Question

From these data, $$\begin{array}{l}\mathrm{S} \text { (rhombic) }+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \\\\\qquad \begin{aligned}\Delta H_{\mathrm{rxn}}^{\circ} &=-296.4 \mathrm{~kJ} / \mathrm{mol}\end{aligned} \\\\\mathrm{S} \text { (monoclinic) }+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \\\\\Delta H_{\mathrm{rxn}}^{\circ}=-296.7 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ calculate the enthalpy change for the transformation \(\mathrm{S}\) (rhombic) \(\longrightarrow \mathrm{S}\) (monoclinic) (Monoclinic and rhombic are different allotropic forms of elemental sulfur.)

Short answer

The enthalpy change for the transformation from rhombic to monoclinic sulfur is \(-0.3 \text{ kJ/mol}\).

Step-by-step solution

Understand the Reactions

We are given two chemical reactions for the formation of \( \text{SO}_2 \) from different allotropes of sulfur: rhombic and monoclinic. Each has its own standard enthalpy change. Our goal is to find the enthalpy change (\( \Delta H \)) for converting rhombic sulfur to monoclinic sulfur.

Use Enthalpy Change Relationships

Enthalpy is a state function, meaning it is independent of the path taken. Hence, we can use the given enthalpy changes to find the desired transformation. We know:1. \( \mathrm{S} \text{ (rhombic)} + \mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g), \Delta H = -296.4 \text{ kJ/mol} \).2. \( \mathrm{S} \text{ (monoclinic)} + \mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g), \Delta H = -296.7 \text{ kJ/mol} \).

Calculate the Difference in Enthalpy Changes

To find the enthalpy change for the transformation from rhombic to monoclinic sulfur, subtract the enthalpy change of the monoclinic reaction from the rhombic reaction:\[ \Delta H = -296.7 \text{ kJ/mol} - (-296.4 \text{ kJ/mol}) = -0.3 \text{ kJ/mol} \].

Interpret the Result

The enthalpy change for the transformation of rhombic sulfur to monoclinic sulfur is \( \Delta H = -0.3 \text{ kJ/mol} \). This indicates that the transformation is exothermic, releasing a small amount of heat.

Key concepts

Allotropes of Sulfur

Sulfur is a fascinating element that exists in more than one structural form called allotropes. Two notable allotropes of sulfur are rhombic and monoclinic. These forms differ in how sulfur atoms are arranged in the solid state.
Rhombic sulfur is the most stable form under normal atmospheric conditions, appearing as bright yellow crystals. Monoclinic sulfur, on the other hand, is stable only at slightly higher temperatures and reverts back to rhombic upon cooling.
Understanding allotropes is crucial because they can affect various chemical properties such as stability and reactivity. In our exercise, we explore the enthalpy change between these two forms, highlighting the energetic effects of atomic arrangement on the chemical state of sulfur.
Sulfur's different forms remind us that even a simple element can exhibit complex behavior based on its molecular arrangement.

State Function

A state function is a property whose value is determined solely by the state of a system, irrespective of how the system reached that state. Enthalpy is a perfect example of a state function. Simplifying further, it means that the change in enthalpy ( abla abla H) in transitioning from one state to another is path-independent.
In chemical reactions, this concept allows us to use known enthalpy changes of specific reactions to find unknown values by constructing alternate pathways.
For instance, we use the enthalpy changes of sulfur oxidation reactions to calculate the enthalpy change for converting rhombic sulfur into monoclinic sulfur. This highlights how understanding state functions facilitates calculations that may otherwise be challenging.

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy, usually in the form of heat. This energy release often makes the surroundings warmer and is a common characteristic in many chemical processes.
In our exercise, the transformation from sulfur in its rhombic form to its monoclinic form has been identified as an exothermic process. This is deduced from the negative value of the calculated enthalpy change ( abla abla H = -0.3 ext{kJ/mol}).
Such transformations, although might have small heat release, are important as they indicate a spontaneous energy shift to a more stable state under particular conditions. Therefore, exothermic reactions are crucial in understanding both thermodynamics and everyday chemical transformations.

Enthalpy Change Calculation

Enthalpy change calculation is an essential process in understanding the thermal dynamics of chemical reactions. In our situation, we aim to determine the heat change when sulfur transforms from its rhombic to monoclinic allotrope.
Using the values provided, we first identify the enthalpy of each related reaction where sulfur changes into sulfur dioxide. The enthalpy change for these reactions are given as \(\Delta H = -296.4 \text{kJ/mol}\) for rhombic sulfur and \(\Delta H = -296.7 \text{kJ/mol}\) for monoclinic sulfur.
Utilizing the concept of state functions, we deduce the enthalpy change for the desired transformation by finding the difference between these two known enthalpies:
\[\Delta H = -296.7 \text{kJ/mol} - (-296.4 \text{kJ/mol}) = -0.3 \text{kJ/mol}\].
This calculation results in a negative value, indicating an exothermic process. Understanding these steps helps clarify enthalpy change and highlights the systematic approach to determining reaction energetics.