1. Gibbs Free Energy
Gibbs Free Energy (G) is a measure of enthalpy (heat) taking entropy (randomness) into account
ΔGR° is a measure of the driving force of a reaction
GR < 0; forward reaction has excess energy, thus favors forward reaction
GR > 0; forward reaction has deficiency of E, thus favors reverse reaction

2. Gibbs Free Energy Two ways to calculate GR and Keq are related:
GR = ΔHR - T ΔSR
GR = niGfi(products) – niGfi(reactants)
GR and Keq are related:
GR = -RT ln Keq
GR = log Keq at 25°C

3. Activity
To apply equilibrium principles to ions and molecules, we need to replace concentrations with activities to account for ionic interactions
ai = i Ci
a < C in most situations

4. Activity Activity coefficients () are a function of ionic strength
I = ½ mi zi2
Use Debye-Hückel or extended Debye-Hückel equation (unless saline solution)
log  = -Az2I½
log  = - Az2I½
(1 - aBI½)

5. Aqueous Complexes
Complex: chemical association of 2 or more dissolved species to form a 3rd dissolved species
Some examples:
Al3+ + OH-  Al(OH)2+
Al(OH)2+ + OH-  Al(OH)2+
Ca2+ + SO42-  CaSO4(aq)
Ca2+ + HCO3-  CaHCO3+(aq)
Note: ΣCa in solution = Ca2+ (ion) + CaSO4° + CaHCO3+ + any other Ca-containing complexes
Aqueous complex distinguished from solid of same composition by subscript (aq) or superscript °

6. Aqueous Complexes
2 main types
Ion pairs
Coordination compounds

7. Ion Pairs
Cations and anions form associations in solution because of electrostatic attraction
Associations are weak bonds; form and decompose rapidly in response to changes in solution chemistry
Generally the greater the concentration, the greater the amount of ion pairs

8. Coordination Compounds
Ions surrounded by sphere of hydration; one or more water molecules displaced by ligands
Ligand = ion (usually anion) or molecule that binds to a central atom (usually a metal)
If a ligand can bind at more than one site, it is called a chelate, and the bond is stronger
Some coordination-type complexes are very stable
e.g., used in cleaning metal waste (EDTA, NTA)

9. Importance of complexes
Increase mineral solubility by decreasing effective concentrations
Equilibrium calculations are usually made with uncomplexed species
Analytical instruments usually measure total amount (uncomplexed + complexed) of a species
ΣmCa = mCa2+ + mCaHCO3+ + mCaSO4° + …
ΣmCa = measured amount
mCa2+ used in thermodynamic calculations
We can’t directly measure mCaHCO3+, mCaSO4°: must calculate

10. Importance of complexes
Many elements exist dominantly as a complex or complexes)
Usually those with low solubilities such as metals
As, Fe, Al, Pb, Hg, Cu, U to name a few
e.g., As5+ usually exists as an oxyanion (H2AsO4-) and As3+ usually exists as an uncharged species (H3AsO3°)

11. Importance of complexes
Adsorption can be increased or inhibited
Adsorption is usually a weak attraction of charged species to aquifer solids
Charged complexes more likely than uncharged complexes to adsorb and be removed from solution
Bioavailability and toxicity
Some complexes of essential nutrients may pass straight through living organisms
Some complexes of toxic species may pass straight through living organisms
CH3Hg+ most toxic form; elemental Hg much less toxic

12. Complexes: General Observations
Low solubility elements exist predominantly as complexes (e.g., metals)
Complexation tends to increase with increasing I
More potential ions to complex with
Species are closer together
Mineral solubility also increases with increasing I
Combined effects of complexation and activity; ions in solution less reactive
Increasing charge density (charge per surface area) results in stronger complexes
Charge density increases with increasing valence or decreasing atomic radius
Function of valence and ion size

13. Complexes and Thermodynamics
The presence and stability of complexes can be predicted using thermodynamics
Ca2+ + SO42-  CaSO4(aq)
Kassoc = association constant (also Ka); also called stability constant
The larger the Kassoc , the more stable the complex
Kassoc have smaller ranges compared to Keq, probably because bonds are weak
As with Keq, Kassoc values have been determined in the lab and are included in thermodynamic databases of geochemical models

14. Calculating complexes
Need complete chemical analyses to calculate concentrations of complexes
If important complexing species are missing, data interpretation may be in error
Speciation often a function of pH, so must have accurate field pH

15. Complexation Example
How much is Ca2+ decreased by complexation with SO42-?

16. pH pH = -log[H+] Many reactions involve H+
Silicate and carbonate weathering
Sulfide weathering (acid mine drainage)
Dissociation of water molecule
Adsorption
Microbial processes; e.g., denitrification
Amphoteric oxyhydroxides; Fe(OH)3, Al(OH)3
Aqueous complexes

17. pH as Master Variable
pH is key parameter affecting species distribution
Therefore useful to consider activity of other species with respect to pH
pH is a “master variable”

18. Acids and Bases

19. Definitions
Acid is a compound that releases H+ when dissolved in water (proton donor)
Base is a compound that releases OH- when dissolved in water (proton acceptor)
Acids and bases can be liquids or solids
e.g., H2CO3  HCO3- + H+
H2CO3 donates a proton when it dissociates = Acid
HCO3- + H+  H2CO3
HCO3- accepts a proton = Base

20. Definitions
Some species can act as both acid and base, depending on reaction
HCO3- + H+  H2CO3
HCO3- accepts a proton = Base
HCO3-  CO32- + H+
HCO3- donates a proton = Acid

21. Acid/Base Strength
Strength is a measure of the tendency of an acid or base to give or accept protons
Strong acids/bases release all/most available H+/OH-
Strong acids almost completely dissociate in water; large Ka
HCl  H+ + Cl-
Sulfuric acid: H2SO4 – acid rain (burning fossil fuels), AMD
Nitric acid: HNO3 – acid rain, nitrification (NH4+  NO3-)
Not usually large natural source of acid
Strong bases: hydroxides of alkali metals (Li, Na, K, Rb, Cs, Fr) and many alkaline earths (Mg, Ca, Sr, Ba, Ra)

22. Alkali
Metals
Alkaline
Earths

23. Acid/Base Strength Usually measure using Normality (N)
Weak acids/bases release only a small fraction of available H+/OH-
Acetic acid (CH3COOH), H2CO3, H3PO4, H4SiO4
Small Ka
Ammonium hydroxide (NH4OH), nickel hydroxide (Ni(OH)2)
In real world geochemistry, we’re mainly interested in weak acids and bases
Strength has nothing to do with concentration
HCl is still a strong acid even if it is greatly diluted
Acetic acid is still weak even if in a concentrated solution
Usually measure using Normality (N)

24. Important Acids in Groundwater
Carbonic acid: H2CO3 – CO2
Dominant source of H+ in most groundwater
Silicic acid: H4SiO4 – mineral weathering
Acetic acid: CH3COOH – natural and anthropogenic (landfills); organic acid
Other organic acids (formic, oxalic)
Phosphoric: H3PO4

25. Dissociation of Silicic Acid
H4SiO4 ↔ H+ + H3SiO4-
1st dissociation :
Ka1 is small
At pH 7:
H3SiO4- ↔ H+ + H2SiO42-
2nd dissociation:
Ka2 is very small

26. Dissociation of Silicic Acid (cont.)
H2SiO42- ↔ H+ + HSiO43-
3rd dissociation:
miniscule
HSiO43- ↔ H+ + SiO44-
4th dissociation: < miniscule

27. Dissociation Reactions
Dissociation reactions reach equilibrium very quickly
e.g. CH3COOH  CH3COO- + H+
Ka = 1.76 x 10-5 at 25°C, 1 atm
Very small number, most remains undissociated
Knowing Ka and the initial concentration of CH3COOH, we can calculate how much dissociates

28. Example
Assume 0.1 moles of acetic acid is dissolved in 1 L H2O, determine fraction (x) that dissociates…
Assume γ = 1

29. Dissociation of Water H2O  H+ + OH- (or H2O + H+ ↔ H3O+)
Kw = [H+] [OH-] = 1 x at 25°C
Remember that [H2O] = 1
Small dissociation constant, but nearly unlimited source of H+ or OH-
For pure H2O at 25°C, [H+] = [OH-] = 10-7 mol/L

30. Dissociation of Water H2O  H+ + OH- pH = -log [H+]
Useful for reflecting on progress of chemical reactions
Easy to measure
pH = 7 for pure water at 25°C, 1 atm
Usually we consider pH values between 0 and 14
pH for most natural waters is between 6 and 9
We can also define pOH = -log [OH-]
Not widely used
At 25°C, pOH = 14 - pH

31. pH in the Environment
Weak acids/bases do not control the pH of the natural environment, but respond to it
pH is an environmental variable determined by all of the simultaneous equilibria existing in a given environment

32. Calculating pH of Acids and Bases
What is the pH of 0.1 M acetic acid?
CH3COOH  CH3COO- + H+
Recall we calculated that [H+] = 1.32 x 10-3 mol/L
pH = 2.88
Note that even though acetic acid is a weak acid, the pH of a fairly concentrated solution of it is quite low

33. Polyprotic Acids/Bases
A weak acid or base that can yield 2 or more H+ or OH- per molecule of acid/base is polyprotic
H2S(aq)  H+ + HS-
HS-  H+ + S2-
Note that 1st reaction contributes much more H+ (K1 >> K2)
Other examples: H2CO3, H2SO4, H3PO4

34. Determining concentrations of species for polyprotic acids/bases
Dissolve 0.1 moles of H2S in pure water at 25°C; what are the concentrations of all the aqueous species?
Again, we’ll assume γ = 1

35. Sparingly Soluble Bases
Many bases do not readily dissolve in water
e.g., Brucite (Mg(OH)2) solubility
Mg(OH)2(s)  Mg(OH)+ + OH-: Keq =
Let’s calculate the concentrations of species as a function of pH

36. Brucite solubility
Plot activity of Mg species vs. pH to get an Activity Diagram
log [Mg(OH)+] = 5.4 – pH
log [Mg2+] = 16.8 – 2pH
get straight lines intersecting at pH = 11.4
pH = 14 – 2.6 = 11.4
Lines represent equilibrium between the two species/compounds on opposite sides
Mg2+ dominates at pH < 11.4 (most geologic environments)

37. Dissociation and pH

38. Dissociation and pH Dissociation of weak acids/bases controlled by pH
Rewrite mass action equations for H2S
H2S(aq)  H+ + HS-

39. Dissociation and pH Can do same for HS- vs. S2- HS-  H+ + S2-
Such relationships occur for all weak acids and bases
Knowing the total amount of S and pH, we can calculate activities of all species and generate curves

40. Total S = 10-4 M
pH = 7
pH = 12.9

41. Total DIC = 10-1 M
pH = 10.33
pH = 6.35