Pregunta
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When performing the molar mass of \( \mathrm{Al} 2(\mathrm{C} 2 \mathrm{O} 4) 3 \) your calculated * 7 poir that the mass was \( 318.0 \mathrm{~g} / \mathrm{mol} \). What would be the percent composition of C? Your answer

Ask by Sullivan Sanders. in the United States
Feb 04,2025

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The percent composition of carbon in \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \) is **22.7%**.

Solución

To determine the percent composition of carbon (C) in the compound \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \), follow these steps: 1. **Calculate the Molar Mass of Each Element in the Compound:** - **Aluminum (Al):** \[ 2 \text{ atoms} \times 26.98 \, \text{g/mol} = 53.96 \, \text{g/mol} \] - **Carbon (C):** \[ 2 \, (\text{per oxalate}) \times 3 \, (\text{oxalate groups}) \times 12.01 \, \text{g/mol} = 72.06 \, \text{g/mol} \] - **Oxygen (O):** \[ 4 \, (\text{per oxalate}) \times 3 \, (\text{oxalate groups}) \times 16.00 \, \text{g/mol} = 192.00 \, \text{g/mol} \] 2. **Total Molar Mass of the Compound:** \[ 53.96 \, \text{g/mol} \, (\text{Al}) + 72.06 \, \text{g/mol} \, (\text{C}) + 192.00 \, \text{g/mol} \, (\text{O}) = 318.02 \, \text{g/mol} \] (This matches the given molar mass of \( 318.0 \, \text{g/mol} \).) 3. **Calculate the Percent Composition of Carbon:** \[ \text{Percent C} = \left( \frac{72.06 \, \text{g/mol}}{318.0 \, \text{g/mol}} \right) \times 100\% \approx 22.7\% \] **Final Answer:** The percent composition of carbon in \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \) is **22.7 %**.

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Bonus Knowledge

To find the percent composition of carbon (C) in the compound \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \), we first need to determine the molar mass of carbon in this compound. The molar mass of carbon (C) is approximately \( 12.01 \, \text{g/mol} \), and in \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \), there are 6 carbon atoms (from 3 \( \mathrm{C}_2\mathrm{O}_4 \)), amounting to \( 6 \times 12.01 \, \text{g/mol} = 72.06 \, \text{g/mol} \). Now, to calculate the percent composition of carbon, we use the formula: \[ \text{Percent composition of C} = \left( \frac{\text{mass of C in the formula}}{\text{molar mass of the compound}} \right) \times 100 \] Substituting the values we found: \[ \text{Percent composition of C} = \left( \frac{72.06 \, \text{g/mol}}{318.0 \, \text{g/mol}} \right) \times 100 \approx 22.65\% \] So, the percent composition of carbon in \( \mathrm{Al}_2(\mathrm{C}_2\mathrm{O}_4)_3 \) is approximately \( 22.65\% \). If you find yourself frequently calculating percent composition, remember that it helps to first get the total molar mass of the entire compound. This not only gives perspective on the relationship of each element but also makes calculations easier and cleaner! Most mistakes happen when the molar masses are added incorrectly or atomic quantities are miscounted. Always double-check your arithmetic and stoichiometry before diving into the final calculation!

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