FundChemReaxEngAppendicesIndex

FundChemReaxEngAppendicesIndex - R eview of Chemical...

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Review of Chemical Equilibria A.1 I Basic Criteria for Equilibrium Reacting Systems The basic criterion for equilibrium with a single reaction is: NCOMP D..G = :L VilLi = ° i~l (Al.l ) where D. .G is the Gibbs function, is the number of components in the sys- tem, Vi is the stoichiometric coefficient of species i, and lLi is the chemical poten- tial of species i. The chemical potential is: (A.I.2) where R g is the universal gas constant, IL? is the standard chemical potential of species i in a reference state such that ai = 1, and is the activity of species The reference states are: (1) for gases (i.e., JO = 1) (ideal gas, P = 1 atm) where 1 is the fugacity, (2) for liquids, the pure liquid at T and one atmosphere, and (3) for solids, the pure solid at T and one atmosphere. If multiple reactions are occurring in a network, then Equation (AI. 1) can be extended to give: NCOMP j Vi,jlLi = 0, j 1, "', NRXN i~ I (Al.3) where NRXN is the number of independent reactions in the network. In general it is not true that the change in the standard Gibbs function, D..Go, is zero. Thus, D..Go VilL;) *' ° i~ I (A.I.4)
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340 AppEND. X A Review of Chemical EqIJilibrLa. .. _ Therefore, NCOMP I1C - I1Co 2: Vj(ILj IL?) i~l or by using Equation (A.I.2): Now consider the general reaction: CiA + bB + ... = wW + sS (Al.5) (Al.6) (A 1.7) Application of Equation (Al.6) to Equation (Al.7) and recalling that I1C = 0 at equilibrium gives: Thus, the equilibrium constant K a is defined as: K a II aY; i=l Differentiation of Equation (AI.8) with respect to T yields: (AI.8) (A.I.9) (A1.10) Note that = I1Ho - TI1So, where and I1So are the standard enthalpy and entropy, respectively, and differentiation of this expression with respect to T gives: (A 1.1I) Equating Equations (Al. 10) and (A1.1!) provides the functional form for the tem- perature dependence of the equilibrium constant: R g T 2 or after integration (assume is independent of T): (A.1.12) (Al.13) Notice that when the reaction is exothennic (I1Ho is negative), K a increases with decreasing T. For endothermic reactions the opposite is true. From Equation (Al.8):
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_______ Jl2J>LN~JX A Revjnw of CJocBmicaLEqlJi'ibria (A.1.l4) and (A. l.l 5) Since LlCo is not a function of pressure, it is clear that pressure has no influence on K a . A.2 I Determination of Equilibrium Compositions Consider a gas-phase reaction. If the Lewis and Randall mixing rules are used (simplest form of mixing rules-more sophisticated relatio l1 ships could be applied if deemed necessary) to give for the fugacity of species i, Ii: where - /-0//-0 0 a -. i. i (A.2.1) and 1Ji fugacity coefficient of pure i at T and P of system for any mole fraction Xi' Substituting the above expression into Equation (A.1.9) for the reaction given in Equation (A.I.7) yields (let all .17 I): (A.2.2) or where X.= I f J1inert + n .I Equation (A.2.2) can be written in terms of moles as: rn. ·.. lr P = K, 1 tv _ 1 ----- K a (/) I b 11 ,""" L n B •..
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This note was uploaded on 07/19/2011 for the course ENG 101 taught by Professor Calt during the Spring '11 term at Caltech.

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FundChemReaxEngAppendicesIndex - R eview of Chemical...

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