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:

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

Mixing, ideal systems

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)

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)

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

P-X stability and mixing

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 Miscibility Gap microcline orthoclase sanidine anorthoclase monalbite high albite low albite intermediate albite Orthoclase KAlSi3O8 Albite NaAlSi3O8 % NaAlSi3O8 Temperature (ºC) 300 900 700 500 1100 10 90 70 50 30 Need figure 5-11 or equivalent showing miscibility

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