Free energy geochemistry

1. Energy
• Many ways to describe energy changes in
thermodynamics
• Originally developed to describe changes in
heat and ‘work’ (think a steam engine
piston)
• Energy flow also describes chemical
reactions in systems – but since there is no
energy ‘particle’ we must do all of this in a
relative sense i.e. one think has more
‘energy’ than another and wins…

2. Reference States
• We recall that we do not know absolute
energies!!!
• We can describe any reaction or description
of reaction relative to another  this is all we
need to describe equilibrium and predict
reaction direction, just need an anchor…
• Reference States:
– Standard state: 1 atm pressure, 25°C
– Absolute states – where can a value be defined?
 entropy at 0 Kelvin

3. • Aka the Law of conservation of energy, Gibbs
in 1873 stated energy cannot be created or
destroyed, only transferred by any process
• The net change in energy is equal to the heat
that flows across a boundary minus the work
done BY the system
• DU = q + w
– Where q is heat and w is work
– Some heat flowing into a system is converted to work and
therefore does not augment the internal energy
1st Law of Thermodynamics

4. Directionality from the 2nd Law
• For any spontaneous irreversible process,
entropy is always increasing
• How can a reaction ever proceed if order
increases?? Why are minerals in the earth not
falling apart as we speak??
T
dq
dS 

5. 3rd Law of Thermodynamics
• The heat capacities of pure crystalline
substances become zero at absolute zero
• Because dq = CdT and dS = dq / T
• We can therefore determine entropies of
formation from the heat capacities (which are
measureable) at very low temps
 









T
config
p
abs S
dT
T
C
S
0







T
dT
C
dS p

6. Heat Capacity
• When heat is added to a phase it’s temperature
increases (No, really…)
• Not all materials behave the same though!
• dq=CVdT  where CV is a constant (heat capacity
for a particular material)
• Or at constant P: dq=CpdT
• Recall that dqp=dH then: dH=CpdT
• Relationship between CV and Cp:
T
V
C
C V
p

2


Where a and b are coefficients of isobaric thermal expansion
and isothermal compression, respectively

7. Enthalpy at different temps…
• HOWEVER  C isn’t really constant….
• C also varies with temperature, so to really
describe enthalpy of formation at any
temperature, we need to define C as a
function of temperature
• Maier-Kelley empirical determination:
• Cp=a+(bx10-3)T+(cx10-6)T2
– Where this is a fit to experimental data and a,
b, and c are from the fit line (non-linear)

8. • Heat absorbed by a chemical reaction
• Heat of reaction DH0
R
• DH0
R is positive  exothermic
• DH0
R is negative  endothermic
• Example: 2A + 3B  A2B3
• DH0
R =H0
f(A2B3)-[2H0
f(A) + 3H0
f(B)]
)
(
)
( 0
0
0
reactants
H
n
products
H
n
H
i
fi
i
fi
i
i
R 
 

D
Heat of Reaction

9. Entropy of reaction
• A function of energy ‘dispersing’
• Entropy of reaction S0
R:
• When DS0
R is positive  entropy increases as a
result of a change in state
• When DS0
R is negative  entropy decreases as
a result of a change in state
)
(
)
( 0
0
0
reactants
S
n
products
S
n
S i
i
i
i
i
i
R 
 

D

10. Entropy of the Universe
• 2nd law of thermodynamics – entropy
always increases.
• Certain amount of heat ‘energy’ in room,
an isolated system
• Glass of ice – melts in time  energy is
dispersing to a point where everything has
the same energy
• Gives direction to any process…

11. Equilibrium Constant
DGR – DG0
R = RT ln K
AT equilibrium, DGR=0, therefore:
DG0
R = -RT ln Keq
where Keq is the equilibrium constant

12. Equilibrium constants
DG0
R = -RT ln K
Rearrange:
ln K = -DG0
R / 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
e
K
0
D







i
n
i
n
products
Q
]
reactants
[
]
[

13. J. Willard Gibbs
• Gibbs realized that for a reaction, a certain
amount of energy goes to an increase in
entropy of a system and a certain amount
goes to a heat exchange for a reaction.
• G = H –TS or DG0
R = DH0
R – TDS0
R
• Gibbs Free Energy (G) is a state variable,
measured in KJ/mol
• Tabulated values of DG0
R are in Appendix
)
reactants
(
)
( 0
0
0
i
i
i
i
i
i
R G
n
products
G
n
G 
 

D

14. G is a measure of driving force
• DGR = DHR – TDSR
• When DGR is negative  forward reaction
has excess energy and will occur
spontaneously
• When DGR is positive  there is not enough
energy in the forward direction, and the
BACKWARD reaction will occur
• When DGR is ZERO  reaction is AT
equilibrium
DGR – DG0
R = RT ln K

15. Free Energy Examples
DG0
R = DH0
R – TDS0
R
H2O(l)=-63.32 kcal/mol (NIST value:
http://webbook.nist.gov/chemistry/)
• Fe2+ + ¼ O2 + H+  Fe3+ + ½ H2O
=[-4120+(-63320*0.5)]-[-21870+(3954*0.25)]
=[-67440]-[-19893]=-47547 cal/mol
)
reactants
(
)
( 0
0
0
i
i
i
i
i
i
R G
n
products
G
n
G 
 

D

16. Using Keq to define equilibrium
concentrations
DG0
R = -RT ln Keq
DGR = DG0
R + RT ln Q
• Keq sets the amount of ions present relative
to one another for any equilibrium condition




i
n
i
n
eq
reactants
products
Q
K
]
[
]
[
AT Equilibrium



i
n
i
n
eq
reactants
products
K
]
[
]
[
DGR = 0