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Fundamentals of Distribution Separations (I) (8/26/13)

Fundamentals of Distribution Separations (I) (8/26/13). 1. Principles of distribution equilibria -- Driving force for separative displacement. 1. Principles of distribution equilibria -- Driving force for separative displacement. 2. Intermolecular interactions

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Fundamentals of Distribution Separations (I) (8/26/13)

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  1. Fundamentals of Distribution Separations (I) (8/26/13) 1. Principles of distribution equilibria -- Driving force for separative displacement 1. Principles of distribution equilibria -- Driving force for separative displacement 2. Intermolecular interactions -- Major factors controlling equilibrium between phases This is the base for understanding chemical separations such as chromatography and gel electrophoresis.

  2. LC Two Important Classes of Equilibrium (a) Mechanical equilibrium: the resting place of macroscopic bodies (b) Molecular equilibrium: the spatial distribution of molecules and colloids at equilibrium

  3. dp 0 dx Mechanical Equilibrium 1. With macroscopic bodies, it is unnecessary to worry about the thermal (Brownian) motion, which greatly complicates the equilibrium in microscopic (molecular) systems. 2. Entropy effect is negligible 3. Mechanical equilibrium is subject to the simple criterion (no balanced forces) dp , potential energy p = 0 dx

  4. < < Molecular Equilibrium in Closed Systems (I) A closed system is one with boundaries across which no matter may pass, either in or out. However other changes may occur, including expansion, contraction, heating and cooling. dU = q + w …………… the first law of thermodynamics w = -pdV * dS > q / T …………….. the second law of thermodynamics dUT dS – p dV * * G = H – TS = U + pV -TS dG -S dT + V dP * *

  5. Then, dG0 0oC, 1 atm 10oC, 1 atm ice ice < < Spontaneous irreversible Melting, dG < 0. Ice-water equilibrium Reversible, dG = 0 Molecular Equilibrium in Closed Systems (II) dG -S dT + V dP * * At the typical separation conditions, T and p are constant. dG = 0, ………… molecular equilibrium

  6. = dG -S dT + V dP * * әG dni dG = әni T, p, ni Chemical potential әG µi = әni T, p, ni µi dni dG = Molecular Equilibrium in Open Systems (I) An open system is one which can undergo all the changes in the close system. In addition, it allows mass transfer across its boundaries. Equilibrium point for a close system dni mole of i molecules enter the system, T & p are constant,

  7. dG -S dT + V dP + Σµi dni = * * Two-phase open system: α + β a close system dG = dGβ + dGα = (µi - µi ) dni = 0 β α For transfer component i from αtoβ at equilibrium µi = β µi α Molecular Equilibrium in Open Systems (I) Σµi dni dG = General equilibrium expression (if T, p are allowed to vary) entering: dn is positive Leaving: dn is negative

  8. μi = μi + RT ln ci μi = μi + RT ln pi μi = μi + RT ln ci μi = μi + RT ln γici 0 0 0 0 μi:standard-state chemical potential 0 β -Δμi ci 0 = exp α ci RT 0, β Δμi = μi -μi 0, α 0 γi active coefficient -Δμi 0 = exp K ,distribution coefficient RT for gas The Nature of Chemical Potential (μi) • Chemical potential, μi, for solute i in give phase depends on two factors • intrinsic thermodynamic affinity of solute to the phase, (b) dilution of • Solute (affect μi through entropy: entropy of dilution).

  9. Example: Sufficiently diluted, ethyl acetate has an equilibrium concentration at 20 oC in an isobutanol-rich phase that is 7.20 times higher than that in a water-rich phase (that is, the distribution coefficient K for isobutanol/H2O is 7.20). What is the value of o for the transfer of ethyl acetate from water to isobutanol solutions?

  10. dG = -S dT + V dP + Σµi dni * * Electric field = int ext dG -S dT + V dP + Σ(µi +µi )dni * * μi = μi + RT lnci 0 int Equilibrium in External Fields Common fields: electric, magnetic, sedimentation dG = dGβ + dGα = (µi +µi - µI - µi )dni = 0 int, α int, β ext, β ext, α

  11. ext -Δμi - Δμi 0 = exp K Δμi = μi -μi 0, β 0, α 0 RT ext β ext -Δμi - Δμi Comparison: Δμi & Δμi ci 0 0 = exp α ci RT (1) Equal in a mathematical sense Δμi ,abrupt 0 (2) Dissimilar in a physical sense: changes at phase boundaries ext Δμi ,continuous Equilibrium in External Fields (II) ext Δμi = μi -μi ext, β ext, α

  12. The Nature of Chemical Potential (μi ) 0 - - 0 Δμi = ΔHi – TΔSi 0 0 - - 0 0 ΔHi , ΔSi : the partial molar enthalpy and entropy under standard conditions. - 0 ΔSi : randomness of the immediate molecular environment of a species For general separation system involving a partition of components between phases - - 0 ΔHi TΔSi 0 >> Intermolecular interactions

  13. ext Δμi and Δμi 0 6. Comparison of 7. The Nature of Chemical Potential (μi ) 0 What we have learnt: 1. Two Classes of Equilibria 2. Molecular Equilibrium in Closed Systems 3. Molecular Equilibrium in Open Systems 4. The Nature of Chemical Potential (μi) 5. Equilibrium in External Fields

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