Chapter 4, Problem 4A.1ST

Interpretation Introduction

Interpretation:

The reference state of sulfur at 298 K has to be identified using the informations in the resource section.

Concept introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  $\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$

Where,

  $\text{ΔG }$ is the change in free energy of the system

  $\Delta {\rm H}$ is the change in enthalpy of the system

  $\text{T}$ is the absolute value of the temperature

  $\Delta \text{S}$ is the change in entropy in the system

Gibb’s energy is an important factor which greatly affect the thermodynamic stability of a molecule or compound.

For example:  when state A is said to be more thermodynamically stable than state B of a chemical system, if the Gibbs energy of the change from A to B is positive.

The stable state of the chemical system is taken as its reference state.

Explanation of Solution

According to the resource section, two different states of sulfur and its standard Gibbs energy changes are mentioned below,

$\begin{array}{cc}State& \boxed{{\Delta }_r{G}^0\left(kJmo{l}^{-1}\right)}\\ \text{S}\left(\text{s,α}\right)\to \text{rhombic}& 0\\ \text{S}\left(\text{s,β}\right)\to \text{monoclinic}& +0.1\end{array}$

Gibb’s energy is an important factor which greatly affect the thermodynamic stability of a molecule or compound.

For example:  when state A is said to be more thermodynamically stable than state B of a chemical system, if the Gibbs energy of the change from A to B is positive.

The Gibbs energy transition from rhombic sulfur (A) to monoclinic sulfur (B) is +0.1. The positive value of Gibbs energy transition reveals the higher thermodynamic stability of rhombic sulfur over monoclinic sulphur’s stability and so the rhombic sulfur is identified as the reference state of sulfur.