Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 7

576

CHAPTE R 14? Entropy and Free Energy

standard entropies of O3(g) and F2(g).] The more complex a molecular structure, the more
different types of motion the molecule can exhibit. A diatomic molecule such as F2, for
example, exhibits only one type of vibration, whereas a bent triatomic molecule such as O3
exhibits three different types of vibrations. Each mode of motion contributes to the total
number of available energy levels within which a system’s energy can be dispersed. Figure
14.3 illustrates the ways in which the F2 and O3 molecules can rotate and vibrate.
• In cases where an element exists in two or more allotropic forms, the form in which
the atoms are more mobile has the greater entropy. [Compare the standard entropies of
C(diamond) and C(graphite). In diamond, the carbon atoms occupy fixed positions in a
three-dimensional array. In graphite, although the carbon atoms occupy fixed positions
within the two-dimensional sheets (see Figure 12.24, page 504), the sheets are free to move
with respect to one another, which increases the mobility and, therefore, total number of
possible arrangements of atoms within the solid.]
Now let’s consider a process represented by the following chemical equation:
aA + bB

cC + dD

Just as the enthalpy change of a reaction is the difference between the enthalpies of the products
and reactants (Equation 10.10), the entropy change is the difference between the entropies of the
products and reactants:
?S° = [cS°(C) + dS°(D)] ? [aS°(A) + bS°(B)]
rxn

Equation 14.5

Or, using ? to represent summation and m and n to represent the stoichiometric coefficients of the
reactants and products, respectively, Equation 14.5 can be generalized as follows:
?S° = ?nS°(products) ? ?mS°(reactants)
rxn

Equation 14.6

Figure 14.3 In addition to translational
motion, molecules exhibit both vibrations, in which the atoms’ positions relative to one another change, and rotations,
in which the molecule rotates about its
center of mass. (a) A diatomic molecule
such as fluorine only exhibits one type of
vibration. A bent, triatomic molecule such
as ozone exhibits three types of vibration.
(b) A diatomic molecule exhibits two
different rotations, whereas a bent, triatomic molecule exhibits three different
rotations. (Note that rotation of F2 about
the x axis would cause no change in the
positions of either atom in the molecule.)

F2
F2

Time
Time

O3
O3

Time
Time

Time
Time

Time
Time

(a)
(a)
y
y

F2
F2

x
x

y
y
x
x

z
z

O3
O3

bur11184_ch14_570-603.indd 576

x
x

z
z

x
x

z
z

y
y

y
y

z
z

y
y
x
x

(b)
(b)

z
z

y
y
x
x

z
z

9/10/13 12:01 PM