Concise Physical Chemistry

c05 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

THE THIRD LAW 79

Because of the third law, it is possible to obtain a standard molar entropy (often

called the “absolute” entropy) of any pure substance at any temperature. The task is

simple but not easy. One must determine the molar heat capacity at constant pressure

Cpfor the crystal at many temperatures until it undergoes the first phase transition.

By the methods shown in Section 5.2.1, the integral taken down to lowT

S=

∫T 1

0

Cp

T

dT

gives the standard entropy at the transition temperatureT 1. SinceCpis a molar

heat capacity,Sis an standard molar entropy. Normally one wants the entropy at

some higher temperature, say 298 K, and often the phase transition takes place at a

temperatureT 1 lower than 298 K. Therefore we must add the entropy contribution

from the phase transition to the value ofSthat we already have to obtain the standard

molar entropy after the phase change atT 1. The new phase then is heated over a

temperature intervalT 1 →T 2 where the new temperature may be 298 K or may be

the temperature of a new phase change. Melting and vaporization are handled in the

same way as crystalline phase changes. Eventually, over a few or many phase changes,

one arrives at the desired temperature. The standard entropy is the summation of all

the contributions along the way:

S=

∫T 1

0

Cp

T

dT+

∑
Htrans

Ttrans

+

∑∫Thigher

Tlower

Cp

T

dT

5.4.1 Chemical Reactions (Again)

The change in entropy of a chemical reaction can be determined by carrying out a

determination of the standard molar entropies of all of the reactants and all of the

products as just described and taking the sum

Sr=

∑

S(products)−

∑

S(reactants)

The entropy of ordering or disordering that occurs when, for example, the product

state is in the gaseous phase and the reactants are in a condensed phase (liquid or solid)

is included in this sum because terms like
Hvap/Tbare included in

∑

S(products)

but not in

∑

S(reactants). It would be attractive to adopt the simplistic attitude

that all spontaneous chemical and physical reactions produce an entropy increase

for the reacting system, but, once again, things are more complicated than that. A

spontaneous change is driven both by the tendency of a system to reduce its energy

and enthalpy and by the tendency of a system to increase its disorder. A composite

function is needed that includes both the enthalpy and entropy, and this is the function

found and described in mathematical detail by the great American thermodynamicist

J. Willard Gibbs. The composite function the Gibbs free energy or, more simply, the

Gibbs functionG=H−TSnow bears his name. There is a comparable function