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
– 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
↔
matter
heat
closed
↔ heat
isolated
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
Energy
• 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!
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, Enthalpy
• Heat of reaction DH0R
DH R0   ni H 0fi ( products)   ni H 0fi (reactants)
i
i
• DH0R is positive  exothermic
• DH0R is negative  endothermic
• Example: 2A + 3B  A2B3
• DH0R =H0f(A2B3)-[2H0f(A) + 3H0f(B)]
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 S0R:
DS   ni S ( products)   ni S (reactants)
0
R
0
i
i
0
i
i
• 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
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
DG0R = DH0R – TDS0R
• Gibbs Free Energy (G) is a state variable,
measured in KJ/mol and is a measure of all
non-PV work:
DG   ni G ( products)   ni G (reactants )
0
R
0
i
i
0
i
i
• Tabulated values of DG0R are in Appendix B
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
• 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
Free Energy Examples
DG0R = DH0R – TDS0R
DGR0   ni Gi0 ( products)   ni Gi0 (reactants )
i
i
• Al2Si2O5(OH)4 + 6H+ = 5H2O + 2Al3+ + 2SiO2(aq)
kaolinite
• FeOOH + 2H+ = 1.5 H2O + Fe2+ + ¼ O2(aq)
goethite
• 1/8 S8 + H2O + 1.5 O2(aq) = 2 H+ + SO42-
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:
 G 
i   
 n i
• 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:
Law of Mass Action
• Getting ‘out’ of the standard state:

products 

 RT ln
 reactants 
n
DGr  DG
0
r
n
• 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)
Equilibrium Constant
•
For a reaction of ideal gases, P becomes:
 PCc PDd 
for
aA
+
bB

cC
+
dD
  RT ln Q
RT ln 
 P a Pb 
 A B
•
•
Restate the equation as:
DGR – DG0R = RT ln K
AT equilibrium, DGR=0, therefore:
DG0R = -RT ln K
where K is the equilibrium constant
K a.k.a Keq
[ products]
K
[reactants]
n
i
n
i
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
Equilibrium constants
DG0R = RT ln K
Rearrange:
ln K = DG0R / RT
K e
 DGR0
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)
 [ products]
Q
 [reactants]
n
i
i
n
Log K
DG0
R
= -RT ln K
K e
 DGR0
RT
 [ products]
Q
 [reactants]
n
i
i
For any reaction, log K an indication of the
equilibrium conditions
Log K’s are additive:
• CaCO3 = Ca2+ + CO32-8.48
• CO32- + H+ = HCO310.329
• CaCO3 + H+ = Ca2+ + HCO3=1.849
n
DH R0   ni H 0fi ( products)   ni H 0fi (reactants)
i
i
DS   ni S ( products)   ni S (reactants)
0
R
0
i
0
i
i
i
DG0R = DH0R – TDS0R
DG0R = -RT ln K
DGR = DHR – TDSR
K e
 DGR0
RT
Q
n
[
products
]

i
n
[
reactants
]

i
DGR0   ni Gi0 ( products)   ni Gi0 (reactants )
i
i

products 

 RT ln
 reactants 
n
DGr  DG
0
r
n
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
Non ideal mixing
• When components interact, need to interact
a term to account, ω, called the excess free
energy of mixing DG0mix(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…