Questions: Al2O3(s) -> 2 Al(s) + 3/2 O2(g) ΔH° = 1675 kJ / molrxn Calculate the energy required to decompose 400 g of Al2O3. Answer in kJ.

Transcript text: \[ \mathrm{Al}_{2} \mathrm{O}_{3}(s) \rightarrow 2 \mathrm{Al}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \quad \Delta H ゚=1675 \mathrm{~kJ} / \mathrm{mol}_{\mathrm{rxn}} \] Calculate the energy required to decompose $400 . \mathrm{g}$ of $\mathrm{Al}_{2} \mathrm{O}_{3}$. Answer in kJ .

Solution

Solution Steps

Step 1: Determine the Molar Mass of $\mathrm{Al}_{2}\mathrm{O}_{3}$

Calculate the molar mass of $\mathrm{Al}_{2}\mathrm{O}_{3}$ using the atomic masses of aluminum (Al) and oxygen (O):

Aluminum (Al): $26.98 \, \text{g/mol}$
Oxygen (O): $16.00 \, \text{g/mol}$

\[ \text{Molar mass of } \mathrm{Al}_{2}\mathrm{O}_{3} = 2 \times 26.98 + 3 \times 16.00 = 101.96 \, \text{g/mol} \]

Step 2: Calculate the Number of Moles of $\mathrm{Al}_{2}\mathrm{O}_{3}$

Use the mass of $\mathrm{Al}_{2}\mathrm{O}_{3}$ given in the problem to find the number of moles:

\[ \text{Number of moles} = \frac{400 \, \text{g}}{101.96 \, \text{g/mol}} \approx 3.92 \, \text{mol} \]

Step 3: Calculate the Energy Required

Use the enthalpy change $\Delta H$ given for the reaction to find the total energy required for the decomposition:

\[ \text{Energy required} = 3.92 \, \text{mol} \times 1675 \, \text{kJ/mol} \approx 6566 \, \text{kJ} \]

Final Answer

$\boxed{6566 \, \text{kJ}}$

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