Beng 130 Lecture 11

Beng 130 Lecture 11 - Free Energy and Physical Equilibria...

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1 Free Energy and Physical Equilibria Relating Chemical Potential to Equilibrium We have seen that chemical equilibrium establishes a state that minimizes the system’s Gibbs energy. However, a more useful definition of equilibrium is one based on intensive properties. Thermal: Spatial uniformity of T Mechanical: Spatial uniformity of P Chemical: Spatial uniformity of µ i For now, consider a two-phase system of k components: The vessel as a whole (vap+liq) is closed , as energy may be exchanged with its surroundings but material cannot. Each phase, however, is an open system, as it may exchange matter with the other phase. Vap, k components Liq, k components @ uniform T,P
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2 Gibbs Energy Changes for a Closed System For the total vessel contents (vapour+liquid phases), we can write the fundamental equation for a closed system. Recall, (A) where n is the total number of moles of material; mole G is the total molar Gibbs energy; J/mole V is the molar Volume of the total system; m 3 /mole P represents the system pressure; Pa S is the total molar Entropy; J/moleK T represents the system temperature; K Note that because the composition of the entire system (vap + liq) cannot change, only changes in pressure and temperature can influence the Gibbs energy of the whole system. ¾ Composition is invariant, so no chemical potential terms are included in the closed system expression. dT ) nS ( dP ) nV ( ) nG ( d = Gibbs Energy Changes for an Open System Each phase can exchange not only energy, but material with the other. Therefore the vapour phase and the liquid phase are individual open systems. For the vapour phase (superscript v refers to vapour): (B) For the liquid phase (superscript l refers to liquid): (C) These equations detail how the Gibbs energy of each phase is affected by changes in pressure, temperature, and composition. v i k i 1 i v i v v v v v v dn dT ) S n ( dP ) V n ( ) G n ( d = = µ + = l i k i 1 i l i l l l l l l dn dT ) S n ( dP ) V n ( ) G n ( d = = µ + =
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3 Back to the Overall System The change in the Gibbs energy of the whole, two-phase system is the sum of the vapour and liquid changes. For the whole system (vap + liq), the sum of equations B and C yields the total Gibbs energy change: (B+C) According to this equation, the Gibbs energy of the overall system is affected by changes in T, P and composition. ¾ If we are interested in constant temperature and pressure processes (dT=dP=0), this relation simplifies to: l i k i 1 i l i v i k i 1 i v i l i k i 1 i l i v i k i 1 i v i v v l l v v l l dn dn dT ) nS ( dP ) nV ( dn dn dT ) S n S n ( dP ) V n V n ( ) nG ( d = = = = = = = = µ + µ + = µ + µ + + + = l i k i 1 i l i v i k i 1 i v i P , T dn dn ) nG ( d = = = = µ + µ = Relating Chemical Potential to Equilibrium We now have the tools needed to translate our Gibbs energy criterion for equilibrium into one based on chemical potential.
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This homework help was uploaded on 04/07/2008 for the course BENG 130, 103B, taught by Professor Gough during the Spring '08 term at UCSD.

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Beng 130 Lecture 11 - Free Energy and Physical Equilibria...

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