The reaction SO₂(g) + 2 H₂S(g) ⇌ 3 S(s) + 2 H₂O(g) is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at 298 K? (c) If P_SO2 = P_H2S and the vapor pressure of water is 25 torr, calculate the equilibrium SO₂ pressure in the system at 298 K.

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Identify the reaction: \( \text{SO}_2(g) + 2 \text{H}_2\text{S}(g) \rightleftharpoons 3 \text{S}(s) + 2 \text{H}_2\text{O}(g) \).

Use the standard free energy change \( \Delta G^\circ \) for the reaction, which can be calculated using \( \Delta G^\circ = \sum \Delta G^\circ_{\text{products}} - \sum \Delta G^\circ_{\text{reactants}} \).

Apply the relationship between \( \Delta G^\circ \) and the equilibrium constant \( K_p \) using the equation \( \Delta G^\circ = -RT \ln K_p \), where \( R \) is the gas constant and \( T \) is the temperature in Kelvin.

Express the equilibrium constant \( K_p \) in terms of partial pressures: \( K_p = \frac{(P_{\text{H}_2\text{O}})^2}{(P_{\text{SO}_2})(P_{\text{H}_2\text{S}})^2} \).

Given that \( P_{\text{SO}_2} = P_{\text{H}_2\text{S}} \) and \( P_{\text{H}_2\text{O}} = 25 \text{ torr} \), substitute these into the expression for \( K_p \) and solve for \( P_{\text{SO}_2} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction provided, K can be calculated using the partial pressures of the gases involved. Understanding K is crucial for determining how changes in pressure or concentration affect the position of equilibrium.

Gibbs Free Energy (ΔG)

Gibbs free energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The relationship between ΔG and the equilibrium constant (K) is given by the equation ΔG = -RT ln(K). This concept is essential for predicting the spontaneity of the reaction and understanding how the free energy changes with varying conditions.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle is important in predicting how the equilibrium position will shift in response to changes in pressure, concentration, or temperature, which is relevant for calculating the equilibrium pressure of SO2 in the given reaction.

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Le Chatelier's Principle

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The reaction SO₂(g) + 2 H₂S(g) ⇌ 3 S(s) + 2 H₂O(g) is the basis of a suggested method for removal of SO₂ from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (b) In principle, is this reaction a feasible method of removing SO₂?

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The reaction SO₂(g) + 2 H₂S(g) ⇌ 3 S(s) + 2 H₂O(g) is the basis of a suggested method for removal of SO₂ from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (d) Would you expect the process to be more or less effective at higher temperatures?

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