GEOL 295 Physical Chemistry in the Earth Sciences

1. GEOL 295Physical Chemistry in the Earth Sciences Greg Druschel Delehanty 321 Class times:MWF 9:05 – 9:55 a.m.

2. Class Structure • Lecture over the theory and basic equations governing different processes • Practicum going over example problems • 1 homework over each section • DUE 1 week after assigned • NO TESTS • Individual project – oral presentation at end of class instead of final • Grading: 60% homework, 10% participation, 30% final project

3. Systems • System – the PART of the universe that is under consideration. It is separated from the rest of the universe by it’s boundaries • Open system  when matter CAN cross the boundary • Closed system  when matter CANNOT cross the boundary • Isolated  Boundary seals matter and heat from exchange with another system open closed isolated ↔ matter heat ↔ heat

4. Equilibrium/ Reversibility • Anything at equilibrium is theoretically undergoing equivalent forward and reverse reactions: • A + B ↔ C • A + B  C same degree as C  A +B • Equilibrium has 2 criteria: • Reaction does not appreciably change in time • Perturbation of that equilibrium will result in a return to the equilibrium

5. STABLE VS. METASTABLE EQUILIBRIUM • Stable equilibrium - System is at its lowest possible energy level. • Metastable equilibrium - System satisfies above two criteria, but is not at lowest possible energy.

6. Defining a system • A system at equilibrium has measurable properties • If the system changes from one equilibrium ‘state’ to another  these changes depend of the properties changed and not on the path (or exact process) the change went along In thermodynamics, these 2 reactions are NOT different Example: Catalysis does not affect thermodynamic calculations! Energy

7. Chemical Properties of a System • We express the composition of materials in a system in terms of components and phases • Component – the chemical constituents by which all of the phases in a system can be completely described • Phase – a uniform, homogeneous, physically distinct, and mechanically separable portion of a system

8. Components and Phases • A phase can be solid, liquid, or gas • What should the components be for a chunk of calcite?? • Can an ion be a phase??

9. Species • In the aqueous phase, there are also a number of species • These are dissolved ions or molecules (do not have to be charged) that are NOT phases unto themselves, but can be components!

10. Heat of Reaction, Enthalpy • Heat of reaction DH0R • DH0R is positive  exothermic • DH0R is negative  endothermic • Example: 2A + 3B  A2B3 • DH0R =H0f(A2B3)-[2H0f(A) + 3H0f(B)]

11. Heat Capacity • When heat is added to a phase it’s temperature increases (No, really…) • Not all materials behave the same though! • dq=CdT  where C is a constant (heat capacity for a particular material) • Or at constant P: dCp=CpdT • Recall that dqp=dH then: dH=CpdT • HT-HT0=Cp(T-T0) to determine enthalpy of formation at temperature

12. Entropy of reaction • Just as was done with enthalpies: • Entropy of reaction S0R: • When DS0R is positive  entropy increases as a result of a change in state • When DS0R is negative  entropy decreases as a result of a change in state

13. MEANING OF ENTROPY AND THE SECOND LAW • Entropy is a measure of the disorder (randomness) of a system. The higher the entropy of the system, the more disordered it is. • The second law states that the universe always becomes more disordered in any real process. • The entropy (order) of a system can decrease, but in order for this to happen, the entropy (disorder) of the surroundings must increase to a greater extent, so that the total entropy of the universe always increases.

14. J. Willard Gibbs • 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 and is a measure of all non-PV work: • Tabulated values of DG0R are in Appendix B

15. Free Energy • Gibbs Free energy describes the potential chemical energy possible between potential reactants • In battery for instance, the fact that there is x driving force when anode and cathode are in contact provides a certain amount of power  determined by G • Any reaction out-of-equilibrium with the potential to go there can supply energy to organisms

16. G is a measure of driving force • DG0R = DH0R – TDS0R • When DG0R is negative  forward reaction has excess energy and will occur spontaneously • When DG0R is positive  there is not enough energy in the forward direction, and the BACKWARD reaction will occur • When DG0R is ZERO  reaction is AT equilibrium

17. Free Energy Examples DG0R = DH0R – TDS0R • Al2Si2O5(OH)4 + 6H+ = 5H2O + 2Al3+ + 2SiO2(aq) • FeOOH + 2H+ = 1.5 H2O + Fe2+ + ¼ O2(aq) • 1/8 S8 + H2O + 1.5 O2(aq) = 2 H+ + SO42- kaolinite goethite

18. 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 m" 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:

19. Law of Mass Action • Getting ‘out’ of the standard state: • Bear in mind the difference between the standard state G0 and m0 vs. the molal property G and m (not at standard state  25 C, 1 bar, a mole)

20. Equilibrium Constant • For a reaction of ideal gases, P becomes: for aA + bB  cC + dD • Restate the equation as: DGR – DG0R = RT ln K • AT equilibrium, DGR=0, therefore: DG0R = -RT ln K where K is the equilibrium constant

21. K a.k.a Keq If DGR – DG0R = RT ln K, and for equilibrium DG0R = 0, then: At Equilibrium define DGR from the expression RT ln K, the product of the activities for products over reactants

22. DG0R = RT ln K Rearrange: ln K = DG0R / RT Find K from thermodynamic data for any reaction Q is also found from the activities of the specific minerals, gases, and species involved in a reaction (in turn affected by the solution they are in) Equilibrium constants

23. Log K DG0R = -RT ln K For any reaction, log K an indication of the equilibrium conditions Log K’s are additive: • CaCO3 = Ca2+ + CO32- -8.48 • CO32- + H+ = HCO3- 10.329 • CaCO3 + H+ = Ca2+ + HCO3- =1.849

24. DG0R = DH0R – TDS0R DGR = DHR – TDSR DG0R = -RT ln K

25. Mixtures • Henry’s and Raoult’s laws describe how components mix together • Mixing  mechanical mixing, but components interact • Ideal mixing (Raoult’s law followed for all): • Enthalpy does not change • DS0mix=-R(N1lnN1+N2lnN2+…) • DG0mix=-R(N1lnN1+N2lnN2+…) • Gss = N1G10 + N2G10 + … + DG0mix

26. Non ideal mixing • When components interact, need to interact a term to account, ω, called the excess free energy of mixing DG0mix(excess)

27. Gases • Measure gases in partial pressures: ai=NiPi • While most gases behave ideally, do need to account for water vapor: Pi=Xgas(PT-PH2O) • Here Ni and Xgas are both the mole fraction… • Equilibrium partitioning between a gas and the dissolved fraction of that gas described by Henry’s Law Constants, KH • KH=[O2(aq)]/PO2 larger KH, more soluble…