Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

Reference the values of Gibbs free energy (G) for Ag(s), Cl₂(g), and AgCl(s).

Calculate the change in Gibbs free energy (∆G) using the equation: ∆G = ∆G(products) - ∆G(reactants) ∆G = [2 × G(AgCl)] - [2 × G(Ag) + G(Cl₂)] Calculate the value of ∆G and determine whether the reaction is spontaneous at 298 K. (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ Repeat the steps from the first reaction. (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ Repeat the steps from the first reaction. (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$ Repeat the steps from the first reaction. For each reaction, if the calculated ∆G is negative, the reaction is spontaneous at 298 K under standard conditions.