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Chemical Potential

Chemical Potential. Enthalpy (H), entropy (S), and Gibbs Free Energy (G) are molal (moles/kg) quantities Chemical potential, m, is the Gibbs free energy per molal unit:

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Chemical Potential

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  1. Chemical Potential • Enthalpy (H), entropy (S), and Gibbs Free Energy (G) are molal (moles/kg) quantities • Chemical potential, m, is the Gibbs free energy per molal unit: • In other words, the "chemical potential mi" is a measure of how much the free energy of a system changes (by dGi) if you add or remove a number dni particles of the particle species i while keeping the number of the other particles (and the temperature T and the pressure P) constant:

  2. Mixing • Putting two components into the same system – they mix and potentially interact: • Mechanical mixture – no chemical interaction: where X is mole fraction of A, B ms = XAmA + XBmB • Random mixture – particles spontaneously (so m must go down) orient randomly: Dmmix=ms – mmechanical mixing Mixing ideal IF interaction of A-A = A-B = B-B  if that is true then DHmix=0, so DSmix must be >0 (because mmix<0 (spontaneous mixing): DSid mix = -RSXilnXi R=molar gas constant X=mole fraction component i

  3. Mixing, ideal systems

  4. Mixing, real systems • When components interact with each other chemically and change the overall solution energy Dmreg = ωXAXB Particularly this formulation is important in geochemistry for solid solutions of minerals, such as olivine (ex: Fo50Fa50)

  5. Mixing, a more complete picture Energy = mechanical mixture + ideal mixing + regular solution Put 2 things together, disperse them, then they interact… mtot= XAm0A+(1-XA)m0B + XARTlnXA+ (1-XA)RTln(1-XA) + ωXA(1-XA)

  6. Mixing and miscibility • What about systems where phases do not mix (oil and water)??

  7. P-X stability and mixing

  8. monalbite anorthoclase 1100 high albite sanidine 900 intermediate albite Temperature (ºC) 700 orthoclase low albite microcline 500 Miscibility Gap 300 10 70 30 50 90 Orthoclase KAlSi3O8 Albite NaAlSi3O8 % NaAlSi3O8 Melt-crystal equilibrium 2 - miscibility • 2 component mixing and separation  chicken soup analogy, cools and separates • Fat and liquid can crystallize separately if cooled slowly • Miscibility Gap – no single mineral is stable in a composition range for x temperature

  9. Mixing in water • Solutions dominated by water (1 L=55.51 moles H2O) • aA=kHXA where KH is Henry’s Law coefficient – where is this valid? Low concentration of A 1.0 Raoult’s Law – higher concentration ranges (higher XA): mA=mA0+RTlnGAXA where GA is Rauolt’s law activity coefficient aH2O aA Activity Ideal mixing 0.0 0.0 1.0 H2O Mol fraction A A

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