15 CHAPTER Chemical and Phase Equilibrium

15-1 Equilibrium Criteria for a Chemical Reaction That Takes Place Adiabatically (fig. 15-2) © The McGraw-Hill Companies, Inc.,1998

15-2 Criteria for Chemical Equilibrium at a Specified Temperature and Pressure (Fig. 15-4)

Three Equivalent KP Reactions for Reacting ideal-gas mixtures 15-3 Three Equivalent KP Reactions for Reacting ideal-gas mixtures

The Larger the KP Reaction, the More Complete the Reaction 15-4 The Larger the KP Reaction, the More Complete the Reaction (Fig. 15-9)

Exothermic Reactions are Less Complete at Higher Temperatures 15-5 Exothermic Reactions are Less Complete at Higher Temperatures (Fig. 15-16)

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

15-7 Equilibrium Diagram for a Two-Phase Mixture of Oxygen and Nitrogen at 0.1 MPa

Mole Fraction of Species on the Two Sides of a liquid-Gas Interface 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)

Dissolved Gases in a Liquid can be Driven Off by Heating the Liquid 15-9 Dissolved Gases in a Liquid can be Driven Off by Heating the Liquid (Fig. 15-23) Gas: A Liquid: B

15-10 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.

15-11 Chapter Summary 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.

15-12 Chapter Summary For reacting systems that consist of ideal gases only, the equilibrium constant KP can be expressed as 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.

15-13 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.

15-14 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.

15-15 Chapter Summary 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.

15-16 Chapter Summary For small temperature intervals, the van't Hoff equation can be integrated to yield This equation shows that combustion processes will be less complete at higher temperatures since KP decreases with temperature for exothermic reactions.

15-17 Chapter Summary 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

15-18 Chapter Summary 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

15-19 Chapter Summary 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.

15-20 Chapter Summary 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.

15-21 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