Chemical Engineering Thermodynamics
Lecturer: Zhenxi Jiang (Ph.D. U.K.)
School of Chemical Engineering
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Chapter 13: Chemical Reaction Equilibria
The transformation of raw materials into
products of greater value by means of chemical
reaction is a major industry, and a vast array of
commercial products is obtained by chemical
synthesis. Sulfuric acid, ammonia, ethylene,
propylene, phosphoric acid, chlorine, nitric acid,
urea, benzene, methanol, ethanol, and ethylene
glycol are examples of chemicals produced in
the United States in billions of kilograms each
year.
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Chapter 13: Chemical Reaction Equilibria
These in turn are used in the large-scale
manufacture of fibers, paints, detergents,
plastics, rubber, paper, fertilizers, insecticides,
etc. Clearly, the chemical engineer must be
familiar with chemical-reactor design and
operation.
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Chapter 13: Chemical Reaction Equilibria
Both the rate and the equilibrium conversion of
a chemical reaction depend on the temperature,
pressure, and composition of reactants. Often, a
reasonable reaction rate is achieved only with a
suitable catalyst. For example, the rate of
oxidation of sulfur dioxide to sulfur trioxide,
carried out with a vanadium pentoxide catalyst,
becomes appreciable at about 300°C and
increases at higher temperatures.
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Chapter 13: Chemical Reaction Equilibria
On the basis of rate alone, one would operate
the reactor at the highest practical temperature.
However, the equilibrium conversion to sulfur
trioxide falls as temperature rises, decreasing
from about 90% at 520"C to 50% at about
680°C. These values represent maximum
possible conversions regardless of catalyst or
reaction rate. The evident conclusion is that
both equilibrium and rate must be considered in
the exploitation of chemical reactions for
commercial purposes.
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Chapter 13: Chemical Reaction Equilibria
Although reaction rates are not susceptible to
thermodynamic treatment, equilibrium
conversions are. Therefore, the purpose of this
chapter is to determine the effect of
temperature, pressure, and initial composition
on the equilibrium conversions of chemical
reactions.
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Chapter 13: Chemical Reaction Equilibria
Many industrial reactions are not carried to
equilibrium; reactor design is then based
primarily on reaction rate. However, the choice
of operating conditions may still be influenced
by equilibrium considerations. Moreover, the
equilibrium conversion of a reaction provides a
goal by which to measure improvements in a
process. Similarly, it may determine whether or
not an experimental investigation of a new
process is worthwhile.
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Chapter 13: Chemical Reaction Equilibria
For example, if thermodynamic analysis
indicates that a yield of only 20% is possible at
equilibrium and if a 50% yield is necessary for
the process to be economically attractive, there
is no purpose to an experimental study. On the
other hand, if the equilibrium yield is 80%, an
experimental program to determine the reaction
rate for various conditions of operation (catalyst,
temperature, pressure, etc.) may be warranted.
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Chapter 13: Chemical Reaction Equilibria
Reaction stoichiometry is treated in Sec. 13.1,
and reaction equilibrium, in Sec. 13.2. The
equilibrium constant is introduced in Sec. 13.3,
and its temperature dependence and evaluation
are considered in Sees. 13.4 and 13.5. The
connection between the equilibrium constant
and composition is developed in Sec. 13.6. The
calculation of equilibrium conversions for single
reactions is taken up in Sec. 13.7. In Sec. 13.8,
the phase rule is reconsidered; multireaction
equilibrium is treated in Sec, 13.9; finally, in Sec.
13.10 the fuel cell is given an introductory
treatment.
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13.1 The Reaction Coordinate
The general chemical reaction as written in Sec.
4.6 is:
v1 A1  v2 A2   v3 A3  v4 A4 
(13.1)
where |vi | is a stoichiometric coefficient and Ai
stands for a chemical formula. The symbol v,
itself is called a stoichiometric number, and by
the sign convention of Sec. 4.6 it is:
positive (+) for a product and
negative (-) for a reactant
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13.1 The Reaction Coordinate
Thus for the reaction,
CH4 + H20 → CO + 3H2
the stoichiometric numbers are:
vCH4 = -1 vH2O = -1 vCO = 1 vH2 = 3
The stoichiometric number for an inert species is
zero.
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13.1 The Reaction Coordinate
As the reaction represented by Eq. (13.1)
progresses, the changes in the numbers of
moles of species present are in direct proportion
to the stoichiometric numbers. Thus for the
preceding reaction, if 0.5 mol of CH4 disappears
by reaction, 0.5 mol of H20 also disappears;
simultaneously 0.5 mol of CO and 1.5 mol of H2
are formed. Applied to a differential amount of
reaction, this principle provides the equations:
dn2 dn1

v2
v1
dn3 dn1

v3
v1
etc.
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13.1 The Reaction Coordinate
The list continues to include all species.
Comparison of these equations yields:
dn3 dn4
dn1 dn2




v1
v2
v3
v4
All terms being equal, they can be identified
collectively by a single quantity representing an
amount of reaction. Thus a definition of d 
dεis given by the equation:
dn1 dn2 dn3 dn4




v1
v2
v3
v4
 d
(13.2)
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13.1 The Reaction Coordinate
The general relation connecting the differential
change dni with d  is therefore:
dni  vi d
(i  1, 2,..., N )
(13.3)
This new variableε, called the reaction
coordinate, characterizes the extent or degree to
which a reaction has taken place. Only changes
inεwith respect to changes in a mole number are
defined by Eq. (13.3). The definition ofεitself
depends for a specific application on setting it
equal to zero for the initial state of the system
prior to reaction.
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13.1 The Reaction Coordinate
Thus, integration of Eq. (13.3) from an initial
unreacted state where ε= 0 and ni = ni0 to a
state reached after an arbitrary amount of
reaction gives:

ni
ni 0

dni  vi  d 
0
or
n i  ni 0  vi
(i=1,2,...,N)
(13.4)
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13.1 The Reaction Coordinate
Summation over all species yields:
n   ni   ni 0    vi
i
i
i
or
n  n0  v
where
n   ni
i
n0   ni 0
i
v    vi
i
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13.1 The Reaction Coordinate
Thus the mole fraction yi of the species
present are related to εby:
ni ni 0  vi
yi  
n n0  v
(13.5)
Application of this equation is illustrated in
the following examples.
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.1 The Reaction Coordinate
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
In Sec. 14.3 it is shown that the total Gibbs
energy of a closed system at constant T and P
must decrease during an irreversible process
and that the condition for equilibrium is reached
when G t attains its minimum value. At this
equilibrium state,
(dGt)T,P = 0
(14.68)
Thus if a mixture of chemical species is not in
chemical equilibrium, any reaction may occurs at
constant T and P must lead to a decrease in the
total Gibbs energy of the system.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
The significance of this for a single chemical
reaction is seen in Fig. 13.1, which shows a
schematic diagram of G t vs. ε, the reaction
coordinate. Because ε is the single variable that
characterizes the progress of the reaction, and
therefore the composition of the system, the
total Gibbs energy at constant T and P is
determined byε.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
The arrows along the curve in Fig. 13.1 indicate
the directions of changes in (G t)T,P that are
possible on account of reaction. The reaction
coordinate has its equilibrium value εe at the
minimum of the curve. The meaning of Eq.
(14.68) is that differential displacements of the
chemical reaction can occur at the equilibrium
state without causing changes in the total Gibbs
energy of the system.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
Each of these may serve as a criterion of
equilibrium. Thus, we may write an expression
for G t as a function of £ and seek the value of £
which minimizes, or we may differentiate the
expression, equate it to zero, and solve forε.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
The latter procedure is almost always used for
single reactions (Fig. 13.1), and leads to the
method of equilibrium constants, as described in
the following sections. It may also be extended
to multiple reactions, but in this case the direct
minimization of G t is often more convenient,
and is considered in Sec. 13.9.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
Although the equilibrium expressions are
developed for closed systems at constant T and
P, they are not restricted in application to
systems that are actually closed and reach
equilibrium states along paths of constant T and
P.
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13.2 Application of Equilibrium Criteria
to Chemical Reaction
Once an equilibrium state is reached, no further
changes occur, and the system continues to
exist in this state at fixed T and P. How this
state was actually attained does not matter.
Once it is known that an equilibrium state exists
at given T and P, the criteria apply.
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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13.3 The Standard Gibbs-energy Change
and the Equilibrium Constant
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That is all for today
Homework
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12.4 Heat Effects of Mixing Processes
Thanks!
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