QuestionMay 29, 2025

8) How many grams of Fe_(2)O_(3) are required in order to produce 4.2 moles of CO_(2) (P.58)

8) How many grams of Fe_(2)O_(3) are required in order to produce 4.2 moles of CO_(2) (P.58)
8) How many grams of Fe_(2)O_(3) are required in order to produce 4.2 moles of CO_(2) (P.58)

Solution
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Answer

223.58 grams of Fe_2O_3 are required. Explanation 1. Write the balanced chemical equation The reaction is Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2. 2. Determine mole ratio From the equation, 3 moles of CO_2 are produced per mole of Fe_2O_3. 3. Calculate moles of Fe_2O_3 needed Moles of Fe_2O_3 = \frac{4.2 \text{ moles } CO_2}{3} = 1.4 \text{ moles } Fe_2O_3. 4. Convert moles of Fe_2O_3 to grams Molar mass of Fe_2O_3 = 2(55.85) + 3(16.00) = 159.7 \text{ g/mol}. Grams of Fe_2O_3 = 1.4 \text{ moles} \times 159.7 \text{ g/mol} = 223.58 \text{ g}.

Explanation

1. Write the balanced chemical equation<br /> The reaction is $Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$.<br /><br />2. Determine mole ratio<br /> From the equation, 3 moles of $CO_2$ are produced per mole of $Fe_2O_3$.<br /><br />3. Calculate moles of $Fe_2O_3$ needed<br /> Moles of $Fe_2O_3 = \frac{4.2 \text{ moles } CO_2}{3} = 1.4 \text{ moles } Fe_2O_3$.<br /><br />4. Convert moles of $Fe_2O_3$ to grams<br /> Molar mass of $Fe_2O_3 = 2(55.85) + 3(16.00) = 159.7 \text{ g/mol}$.<br /> Grams of $Fe_2O_3 = 1.4 \text{ moles} \times 159.7 \text{ g/mol} = 223.58 \text{ g}$.
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