L 17 - "Phase Equilibria" Prof. Gianluigi Veglia...

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“Phase Equilibria” Prof. GianluigiVeglia
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The chemical potential So far we have discussed only systems of fixed compositions that are closed for which: where G=G(T,P) What about an open system (e.g. liquid water evaporating) or a closed system of changing composition. For instance: VdP Sdt dG + = ) ( 2 ) ( 3 ) ( 3 2 2 g NH g H g N +
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Consider a system containing an arbitrary number of components (k components). We cannot longer write G=G(T,P). Now we need to write G=G(T,P,n 1 , n 2 , n 3 , …n k-1 , n k ). So for an infinitesimal change: Therefore, we can write: k k n P T j n P T j n T n P dn n G dn n G dP P G dT T G dG j j j j + + + + = , , 1 1 , , , , ... + + = i i n P T i dn n G VdP SdT dG j 1 , ,
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We call the chemical potential of is and we designate it by the symbol µ i . The chemical potential has units of energy per mole. We have now: The chemical potential is the most important quantity in chemical thermodynamics and we will be discussing this at length. For a system consisting of a single substance the chemical potential is just the Gibbs energy of one mole of pure substance: 1 , , j n P T i n G + + = j i i dn VdP SdT dG µ i n P T i i G n G j = = 1 , ,
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We can use the above insight with the previous derivations to show that for an ideal gas: this is the chemical potential of an ideal gas. Note that this expression applies to mixtures of gases as well. + = 0 0 ln P P RT A A A µ
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Let’s consider a system consisting of a single component i that is distributed between two phases (a and b). An example might be water in equilibrium between the liquid and vapor phases: Since the variation of the free energy in equilibrium is zero: The above expression re ally applies to a single phase system. For a two-phase system, we divide S into S α and S β and V into V α and V β and: 0 = + + = j i i dn VdP SdT dG µ β α i i i i dn dn dP V dP V dT S dT S dG + + + + =
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If the system is at constant T and P: Since the system is closed: Equilibrium is a dynamic process, so dn a I is never zero. The only way of ensuring that the above equation is true, we need to take 0 = + β α µ i i i i dn dn 0 = + i i dn dn i i dn dn = ( ) 0 = i i i dn i i =
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L 17 - "Phase Equilibria" Prof. Gianluigi Veglia...

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