Questions: Using the thermodynamic information in the ALEKS Data tab, calculate the standard reaction free energy of the following chemical rear Al2O3(s) + 3 H2(g) → 2 Al(s) + 3 H2O(g) Round your answer to zero decimal places. kJ

Using the thermodynamic information in the ALEKS Data tab, calculate the standard reaction free energy of the following chemical rear
Al2O3(s) + 3 H2(g) → 2 Al(s) + 3 H2O(g)

Round your answer to zero decimal places.
kJ

Transcript text: Using the thermodynamic information in the ALEKS Data tab, calculate the standard reaction free energy of the following chemical rear \[ \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Al}(\mathrm{~s})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{~g}) \] Round your answer to zero decimal places. $\square$ kJ

Solution

Solution Steps

Step 1: Identify the Standard Gibbs Free Energy of Formation ($\Delta G_f^\circ$) for Each Substance

From the thermodynamic data, we need the standard Gibbs free energy of formation for each substance involved in the reaction:

$\Delta G_f^\circ (\mathrm{Al}_2\mathrm{O}_3(\mathrm{s}))$
$\Delta G_f^\circ (\mathrm{H}_2(\mathrm{g}))$
$\Delta G_f^\circ (\mathrm{Al}(\mathrm{s}))$
$\Delta G_f^\circ (\mathrm{H}_2\mathrm{O}(\mathrm{g}))$

Step 2: Write the Standard Gibbs Free Energy of Formation Values

Assuming the following standard Gibbs free energy of formation values (in kJ/mol):

$\Delta G_f^\circ (\mathrm{Al}_2\mathrm{O}_3(\mathrm{s})) = -1582.3$
$\Delta G_f^\circ (\mathrm{H}_2(\mathrm{g})) = 0$
$\Delta G_f^\circ (\mathrm{Al}(\mathrm{s})) = 0$
$\Delta G_f^\circ (\mathrm{H}_2\mathrm{O}(\mathrm{g})) = -228.6$

Step 3: Calculate the Standard Reaction Free Energy ($\Delta G^\circ_{\text{reaction}}$)

The standard reaction free energy is calculated using the formula: \[ \Delta G^\circ_{\text{reaction}} = \sum \Delta G_f^\circ (\text{products}) - \sum \Delta G_f^\circ (\text{reactants}) \]

For the given reaction: \[ \mathrm{Al}_2\mathrm{O}_3(\mathrm{s}) + 3 \mathrm{H}_2(\mathrm{g}) \rightarrow 2 \mathrm{Al}(\mathrm{s}) + 3 \mathrm{H}_2\mathrm{O}(\mathrm{g}) \]

\[ \Delta G^\circ_{\text{reaction}} = [2 \cdot \Delta G_f^\circ (\mathrm{Al}(\mathrm{s})) + 3 \cdot \Delta G_f^\circ (\mathrm{H}_2\mathrm{O}(\mathrm{g}))] - [\Delta G_f^\circ (\mathrm{Al}_2\mathrm{O}_3(\mathrm{s})) + 3 \cdot \Delta G_f^\circ (\mathrm{H}_2(\mathrm{g}))] \]

Substitute the values: \[ \Delta G^\circ_{\text{reaction}} = [2 \cdot 0 + 3 \cdot (-228.6)] - [-1582.3 + 3 \cdot 0] \]

\[ \Delta G^\circ_{\text{reaction}} = [0 - 685.8] - [-1582.3] \]

\[ \Delta G^\circ_{\text{reaction}} = -685.8 + 1582.3 \]

\[ \Delta G^\circ_{\text{reaction}} = 896.5 \, \text{kJ} \]