To calculate the standard Gibbs free energy change for the reaction, ΔG°ₓₙ, we use the Gibbs free energy of formation values (ΔG°f) for each compound involved in the reaction. The general formula is:

$\Delta G^\circ_{\text{rxn}} = \sum \Delta G^\circ_f \text{(products)} - \sum \Delta G^\circ_f \text{(reactants)}$

Step 1: Write down the reaction and the corresponding ΔG°f values.

For the reaction:

$2 \, \text{H}_2\text{S(g)} + 3 \, \text{O}_2\text{(g)} \rightarrow 2 \, \text{SO}_2\text{(g)} + 2 \, \text{H}_2\text{O(g)}$

we have the following values for ΔG°f:

• $\Delta G^\circ_f (\text{H}_2\text{S}) = -33.4 \, \text{kJ/mol}$
• $\Delta G^\circ_f (\text{SO}_2) = -300.1 \, \text{kJ/mol}$
• $\Delta G^\circ_f (\text{H}_2\text{O}) = -228.6 \, \text{kJ/mol}$
• $\Delta G^\circ_f (\text{O}_2) = 0 \, \text{kJ/mol}$ (by convention, as O₂ is an element in its standard state)

Step 2: Apply the formula.

Now, calculate ΔG°ₓₙ:

[ \Delta G^\circ_{\text{rxn}} = \left[ 2 \times \Delta G^\circ_f (\text{SO}_2) + 2 \times \Delta G^\circ_f (\text{H}_2\text{O}) \right] - \left[ 2 \times \Delta G^\circ_f (\text{H}_2\text{S}) + 3 \times \Delta G^\circ_f (\text{O}_2) \right] ]

Step 3: Substitute the values.

[ \Delta G^\circ_{\text{rxn}} = \left[ 2 \times (-300.1) + 2 \times (-228.6) \right] - \left[ 2 \times (-33.4) + 3 \times 0 \right] ]

Calculate each term:

1. Products: $= 2 \times (-300.1) + 2 \times (-228.6) = -600.2 - 457.2 = -1057.4 \, \text{kJ}$

2. Reactants: $= 2 \times (-33.4) + 3 \times 0 = -66.8 \, \text{kJ}$

3. ΔG°ₓₙ: $= -1057.4 - (-66.8) = -1057.4 + 66.8 = -990.6 \, \text{kJ}$

Answer:

$\Delta G^\circ_{\text{rxn}} = -990.6 \, \text{kJ}$

Would you like a further breakdown, or have any questions?

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Here are five related questions for further exploration:

1. How would changes in temperature affect the Gibbs free energy of this reaction?
2. What is the significance of a negative ΔG°ₓₙ in terms of reaction spontaneity?
3. How would you calculate ΔG°ₓₙ if pressure conditions varied from standard state?
4. What role does entropy play in determining ΔG°ₓₙ in reactions involving gases?
5. How does the formation enthalpy relate to the Gibbs free energy for a given reaction?

Tip: In reactions, a negative ΔG°ₓₙ typically indicates that the reaction is spontaneous under standard conditions.