2. 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:

3. 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

4. Mixing, ideal systems

5. 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)

6. 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)

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

8. P-X stability and mixing

9. 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

10. 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