geol 295 physical chemistry in the earth sciences
DESCRIPTION
GEOL 295 Physical Chemistry in the Earth Sciences. Greg Druschel Delehanty 321 Class times:MWF 9:05 – 9:55 a.m. Class Structure. Lecture over the theory and basic equations governing different processes Practicum going over example problems 1 homework over each section - PowerPoint PPT PresentationTRANSCRIPT
GEOL 295Physical Chemistry in the Earth
Sciences
Greg DruschelDelehanty 321
Class times:MWF 9:05 – 9:55 a.m.
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
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↔↔ matterheat heat
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
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.
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
Ene
rgy
In thermodynamics, these 2 reactions are NOT differentExample: Catalysis does not affect thermodynamic calculations!
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
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??
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!
• Heat of reaction H0R
• H0R is positive exothermic
• H0R is negative endothermic
• Example: 2A + 3B A2B3
• H0R =H0
f(A2B3)-[2H0f(A) + 3H0
f(B)]
)()( 000 reactantsHnproductsHnHi
fiifii
iR
Heat of Reaction, Enthalpy
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
Entropy of reaction
• Just as was done with enthalpies:• Entropy of reaction S0
R:
• When S0R is positive entropy increases as a
result of a change in state• When S0
R is negative entropy decreases as a result of a change in state
)()( 000 reactantsSnproductsSnS ii
iii
iR
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.
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 G0R = H0
R – TS0R
• Gibbs Free Energy (G) is a state variable, measured in KJ/mol and is a measure of all non-PV work:
• Tabulated values of G0R are in Appendix B
)reactants()( 000i
iii
iiR GnproductsGnG
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
G is a measure of driving force
• G0R = H0
R – TS0R
• When G0R is negative forward reaction
has excess energy and will occur spontaneously
• When G0R is positive there is not
enough energy in the forward direction, and the BACKWARD reaction will occur
• When G0R is ZERO reaction is AT
equilibrium
Free Energy ExamplesG0
R = H0R – TS0
R
• 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-
)reactants()( 000i
iii
iiR GnproductsGnG
kaolinite
goethite
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:
ii n
G
Law of Mass Action• Getting ‘out’ of the standard state:
• Bear in mind the difference between the standard state G0 and 0 vs. the molal property G and (not at standard state 25 C, 1 bar, a mole)
n
n
rr RTGG
reactants
productsln0
Equilibrium Constant
• For a reaction of ideal gases, P becomes:for aA + bB cC + dD
• Restate the equation as:GR – G0
R = RT ln K
• AT equilibrium, GR=0, therefore:
G0R = -RT ln K
where K is the equilibrium constant
QRTPPPPRT bB
aA
dD
cC lnln
K a.k.a Keq
IfGR – G0R = RT ln K, and for equilibrium
G0R = 0, then:
At Equilibrium define GR from the expression RT ln K, the product of the activities for products over reactants
i
ni
n
reactants
productsK
][
][
Equilibrium constantsG0
R = RT ln K
Rearrange:
ln K = G0R / 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)RT
GR
eK0
i
ni
n
reactants
productsQ
][
][
Log K
G0R = -RT ln K
For any reaction, log K an indication of the equilibrium conditions
Log K’s are additive:• CaCO3 = Ca2+ + CO3
2- -8.48
• CO32- + H+ = HCO3
- 10.329
• CaCO3 + H+ = Ca2+ + HCO3- =1.849
RTGR
eK0
i
ni
n
reactants
productsQ
][
][
G0R = H0
R – TS0R GR = HR – TSR
G0R = -RT ln K
)reactants()( 000i
iii
iiR GnproductsGnG
RTGR
eK0
i
ni
n
reactants
productsQ
][
][
n
n
rr RTGG
reactants
productsln0
)()( 000 reactantsHnproductsHnHi
fiifii
iR
)()( 000 reactantsSnproductsSnS ii
iii
iR
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• S0
mix=-R(N1lnN1+N2lnN2+…)
• G0mix=-R(N1lnN1+N2lnN2+…)
• Gss = N1G10 + N2G1
0 + … + DG0mix
Non ideal mixing• When components interact, need to interact
a term to account, ω, called the excess free energy of mixing G0
mix(excess)
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…