Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. $\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$ b. $2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$ c. \(\mathrm{HCl}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

For each reaction, we will analyze the change in the number of particles and the phase change (if any). If the reaction results in an increase in the number of particles or a change in phase from a more ordered state to a less ordered state (e.g., solid to gas), it will have a positive ΔS°. In contrast, if the reaction leads to a decrease in the number of particles or a change in phase from a less ordered state to a more ordered state (e.g., gas to solid), it will have a negative ΔS°. a. H2(g) + 1/2 O2(g) -> H2O(l) There is a net decrease in gas molecules from the reactants to products, resulting in a decrease in randomness but no phase change. Hence, ΔS° should be negative. b. 2 CH3OH(g) + 3 O2(g) -> 2 CO2(g) + 4 H2O(g) There is an increase in gas molecules from the reactants to products, which results in an increase in randomness. ΔS° should be positive. c. HCl(g) -> H+(aq) + Cl^-(aq) Here, there is no change in the number of particles, but there is a change in the phase from gas to aqueous, which leads to a more ordered state. Thus, ΔS° should be negative.

To compute ΔS° for each reaction, we will apply the formula: ΔS° = Σ [entropy of products] - Σ [entropy of reactants] For each substance, we will use its given standard entropy value (S°) from reference tables. These entropy values are usually in the units of J/mol K. a. H2(g) + 1/2 O2(g) -> H2O(l) ΔS° = [S°(H2O(l))] - [S°(H2(g)) + 1/2 S°(O2(g))] b. 2 CH3OH(g) + 3 O2(g) -> 2 CO2(g) + 4 H2O(g) ΔS° = [2S°(CO2(g)) + 4S°(H2O(g))] - [2S°(CH3OH(g)) + 3S°(O2(g))] c. HCl(g) -> H+(aq) + Cl^-(aq) ΔS° = [S°(H+(aq)) + S°(Cl^-(aq))] - [S°(HCl(g))] Calculate the values using the standard entropy values from reference tables for each substance and obtain the ΔS° for each reaction.