Chapter 17, Problem 17.4P

Interpretation Introduction

Interpretation:

The entropy of the disorder state of the crystal should be determined.

Concept introduction: The entropy S can be expressed as:

$S=k_{B}ln\Omega$

where O is the probability or number of arrangements possible and k_B is a proportionality constant.

$\Omega =a^N$

a = number of configurations possible for the molecule

N = number of molecules.

This entropy is an extensive property and relies on the number of molecules.Doubling the number of molecules doubles the entropy.

In terms of moles of gas and not molecules by setting

$k=R{N}_A$

Where k = Boltzmann constant = 1.3807 x 10 -23 joule s per kelvin (J. K -1)

R= gas constant = R is 8.314 (J. K -¹mol-1)

N_A= Avogadro number

Given: A disordered crystal of phosgene in which each trigonal planar $COC{l}_2$ molecule is oriented randomly in one of the three possible ways.

Use Boltzmann’s equation.

The crystal contains-

1. 100 molecules
2. 1 mol

To determine:

To determine the entropy of the disordered state of the crystal.