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Chapter 20: Problem 89

There are two forms of solid sulfur: rhombic and monoclinic. The stable form of sulfur at \(25^{\circ} \mathrm{C}\) is the rhombic form. Upon heating, the rhombic form converts to the monoclinic form, which is the stable form of sulfur at high temperatures. Consider the process: $$ \mathrm{S}_{\text { rhombic }}(s) \longrightarrow \mathrm{S}_{\text { monoclinic }}(s) $$ Predict the signs of \(\Delta H\) and \(\Delta S\) for this process. Which form of sulfur has the more ordered structure (has the smaller positional probability)?

Short Answer

Expert verified
The process of converting rhombic sulfur to monoclinic sulfur is endothermic with \(\Delta H > 0\) and an increase in entropy (\(\Delta S > 0\)). The rhombic form of sulfur has a more ordered structure and smaller positional probability compared to the monoclinic form.

Step by step solution

01

Analyze given information and understand transitions

We are given that the rhombic form of sulfur is stable at 25°C and upon heating, it converts to the monoclinic form which is stable at higher temperatures.
02

Predict the sign of ∆H (Enthalpy Change)

For the transition from rhombic sulfur to monoclinic sulfur to occur when heated, the process has to be endothermic. An endothermic process occurs when heat is absorbed from the surroundings to break bonds or change the structure. Therefore, the enthalpy change ∆H for the process must be positive. Prediction: \(\Delta H > 0\)
03

Predict the sign of ∆S (Entropy Change)

Entropy measures the dispersal of energy, and an increase in entropy (∆S > 0) represents a more disordered structure. Since heat is absorbed in the process, it suggests that the molecules are becoming more disordered, leading to an increase in entropy. Prediction: \(\Delta S > 0\)
04

Determine the more ordered structure

We have determined that the process increases the entropy (∆S > 0), which means that the structure of monoclinic sulfur is more disordered than that of rhombic sulfur. Therefore, the rhombic form has a more ordered structure, or a smaller positional probability. In conclusion, the process of converting rhombic sulfur to monoclinic sulfur is endothermic (\(\Delta H > 0\)) with an increase in entropy (\(\Delta S > 0\)). Rhombic sulfur has a more ordered structure with a smaller positional probability compared to the monoclinic form of sulfur.

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