Question

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

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

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.

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: \(\Delta H > 0\)

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: \(\Delta S > 0\)

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.

Key concepts

Rhombic Sulfur

Rhombic sulfur is one of the two crystalline forms of elemental sulfur. At room temperature, especially around 25°C, rhombic sulfur is the stable form. It features a highly ordered structure, meaning the sulfur atoms are arranged in a regular, repeating pattern which gives it a compact and less chaotic appearance compared to other allotropes.

This ordered structure translates into a lower entropy state. In chemistry, entropy refers to the randomness or disorder in a system. Something that is highly ordered, like rhombic sulfur, has less positional probability for the atoms, meaning the atoms are in a more predictable arrangement. Consequently, rhombic sulfur has smaller entropy compared to its monoclinic counterpart.

Understanding the structure and stability of rhombic sulfur is crucial because any change from this form to another involves energy transitions. For instance, converting this stable form at room temperature to a different form requires specific conditions, like an increase in temperature.

Monoclinic Sulfur

Monoclinic sulfur emerges when rhombic sulfur is heated past a certain threshold, making it the stable form at high temperatures. While structurally still crystalline, monoclinic sulfur has a different geometry than rhombic sulfur. This shift in geometry makes it less ordered than the rhombic form, introducing more randomness in the arrangement of sulfur atoms.

Such disorder leads to an increase in entropy, which means more possible configurations for the sulfur atoms. Imagine trying to organize different shapes on a floor; monoclinic sulfur is like having fewer rules on how to place them, leading to more possible layouts. This increase in entropy ( Delta S > 0) is typical when heating substances as they convert from one form to another, and energy is absorbed from the environment.

While monoclinic sulfur is stable at high temperatures, reverting it back to rhombic sulfur when cooled can involve changes in both enthalpy and entropy, highlighting the reversible nature of some phase transitions.

Enthalpy and Entropy Changes

When rhombic sulfur transitions to monoclinic sulfur, we see both enthalpy and entropy changes. Enthalpy ( Delta H) refers to the total heat content of a system. In the case of sulfur transitioning from rhombic to monoclinic, the process is endothermic. This means it absorbs heat from the surroundings, necessitating an input of energy to facilitate the transition. Consequently, the enthalpy change is positive ( Delta H > 0).

Entropy ( Delta S), as previously discussed, also changes. It measures the degree of disorder or randomness within the system. With the crystal structure becoming less orderly in the monoclinic form, entropy increases. So, the entropy change is also positive ( Delta S > 0).

Understanding these changes is key in the study of phase transitions. Entropy and enthalpy together help predict the spontaneity and nature of reactions under constant pressure and temperature. The combined insights from changes in enthalpy and entropy offer a clearer picture of why and how particular substances favor certain forms under given conditions.