## Gas Phase Reaction Equilibria

Suppose generic reaction Eq (9.5) consists exclusively of gaseous species. Except for the small fraction of the intermolecular collisions that result in changing the elements in the molecules A and B into the products C and D, the components can be treated as ideal gases inhabiting the reaction vessel at partial pressures pA,^pD. Consequently, the chemical potentials in Eq (9.15) are related to the partial pressures by Eq (7.44):

where g° is the molar Free energy of pure gas i at 1 atm pressure. The partial pressures must be expressed in atm. Substituting Eq (9.17) into (9.15) for i = A,...D yields:

RTln(441 = "(cgC + dgD - agA " bgB) = "AG° (9.18)

### 1paPBJ

The free energy change of the reaction, AG°, is the analog of the enthalpy and entropy changes of the reaction introduced in Sects. 9.2 and 9.3. These properties of the generic reaction are related by the definition of the Free energy:

Equation (9.18) can be expressed in the alternate fashion:

KP is the equilibrium constant for the generic reaction of Eq (9.5). The subscript P indicates that the concentration units are the partial pressures of the reacting species. The first equality in Eq (9.20) is a form of the law of mass action. This "law" relates the partial pressures in the equilibrium reacting gas to a constant (KP) that is a function of temperature only. The last equality in Eq (9.20) shows that the basic properties of the reaction are AHo and ASo.

The preceding analysis of the generic reaction of Eq (9.5) can be generalized for any gas-phase reaction. The criterion of equilibrium, Eq (9.16), when combined with the chemical potentials of Eq (9.17) yields:

„ products I AGo ) f ASo ) I AHC KP = „ = expl--| = expl-|expl -■

npiVi where

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