Modern Engineering Thermodynamics

636 CHAPTER 15: Chemical Thermodynamics
From Eq. (11.8), we have the relation dg = vdp− sdT, so that, for a constant pressure process, we can write
d g • i
dT = −s• i
Introducing this result along with the definition of the molar specific Gibbs function, g = h − T s, into the equation
for dK e /dT and rearranging gives
or
1
K e
dK e
dT
= dð ln K eÞ
dT
= − 1
RT 2
∑
R ′
The van’t Hoff equation:
dð ln K e Þ
dT
!
v i h • i −∑ v i h • Q
i = _ r
RT
P 2
′
= _ Q r
RT 2 (15.39)
where _Q r istheheattransferrateofthereaction. This equation is known as the van’t Hoffequation.Itshows
that, for a heat-producing (i.e., exothermic) reaction, the value of K e decreases when the reaction temperature
increases and increases when the reaction temperature decreases. While for a heat-absorbing (i.e., endothermic)
reaction, the value of K e increases when the temperature of the reaction increases and decreases when the reaction
temperature decreases. Since the equilibrium constant is a relative measure of the amount of product present,
by changing the reaction temperature, we can change the amount of product formed. For example,
consider the equilibrium equation for the formation of ammonia from hydrogen and nitrogen gas,
N 2 + 3ðH 2 Þ ⇆ 2ðNH 3 Þ − 91:25 kJ. We can increase the amount of ammonia produced by increasing the K e of the
reaction. Since the reaction is exothermic, this can be done by lowering the reaction temperature.
15.15 FUEL CELLS
The highly inefficient heat engine energy conversion technology that provided
the mobile power for the technological developments of the 17th
through the 20th centuries is coming to an end. The thermal combustion of
chemical fuel to propel the heat engines of the past has come to be the
source of numerous worldwide social problems today. Chemical
and thermal pollution of the Earth’s air and water plus a continuously diminishing
supply of suitable fuels is clearly signaling the end of the heat engine
era. But, what other, less ecologically damaging energy conversion technologies
do we have to support the societies of the next few centuries?
What about electrical batteries? Technically, a battery consists of two or
more electrochemical cells that convert chemical energy directly into electrical
energy. The term battery, however, is often used to describe a single cell.
Figure 15.12 illustrates the basic elements of an electrochemical cell.
Ordinary commercial batteries are closed systems because no mass crosses
their boundaries; consequently, as they are used, they consume their stored
electrical energy and become discharged. If the electrolyte needed to operate
the cell were continuously supplied from outside the cell, then it would
become an open system and would never become discharged. Such an open
system electrochemical cell is called a fuel cell.
Since a fuel cell (Figure 15.13) does not produce heat as its primary energy
conversion mode, it is therefore not a heat engine. Consequently, fuel cells
are not subject to the severe limitation of the Carnot (heat engine) efficiency,
and fuel cell efficiencies can approach 100% under the proper conditions.
Consider a general steady state, steady flow, open system. Neglecting any
changes in kinetic or potential energy, the energy rate balance on this system
gives its work transport rate of energy (i.e., power) as
_W = ∑
in
_m i h i −∑
out
_m i h i + _Q = ∑
in
_n i h i −∑ _n i h i + _Q
out
Current
e+ e−
Electrons
−
+
Electrodes
Electrolyte
FIGURE 15.12
The operation of a basic electrochemical
cell using one electrolyte. Electrical
current is the time rate of change of
electrical charge, originally defined by
Benjamin Franklin to flow from the
positive to the negative terminal.
However, since electrons are the charge
carriers for current in conductors and the
charge of an electron is negative, the
direction of electron flow is actually from
the negative to the positive terminal.
Nonetheless, we maintain the old
concept of current flow from positive to
negative and call this the conventional
flow notation.