Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 17

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CHAPTE R 14? Entropy and Free Energy

bch_lb
Thinking Outside the Box
Thermodynamics and Living Systems
Under normal physiological conditions, polypeptides spontaneously fold into unique three-dimensional
structures called native proteins, which can perform various functions. Because the original chain can assume
many possible configurations while the native protein can have only one specific arrangement, the folding
process is accompanied by a decrease in entropy of the system. (Note that solvent molecules, water in this case,
can also play a role in affecting the entropy change.) In accord with the second law of thermodynamics, any
spontaneous process must result in an increase in the entropy of the universe. It follows, therefore, that there
must be an increase in the entropy of the surroundings that outweighs the decrease in the entropy of the system.
The intramolecular attractions between amino acid residues cause the folding of the polypeptide chain to be
exothermic. The energy produced by the process spreads out, increasing molecular motion in the surroundings—
thereby increasing the entropy of the surroundings.

Unfolded

Folded

The Third Law of Thermodynamics
Finally, we consider the third law of thermodynamics briefly in connection with the determination
of standard entropy. We have related the entropy of a system to the number of possible arrangements of the system’s molecules. The larger the number of possible arrangements, the larger the
entropy. Imagine a pure, perfect crystalline substance at absolute zero (0 K). Under these conditions, there is essentially no molecular motion and, because the molecules occupy fixed positions
in the solid, there is only one way to arrange the molecules. From Equation 14.1, we write
S = k ln W = k ln 1 = 0
According to the third law of thermodynamics, the entropy of a perfect crystalline substance is
zero at absolute zero. As temperature increases, molecular motion increases, causing an increase
in the number of possible arrangements of the molecules and in the number of accessible energy
states, among which the system’s energy can be dispersed. (See Figure 14.4.) This results in an
increase in the system’s entropy. Thus, the entropy of any substance at any temperature above 0 K
is greater than zero. If the crystalline substance is impure or imperfect in any way, then its entropy
is greater than zero even at 0 K because without perfect crystalline order, there is more than one
possible arrangement of molecules.
The significance of the third law of thermodynamics is that it enables us to determine experimentally the absolute entropies of substances. Starting with the knowledge that the entropy of a
pure crystalline substance is zero at 0 K, we can measure the increase in entropy of the substance
as it is heated. The change in entropy of a substance, ?S, is the difference between the final and
initial entropy values:
?S = Sfinal ? Sinitial
where Sinitial is zero if the substance starts at 0 K. Therefore, the measured change in entropy is
equal to the absolute entropy of the substance at the final temperature.
?S = Sfinal

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