Department of Geology

Laboratory for Mineral Deposits Research

Chemical Potential

 

Note: in many cases, Free Energy is used instead of chemical potential; however, a reading of Gibbs' original work shows clearly that chemical potential is more fundamental.

 

copyright by Philip A. Candela, 1997-2018.

 

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The chemical potential, µ, of a component in a solution can be thought of in many ways:

 

1. A measure of the "escaping tendency" for a component in a solution;

2. A measure of the reactivity of a component in a solution;

3. For a one component (pure) phase, the chemical potential can be thought of as:

µ = U + PV - TS (note, in this equation, µ,U,S,V, as well as T and P, are intensive quantities).

 

That is, the chemical potential increases as the internal energy, U, of the phase increases, and as the entropy, S, of the phase decreases at a given temperature, T. Further, the µ increases as the volume, V increases for a given pressure, P. So, components that possess HIGHER internal energies are destabilized relative to those with LOWER internal energies, and components with LOWER entropies are destabilized relative to those with HIGHER entropies.

 

4. The chemical potential of a component in a solution is defined as the rate at which the (extensive) internal energy of the solution increases as the number of moles (extensive) of the component in question increases, for a given entropy and volume of the solution.

 

That is, for the chemical potential of a component (i) in a solution (e.g., SrCO3 in the aragonite (CaCO3) of sponge spicules in the ocean, or of fish otoliths from the Chesapeake Bay):

 

µi = {dU/dni}S,V,nj

 

where d = the *partial* differential operator, U = the internal energy of the phase, ni is one component of phase, nj represents all the other components of the system or phase; all variables to the right of the "}" are held constant during the partial differentiation. U,n,S,V must be extensive in this definition; the chemical potential, µ is ALWAYS intensive. IF X (mole fraction) is subbed for n in this, the most basic, fundamental and precise of all definitions for chemical potential, the expression is rendered INCORRECT!

 

5. Yes, it does happen to be true that the chemical potential is equal to the partial molar Gibbs Free Energy (or, Gibbs Potential), BUT... that is NOT a good way to define µ because chemical potential is more fundamental than the Gibbs Potential, G, (defined as G = H - TS, where H = U + PV). G, A, and H were defined by Gibbs as Auxiliary Functions AFTER he defined chemical potential. What most people call "free energy calculations" (i.e., free energy of products minus reactants is greater or less than zero) are really chemical potential calculations. This equivalence is due to that fact that the free energy of a pure phase is equal to the chemical potential of the single component of the pure phase. The use of what is REALLY an auxiliary function (G) to fill a primary role in thermodynamics that is actually better filled by the more fundamental chemical potential is one of the many reasons why student have trouble with the subject. Read Gibbs.

 

6. The chemical potential always refers to components in a (solid, liquid or gaseous) solution, or to the one component in a pure phase. When considering say, dissolved alcohol in aqueous solution, the chemical potential of alcohol= µ(alcohol in solution) = µ(pure alcohol) + RT ln (a), where a = activity of the component (alcohol in this case) in the solution, and where either a = jm or a = j X (where j = activity coefficient, m = molality or molarity, and X = mole fraction). In geology, we might be concerned with the chemical potential of enstatite component in orthorhombic pyroxene, which, skipping some complexities, may be represented by:

 

µ(MgSiO3) = µ(pure MgSiO3) + Rt ln X(MgSiO3), when the solution is ideal (activity coefficent ~ 1).

 

7a.The chemical potential of ethanol increases to the right in the following series of solutions:

beer -> wine -> scotch whisky ->white lightning

 

7b. The chemical potential of O2 increases (all corrected to the same T and P) progressing from a lunar basalt that has accessory native iron, to an awaruite (Fe-Ni alloy) + magnetite-bearing serpentinized ultramafic rock, to fayalite bearing granites, to fayalite + magnetite bearing granites, to granites with magnetite + quartz BUT no fayalite, to hematitically altered granites! O2 chemical potential also increases in going from Po + Mag ores, to Py + Mag ores to Py + hematite bearing ores to jarosite + hematite bearing ores; not to mention from black shales to red sandstones, and from oxygen depleted ground water to an O2-bearing vadose zone!

Acknowledgments

 

This work would not be possible without the support of the National Science Foundation, the Department of Geology, and the University of Maryland.