GEOL 295Physical 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 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

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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 S0R:

• When S0R is positive entropy increases as a

result of a change in state

• When S0R 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 Examples

G0R = H0

R – TS0R

• 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 – G0R = RT ln K

• AT equilibrium, GR=0, therefore:

G0R = -RT ln K

where K is the equilibrium constant

QRTPP

PPRT

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 constants

G0R = 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

eK

0

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+ + CO32- -8.48

• CO32- + H+ = HCO3

- 10.329

• CaCO3 + H+ = Ca2+ + HCO3- =1.849

RT

GR

eK

0

i

ni

n

reactants

productsQ

][

][

G0R = H0

R – TS0R GR = HR – TSR

G0R = -RT ln K

)reactants()( 000i

iii

iiR GnproductsGnG

RT

GR

eK

0

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

• S0mix=-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…