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CHAPTER
6 Reaction Equilibrium

in Ideal

CHAPTER OUTLINE
Gas Mixtures
6.1 Chemical Potentials in an
Ideal Gas Mixture
6.2 Ideal-Gas Reaction
Equilibrium
6.3 Temperature Dependence of The second law of thermodynamics led us to conclude that the entropy of system plus
the Equilibrium Constant
surroundings is maximized at equilibrium. From this entropy maximization condition
6.4 Ideal-Gas Equilibrium we found that the condition for reaction equilibrium in a closed system is n m 0
i
i
i
Calculations [Eq. (4.98)], where the n ’s are the stoichiometric numbers in the reaction and the m ’s
i
i
are the chemical potentials of the species in the reaction. Section 6.2 applies this equi-
6.5 Simultaneous Equilibria librium condition to a reaction in an ideal gas mixture and shows that for the ideal-gas
reaction aA bB ∆ cC dD, the partial pressures of the gases at equilibrium must
6.6 Shifts in Ideal-Gas Reaction be such that the quantity (P /P°) (P /P°) /(P /P°) (P /P°) (where P° 1 bar) is
b
d
c
a
D
C
A
B
Equilibria equal to the equilibrium constant for the reaction, where the equilibrium constant can
be calculated from G° of the reaction. (We learned in Chapter 5 how to use thermo-
6.7 Summary
dynamics tables to find G° from G° data.) Section 6.3 shows how the ideal-gas
f
equilibrium constant changes with temperature. Sections 6.4 and 6.5 show how to cal-
culate the equilibrium composition of an ideal-gas reaction mixture from the equilib-
rium constant and the initial composition. Section 6.6 discusses shifts in ideal-gas
equilibria.
Chapter 6 gives us the power to calculate the equilibrium composition for an
ideal-gas reaction from the initial composition, the temperature and pressure (or T and
V), and G° data.
f
To apply the equilibrium condition n m 0 to an ideal-gas reaction, we need
i
i
i
to relate the chemical potential m of a component of an ideal gas mixture to observ-
i
able properties. This is done in Sec. 6.1.
Chapter 6 is concerned only with ideal-gas equilibria. Reaction equilibrium in
nonideal gases and in liquid solutions is treated in Chapter 11.
In a particular system with chemical reactions, reaction equilibrium might or
might not hold. When the reaction system is not in equilibrium, we need to use chem-
ical kinetics (Chapter 16) to find the composition (which changes with time). In gas-
phase reactions, equilibrium is often reached if the temperature is high (so reaction
rates are high) or if the reaction is catalyzed. High-temperature reactions occur in
rockets and reaction equilibrium is often assumed in rocketry calculations. (Recall the
NIST-JANAF tables of thermodynamic data mentioned in Sec. 5.9. JANAF stands for
Joint Army–Navy–Air Force; these tables originated to provide thermodynamic data
for rocketry calculations.) Industrial gas-phase reactions that are run at elevated tem-
peratures in the presence of solid-phase catalysts include the synthesis of NH from
3
N and H , the conversion of SO to SO for use in preparation of H SO , and the syn-
2
2
4
3
2
2

thesis of CH OH from CO and H . Equilibria involving such species as H, H , e , H ,
3
2

H , He, He , and He 2 determine the composition at the sun’s surface (the photo-
2
sphere), which is at 5800 K and about 1 atm.