Chapter 18, Problem 6QP

Interpretation Introduction

Interpretation:

The number of possible arrangements and the entropy before and after removal of the barrierfor the given number of molecules are to be determined.

Concept introduction:

The quantity that predicts the spontaneity of a process is called Gibbs free energy. The mathematical equation is as follows:

$\Delta G=\Delta H-T\Delta S$ …… (1)

Here, $\Delta G$ is the change in the Gibbs free energy, $\Delta H$ is the enthalpy change of the system, $\Delta S$ is the entropy change of a system, and $T$ is the temperature.

Mathematically, entropy is proposed by Ludwig Boltzmann methodand is given as follows:

$\text{S}\text{=kln}\left(\text{W}\right)$ ….. (2)

Here, $\text{k}$ is Boltzmann Constant $\left(\text{1}{\text{.38×10}}^{\text{-23}}\text{J/K}\right)$ and $\text{W}$ is thenumber of energetically equivalent different ways in which a molecule in a system is arranged.

The number of possible arrangements is given by equation as follows:

$\text{W =}{\text{X}}^{\text{N}}$ ….. (3)

Here, $\text{X}$ is the number of cells and $\text{N}$ is the number of molecules.