Chapter 18, Problem 7QP

Interpretation Introduction

Interpretation:

The number of possible arrangements before and after removal of the central barrier is to be determined and the number of arrangements after the removal of the barriercorresponding to the state in which both molecules are in the left side, right side, and opposite sides of the container, entropy for each state is to be calculated and a comment is to be made on the most probable state of the system after removal of the barrier.

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, and $\Delta S$ is the entropy change of the system.

Mathematically, entropy by Ludwig Boltzmann 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 the 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.