Final answer:
To calculate the number of grams of Fe2O3 needed to react with 14.4 g C, use the stoichiometric ratio in the balanced chemical equation. First, calculate the number of moles of C using its molar mass. Then, use the stoichiometric ratio to calculate the moles of Fe2O3. Finally, convert the moles of Fe2O3 to grams.
Step-by-step explanation:
To calculate the number of grams of Fe2O3 needed to react with 14.4 g C, we need to determine the stoichiometric ratio between Fe2O3 and C in the balanced chemical equation. According to the equation 2Fe2O3(s) + 3C(s) → 4Fe(s) + 3CO2(g), we can see that for every 3 moles of C, we need 2 moles of Fe2O3.
Using the molar mass of C (12.01 g/mol) and Fe2O3 (159.69 g/mol) we can calculate the number of moles of C in 14.4 g:
(14.4 g C) / (12.01 g/mol) = 1.199 moles C
Now, using the stoichiometric ratio, we can calculate the moles of Fe2O3:
(1.199 moles C) x (2 moles Fe2O3 / 3 moles C) = 0.799 moles Fe2O3
Finally, we can convert the moles of Fe2O3 to grams:
(0.799 moles Fe2O3) x (159.69 g/mol) = 127.66 g Fe2O3