13-Solution thermodynamics

13-Solution thermodynamics - BioE 13. Solution...

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Molecular BioEngineering Laboratory BioE 13. Solution Thermodynamics ± Equilibrium and Spontaneous Conditions ± Chemical potential of an ideal gas and real gases ± Chemical potential of a pure liquid or solid ± Ideal solution ± Chemical potential of components in gas mixtures ± Chemical potential of components in Liquid mixtures
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BioE Fundamental Equations ∑∑ + + = + = + + = + = χ μ i i i i i i i i i i i i dn Vdp SdT dG dn pdV SdT dA dn Vdp TdS dH dn pdV TdS dU
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BioE Equilibrium Conditions At equilibrium, ( ) () () () ( ) φ β α χ μ m m m m m m i i i p T V T p S V S V U dn dn dn dn dn dn dn dn dn dn dG dA dH dU dS + + + + + + + + + + + + + + + = = = = = = = ∑∑ L L L L 2 2 1 1 2 2 1 1 2 2 1 1 , , , , , 0 0 , 0 0 , 0 0
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BioE Spontaneous Process ( ) () () () ( ) 0 0 , 0 0 , 0 0 , , , , , < < < < < > i i i p T V T p S V S V U dn dG dA dH dU dS μ
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BioE Phase Equilibrium φ β α χ μ m m m m i i i dn dn dn dn = = = = = = = = = = = = = = ∑∑ = = = L L L L L 2 2 2 1 1 1 2 1 0 0
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BioE Chemical equilibrium 0 0 d ) ( d d d , d d , d d , d d , 0 0 0 0 = + + = + + = = + = = + = = = = = + ⎯→ + D C B A D C B A i i D D D C C C B B B A A A d c b a d c b a n d n d n n c n c n n b n b n n a n a n n dD cC bB aA μ ξ
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Molecular BioEngineering Laboratory BioE Chemical Potentials, Fugacity, and Activity ± Ideal Mixing and nonideal mixing ± Chemical potential description ± Rault’s law and Henry’s law ± Experimental determination of activity
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BioE Chemical Potential ± Ideal Mixing ± Chemical potential of pure gas ± Chemical potential of a pure liquid or solid ± Gas mixture ± Liquid mixture
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BioE Ideal Solution Under a certain temperature and pressure. ± The volume is additive. z V=V A +V B =n A V mA +n B V mB z That is Δ mix V = 0 ± The enthalpy is additive. z H=H A +H B =n A H mA +n B H mB z That is mix H = 0 ± The internal energy is additive. z Δ mix U= Δ mix H-P Δ mix V=0 z U=U A +U B =n A U mA +n B U mB
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BioE Ideal mixing + =
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BioE Nonideal mixing += Heat Heat
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BioE Entropy Change after Ideal Mixing ∴Δ S = - (n A Rlnx A + n B B ) which is true not only for ideal gases. B B A A B A B B B B A A A A V V V x R n x R n S S S V V R n S V V R n S dV T p dS dV T p dT T C dS ln ln ln , ln T, constant at 0 0 = Δ + Δ = Δ = Δ = Δ = + =
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BioE Gibbs Free Energy after Ideal Mixing () ( ) B B A A mB B mA A B B A A mix id mix B B A A x n x n RT G n G n G x n x n RT S T G H S T H G x R n x R n S ln ln ln ln 0 solution ideal ) ln ln ( + + + = + = Δ = Δ = Δ Δ Δ = Δ + = Δ
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BioE Chemical potential of component A in an ideal mixture of A and B ( ) ( ) () + + + = = = + + = A j A j A j A j B j A j n p T A B B B B n p T A B n p T A A A A A n p T A A B B A A mA A n p T B B n p T A A B B A A mB B mA A n x x x x n x nRT n x x x x n x nRT x x x x RT G n G n G x x
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This note was uploaded on 11/11/2010 for the course CHE CH2005 taught by Professor 曹恒光 during the Spring '10 term at National Central University.

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13-Solution thermodynamics - BioE 13. Solution...

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