Fe}_2\text{O}_3 + 3 \times \text{molar mass of CO} = (2 \times 55.85 + 3 \times 16) \text{g/mol} + 3 \times (12.01 + 16) \text{g/mol} = 159.7 \text{g/mol} + 3 \times 28.01 \text{g/mol} = 159.7 \text{g/mol} + 84.03 \text{g/mol} = 243.73 \text{g/mol} \]** ## Step 3: Now, we can substitute these values into the atom economy formula to calculate the atom economy for the production of iron from iron(III) oxide. ### The atom economy is: **\[ \text{Atom Economy} = \frac{111.7 \text{g/mol}}{243.73 \text{g/mol}} \times 100\% = 45.8\% \]**

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4. Calculate the atom economy for the production of iron from iron(III) oxide in the blast furnace. Fe_(2)O_(3)+3COarrow 2Fe+3CO_(2)

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