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Gibbs free energy is an essential concept in chemistry. It helps determine whether a chemical reaction is spontaneous under constant pressure and temperature. Spontaneity in this context does not mean the reaction happens quickly but that it is thermodynamically favorable. Gibbs free energy, represented as \( \Delta G \), can be calculated using the equation:\[ \Delta G = \sum G^\circ_{\text{products}} - \sum G^{\circ}_{\text{reactants}} \]This equation tells us the difference in the free energy between the products and reactants. If \( \Delta G \) is negative, it indicates that the reaction is spontaneous, meaning it can proceed without external input. In the case of our reaction involving sulfur dioxide \( (\text{SO}_2) \) and hydrogen sulfide \( (\text{H}_2\text{S}) \), we calculated \( \Delta G \) to be -89.89 kJ/mol. The negative sign indicates a thermodynamically favorable reaction, aiding in the practical application of removing \( \text{SO}_2 \) from gas emissions. Gibbs free energy thus provides valuable insights into reaction feasibility.

Le Chatelier's principle is a fundamental guideline in chemistry. It predicts how a system at equilibrium reacts to changes in conditions. The principle states that if a dynamic equilibrium is disturbed by changing conditions, the position of equilibrium shifts to counteract the change and restore balance.When considering the effect of temperature on our reaction, which involves gases, Le Chatelier's principle indicates that increasing temperature favors the endothermic direction. In our scenario, when the equilibrium shifts to reduce temperature effects, it may move towards producing more \( \text{SO}_2 \), the reactant, as the forward reaction is exothermic. This principle suggests that at higher temperatures, the equilibrium concentration of \( \text{SO}_2 \) may increase, making the removal process less effective. Hence, understanding how equilibrium adjusts under different conditions allows control over the reaction to achieve desired results.

The Van't Hoff equation is a crucial tool for understanding how temperature affects the equilibrium constant of a chemical reaction. It connects the change in the equilibrium constant with temperature and enthalpy change:\[ \frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2} \]In simple terms, the equation provides a quantitative way to see how \( K \), the equilibrium constant, changes with temperature. For our reaction, the enthalpy change \( \Delta H^\circ \) is negative, indicating the reaction is exothermic.According to the Van't Hoff equation, a negative \( \Delta H^\circ \) suggests that an increase in temperature will cause a decrease in the equilibrium constant \( K \). This means less product will be formed at higher temperatures. Consequently, for the removal of \( \text{SO}_2 \), increasing temperature might not be effective. This underlines the importance of controlling temperature to maintain efficiency in chemical processes.