15
CHAPTER
Çengel
Boles
Thermodynamics
Chemical
and Phase
Equilibrium
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-1
Equilibrium Criteria for a Chemical
Reaction That Takes Place Adiabatically
(fig. 15-2)
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The
McGraw-Hill
Companies,
© The
McGraw-Hill
Companies,Inc.,1998
Inc.,1998
15-2
Criteria for Chemical Equilibrium at
a Specified Temperature and Pressure
(Fig. 15-4)
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-3
Three Equivalent KP Reactions
for Reacting ideal-gas mixtures
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-4
The Larger the KP Reaction,
the More Complete the Reaction
(Fig. 15-9)
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-5
Exothermic Reactions are Less
Complete at Higher Temperatures
(Fig. 15-16)
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-6
Phase Equilibrium
The multicomponent multiphase system is in phase equilibrium when the
specific Gibbs function of each component is the same in all phases
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-7
Equilibrium Diagram for a Two-Phase
Mixture of Oxygen and Nitrogen at 0.1 MPa
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-8
Mole Fraction of Species on the
Two Sides of a liquid-Gas Interface
Unlike temperature, the mole fraction of species on the two sides of a
liquid-gas (or solid-gas or solid-liquid) interface are usually not the same
(Fig. 15-22)
Çengel
Boles
Thermodynamics
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-9
Dissolved Gases in a Liquid can be
Driven Off by Heating the Liquid
(Fig. 15-23)
Çengel
Boles
Thermodynamics
Gas: A
Liquid: B
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-10
Çengel
Boles
Thermodynamics
Third Edition
Chapter Summary
• An isolated system is said to be in chemical
equilibrium if no changes occur in the chemical
composition of the system. The criterion for
chemical equilibrium is based on the second law
of thermodynamics, and for a system at a
specified temperature and pressure it can be
expressed as
For the reaction
where the v's are the stoichiometric coefficients.
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-11
Çengel
Boles
Chapter Summary
Thermodynamics
• The equilibrium criterion can be expressed in
terms of the Gibbs functions as
which is valid for any chemical reaction
regardless of the phases involved.
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-12
Chapter Summary
• For reacting systems that consist of ideal gases
only, the equilibrium constant KP can be
expressed as
Çengel
Boles
Thermodynamics
Third Edition
where the standard-state Gibbs function
change G*(T) and the equilibrium constant KP
are defined as
and
Here, Pi's are the partial pressures of the
components.
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-13
Çengel
Boles
Thermodynamics
Third Edition
Chapter Summary
• The KP of ideal-gas mixtures can also be
expressed in terms of the mole numbers of the
components as
where v = vC + vD - vA - vB, P is the total pressure,
and Ntotal is the total number of moles present in
the reaction chamber, including any inert gases.
The equation above is written for a reaction
involving two reactants and two products, but it
can be extended to reactions involving any
number of reactants and products.
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-14
Çengel
Boles
Thermodynamics
Third Edition
Chapter Summary
• The equilibrium constant KP of ideal-gas mixtures
depends on temperature only. It is independent of
the pressure of the equilibrium mixture, and it is
not affected by the presence of inert gases. The
larger the KP, the more complete the reaction. Very
small values of KP indicate that a reaction will not
proceed to any appreciable degree. A reaction with
KP > 1000 is usually assumed to proceed to
completion, and a reaction with
KP < 0.001 is assumed not to occur at all. The
mixture pressure affects the equilibrium
composition, although it does not affect the
equilibrium constant KP.
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-15
Çengel
Boles
Chapter Summary
Thermodynamics
• The variation of KP with temperature is expressed
in terms of other thermochemical properties
through the van't Hoff equation
where hR(T) is the enthalpy of reaction at
temperature T.
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-16
Çengel
Boles
Chapter Summary
• For small temperature intervals, the van't Hoff
equation can be integrated to yield
Thermodynamics
This equation shows that combustion processes
will be less complete at higher temperatures since
KP decreases with temperature for exothermic
reactions.
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-17
Çengel
Boles
Chapter Summary
Thermodynamics
• Two phases are said to be in phase equilibrium
when there is no transfor-mation from one phase
to the other. Two phases of a pure substance are
in equilibrium when each phase has the same
value of specific Gibbs function. That is,
gf = gg
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-18
Çengel
Boles
Chapter Summary
Thermodynamics
• In general, the number of independent variables
associated with a multi-component, multiphase
system is given by the Gibbs phase rule,
expressed as
IV = C - PH + 2
where IV = the number of independent variables, C
= the number of components, and PH = the
number of phases present in equilibrium
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-19
Çengel
Boles
Chapter Summary
Thermodynamics
• A multicomponent, multiphase system at a
specified temperature and pressure will be in
phase equilibrium when the specific Gibbs
function of each component is the same in all
phases.
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-20
Çengel
Boles
Chapter Summary
Thermodynamics
• For a gas i that is weakly soluble in a liquid (such
as air in water), the mole fraction of the gas in the
liquid yi liquid side is related to the partial pressure of
the gas Pi, gas side by Henry's Law expressed as
where H is Henry's constant.
Third Edition
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998
15-21
Çengel
Boles
Thermodynamics
Third Edition
Chapter Summary
• When a gas is highly soluble in a liquid (such as
ammonia in water), the mole fractions of the
species of a two-phase mixture in the liquid and
gas phases are given approximately by Raoult's
law expressed as
where Ptotal is the total pressure of the mixture,
Pi,sat(T) is the saturation pressure of species i at the
mixture temperature, and yi, liquid side and
yi, gas side are the mole fractions of species i in the
liquid and vapor phases, respectively
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc.,1998