91Ó°ÊÓ

Solubility: The maximum amount of solute that can be dissolved in the solvent at equilibrium is defined as solubility.

Constant of soluble product: For equilibrium between solids and their respective ions in a solution, the solubility product constant is defined. In general, the term "solubility product" refers to water-equilibrium insoluble or slightly soluble ionic substances.

Considering the given reaction:

$\text{S(rhombic)}⇌\text{S(monoclinic)}$

First, use the enthalpy constants from Appendix B to solve for${\text{Δ±á}}^{\text{°}}$ .

$\begin{array}{c}{\text{Δ±á}}^{\text{°}}\text{=}∑{\text{n}}_{\text{p}}{\text{Δ±á}}_{\text{f}}^{\text{°}}\text{(product)-}∑{\text{n}}_{\text{r}}{\text{Δ±á}}_{\text{f}}^{\text{°}}\text{(reactant)}\\ \text{=}\left[{\text{nΔ±á}}_{\text{f}}^{\text{°}}\text{(S(monoclinic))}\right]\text{-}\left[{\text{nΔ±á}}_{\text{f}}^{\text{°}}\text{(S(rhombic))}\right]\\ {\text{=([1(0.3)]-[1(0)])kJΔ±á}}^{\text{°}}\\ \text{=0.3kJ}\end{array}$

Then, using the entropy constants in Appendix B, solve for${\text{Δ³§}}^{\text{°}}$ .

$\begin{array}{c}{\text{Δ³§}}^{\text{°}}\text{=}∑{\text{n}}_{\text{p}}{\text{S}}^{\text{°}}\text{(product)-}∑{\text{n}}_{\text{r}}{\text{S}}^{\text{°}}\text{(reactant)}\\ \text{=}\left[{\text{nS}}^{\text{°}}\text{(S(monoclinic))}\right]\text{-}\left[{\text{nS}}^{\text{°}}\text{(S(rhombic))}\right]\\ {\text{=([1(32.6)]-[1(31.9)])J/KΔ³§}}^{\text{°}}\\ \text{=0.7J/K}\end{array}$

Finally, find T at equilibrium.${\text{Δ³Ò}}^{\text{°}}\text{=0}$ ,

$\begin{array}{c}{\text{Δ³Ò}}^{\text{°}}{\text{=Δ±á}}^{\text{°}}{\text{-TΔ³§}}^{\text{°}}\\ {\text{0=Δ±á}}^{\text{°}}{\text{-TΔ³§}}^{\text{°}}\\ {\text{TΔ³§}}^{\text{°}}{\text{=Δ±á}}^{\text{°}}\\ \text{T=}\frac{{\text{Δ±á}}^{\text{°}}}{{\text{Δ³§}}^{\text{°}}}\\ \text{=}\frac{\text{0.3°ì´³Ã—}\frac{\text{1000J}}{\text{1kJ}}}{\text{0.7J/K}}\\ \text{T=429K}\end{array}$

Therefore, the T at equilibrium of sulfur allotropes is at $\text{429K}$.