The Foundations of Chemistry

The Third Law of Thermodynamicsestablishes the zero of the entropy scale.

The entropy of a pure, perfect crystalline substance (perfectly ordered) is zero at

absolute zero (0 K).

As the temperature of a substance increases, the particles vibrate more vigorously, so

the entropy increases (Figure 15-14). Further heat input causes either increased temper-

ature (still higher entropy) or phase transitions (melting, sublimation, or boiling) that also

result in higher entropy. The entropy of a substance at any condition is its absolute

entropy,also called standard molar entropy. Consider the absolute entropies at 298 K

listed in Table 15-5. At 298 K, anysubstance is more disordered than if it were in a perfect

crystalline state at absolute zero, so tabulated S^0298 values for compounds and elements

are always positive.Notice especially that S^0298 of an element, unlike its 
Hf^0 , is notequal

to zero. The reference state for absolute entropy is specified by the Third Law of Ther-

Enthalpies are measured only as
differenceswith respect to an arbitrary
standard state. Entropies, in contrast,
are defined relative to an absolute zero
level. In either case, the per mole
designation means per mole of substance
in the specified state.

624 CHAPTER 15: Chemical Thermodynamics

TABLE 15-4 Entropy Effects Associated with Melting and Freezing

Sign of (Magnitude of 
Ssys)

Compared with 
Suniv

Change Temperature 
Ssys 
Ssurr (Magnitude of 
Ssurr) 
Ssys
Ssurr Spontaneity

1. Melting (a) mp  0 Spontaneous


2. (solid nliquid) (b)mp  0 Equilibrium

(c) mp  0 Nonspontaneous

2. Freezing (a) mp  0 Nonspontaneous


3. (liquid nsolid) (b)mp  0 Equilibrium
   (c) mp  0 Spontaneous

Figure 15-14 (a) A simplified representation of a side view of a “perfect” crystal of a polar

substance of 0 K. Note the perfect alignment of the dipoles in all molecules in a perfect

crystal. This causes its entropy to be zero at 0 K. There are no perfect crystals, however,

because even the purest substances that scientists have prepared are contaminated by traces

of impurities that occupy a few of the positions in the crystal structure. Additionally, there

are some vacancies in the crystal structures of even very highly purified substances such as

those used in semiconductors (see Section 13-17). (b) A simplified representation of the

same “perfect” crystal at a temperature above 0 K. Vibrations of the individual molecules

within the crystal cause some dipoles to be oriented in directions other than those in a

perfect arrangement. The entropy of such a crystalline solid is greater than zero, because

there is disorder in the crystal.

+ –+ –+ –+ –+ –

• +– +– +– +– +

• –+ –+ –+ –+ –

• +– +– +– +– +

+ –+ –+ –+ –+ –

+ –+ –+ –

+

• 
  
  
  
  • –
  
  
  
  


• +– ++ – – +– +

• –+ –+ –+ – – +

• ++ – – +– + – +

+ – + –+ –+ –+ –

(a) (b)

TABLE 15-5 Absolute

Entropies at

298 K for a

Few Common

Substances

Substance S^0 ( J/molK)

C(diamond) 2.38

C(g) 158.0
H 2 O(
) 69.91

H 2 O(g) 188.7
I 2 (s) 116.1

I 2 (g) 260.6