1 / 13

Gibbs Phase Rule

Gibbs Phase Rule. The number of variables which are required to describe the state of a system: p+f=c+2 f=c-p+2 Where p=# of phases, c= # of components, f= degrees of freedom

denton-mcdowell
Download Presentation

Gibbs Phase Rule

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Gibbs Phase Rule • The number of variables which are required to describe the state of a system: • p+f=c+2 f=c-p+2 • Where p=# of phases, c= # of components, f= degrees of freedom • The degrees of freedom correspond to the number of intensive variables that can be changed without changing the number of phases in the system

  2. Variance and f • f=c-p+2 • Consider a one component (unary) diagram • If considering presence of 1 phase (the liquid, solid, OR gas) it is divariant • 2 phases = univariant • 3 phases = invariant

  3. Free Energy • Gibbs realized that for a reaction, a certain amount of energy goes to an increase in entropy of a system. • G = H –TS or DG0R = DH0R – TDS0R • Gibbs Free Energy (G) is a state variable, measured in KJ/mol • Tabulated values of DG0R are in Appendix

  4. Now, how does free energy change with T and P? • From DG=DH-TDS: • T and P changes affect free energy and can drive reactions!!

  5. Volume Changes (Equation of State) For Minerals: Volume is related to energy changes: Mineral volume changes as a function of T: a, coefficient of thermal expansion Mineral volume changes as a function of P: b, coefficient of isothermal expansion

  6. Volume Changes (Equation of State) • Gases and liquids undergo significant volume changes with T and P changes • Number of empirically based EOS solns.. • For metamorphic environments: • Redlich and Kwong equation: • V-bar denotes a molar quatity, aRw and bRK are constants

  7. Phase Relations • Rule: At equilibrium, reactants and products have the same Gibbs Energy • For 2+ things at equilibrium, can investigate the P-T relationships  different minerals change with T-P differently… • For DGR = DSRdT + DVRdP, at equilibrium, DG=0, rearranging: Clausius-Clapeyron equation Remember that a line on a phase diagram describes equilibrium, DGR=0!!

  8. V = Vº(1-bDP) DSR change with T or P? DV for solids stays nearly constant as P, T change, DV for liquids and gases DOES NOT • Solid-solid reactions linear  S and V nearly constant, DS/DV constant  + slope in diagram • For metamorphic reactions involving liquids or gases, volume changes are significant, DV terms large and a function of T and P (and often complex functions) – slope is not linear and can change sign (change slope + to –)

  9. Example – Diamond-graphite • To get C from graphite to diamond at 25ºC requires 1600 MPa of pressure, let’s calculate what P it requires at 1000ºC:

  10. Clausius-Clapyron Example

  11. Phase diagram • Need to represent how mineral reactions at equilibrium vary with P and T

More Related