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 i" 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:

ii n

G

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, Bs = XAA + XBB

• Random mixture – particles spontaneously (so must go down) orient randomly:

mix=s – mechanical mixing

Mixing ideal IF interaction of A-A = A-B = B-B if that is true then Hmix=0, so Smix must be >0 (because mix<0 (spontaneous mixing):Sid mix = -RXilnXi 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

reg = 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 solutionPut 2 things together, disperse them, then they interact…

tot= XA0A+(1-XA)0

B + 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 Gapmicrocline

orthoclase

sanidine

anorthoclasemonalbite

high albite

low albite

intermediate albite

OrthoclaseKAlSi3O8

AlbiteNaAlSi3O8

% NaAlSi3O8

Tem

pera

ture

(Te

mpe

ratu

re ( º

C)

ºC)

300300

900900

700700

500500

11001100

1010 9090707050503030

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

Mol fraction AH2O A

Act

ivity

0.0

1.0

0.0 1.0

Ideal mixing

aAaH2O Raoult’s Law – higher

concentration ranges (higher XA):

A=A0+RTlnAXA

where A is Rauolt’s law activity coefficient