Chemical equilibrium: the principles 자연과학대학 화학과 박영동 교수

Chemical equilibrium: the principles 7.1 Thermodynamic background 7.1.1 The reaction Gibbs energy 7.1.2 The variation of ΔrG with composition 7.1.3 Reactions at equilibrium 7.1.4 The standard reaction Gibbs energy 7.1.5 The equilibrium composition 7.1.6 The equilibrium constant in terms of concentration 7.2 The response of equilibria to the conditions 7.2.7 The presence of a catalyst 7.2.8 The effect of temperature 7.2.9 The effect of compression

Chapter 7. Chemical equilibrium: the principles Be familiar with the following terminologies or ideas: The reaction Gibbs energy ΔGR The variation of ΔGR with composition Determination of equilibrium constants and the equilibrium concentration The effect of temperature on the equilibrium constant The effect of pressure

Derivation of the general equilibrium expression dGR = VdP - SdT + (i=from 1 to Ns) μi dni Let ξ be the extent of chemical reaction and if the sign of (G/ ξ)T,P at constant T and P determines whether the reaction has the spontaneity. (G/ ξ)T,P ≤ 0 where “<” implies that it has spontaneity and “=” means the equilibrium. It can be shown that ΔGR = (G/ ξ)T,P. For any reaction aA + bB → cC + dD the reaction Gibbs energy at const T and P can be expressed as in ΔGR = (i= 1 to Ns) νi μi (1) where νi denotes the stoichiometric coefficients like a, b, c, d. Remember that μi = μio + RT ln ai and substitute this for eq (1), then ΔGR =νi μi = νi μio + RT νi ln ai =ΔGRo + RT ln Π ai νi =ΔGRo + RT ln Q (2) where Q ≡ Π ai νi = (aCc aDd)/(aAaaBb) (3) At equilibrium ΔGR = 0 and ΔGRo = - RT ln K (4) where K ≡ (aC,eqc aD,eqd)/(aA,eqaaB,eqb) The standard reaction Gibbs energy, ΔGRo, can be obtained by two different methods. (method 1) ΔGRo = ΔHRo - T ΔSRo (method 2) ΔGRo = νi ΔGfo(product,i) - νi ΔGfo(reactant,i)

Determination of equilibrium composition (Example) Find the equilibrium constant K of N2O4 (g) ⇄ 2 NO2 (g) at a given temperature T and the composition at equilibrium (Answer) (1) K can be obtained from eq (4) if ΔGRo of the reaction is known. (2) N2O4 (g) ⇄ 2 NO2 (g) Initial amount 1 0 Equilibrium amount 1-ξ 2ξ Total amount = 1 + ξ Equilibrium mole fraction (1-ξ)/ (1+ξ) 2ξ/ (1+ξ) K = [P(NO2)/Po)2 / [P(N2O4)/Po) = {[2ξ/(1+ξ)](P/Po)}2 / {[(1-ξ)/(1+ξ)](P/Po)} = 4ξ2 (P/Po) / (1 -ξ2) Then the extent of the reaction ξ is given by ξ = 1 / [ 1 + (4/K)(P/Po)]1/2

Temperature effect on K Let us first derive the Gibbs-Helmholtz equation. Remember that G=H - TS=H + T(G/ T)P,{ni} (see eq. 13-2 of the special lecture) (6) [((G/T)/ T]P,{ni} = -G/T2 + (1/T) (G/ T)P,{ni} (7) From eqs. (6) and (7) we obtain H = -T2 [((G/T)/ T]P,{ni} (8) Equation (8) is referred to as the Gibbs-Helmholtz equation. For a change between state 1 and state 2, this equation can be written ΔH = -T2 [((ΔG/T)/ T]P,{ni} For a chemical reaction occurring at standard state (constant pressure) with a fixed composition ΔHRo = -T2 [(d(ΔGRo /T)/ dT] = RT2 (d lnK/dT) Or (d lnK/dT) = ΔHRo / RT2 (9) Eq. (9) is known as the van’t Hoff equation. The integral of eq (9) from T1 to T2 yields ln(K2/K1) = (ΔHRo/R) (1/T1 - 1/T2) Also remember that ln K = -ΔGRo / RT = - ΔHRo / RT + ΔSRo /R

Reaction Gibbs Energy

The variation of ΔrG with composition

The standard reaction Gibbs energy

The endothermic reaction and temperature

The standard Gibbs energy of formation

The effect of temperature