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 = ΔHR - T ΔSR

– GR = niGfi(products) – niGfi(reactants)

• GR and Keq are related:– GR = -RT ln Keq – GR = -5.708 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+ + SO4

2- 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 SO4

2-?

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- CO3

2- + 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

AlkaliMetals Alkaline

Earths

23

Acid/Base Strength• 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+ + H2SiO4

2-

– 2nd dissociation: – Ka2 is very small

26

Dissociation of Silicic Acid (cont.)

• H2SiO42- ↔ H+ + HSiO4

3-

– 3rd dissociation: – miniscule

• HSiO43- ↔ H+ + SiO4

4-

– 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 10-14 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 = 10-8.6

– 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

0 2 4 6 8 10 12 14–10

–8

–6

–4

–2

0

pH

log

a M

g++

Mg++

MgOH+

Brucite

25°C

Walt Mon Feb 06 2006

Dia

gram

Mg+

+,

T

=

25 °

C ,

P

=

1.01

3 ba

rs,

a [H

2O

] =

1

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

40Walt Tue Feb 14 2006

2 3 4 5 6 7 8 9 10 11 12 13 14–20

–18

–16

–14

–12

–10

–8

–6

–4

–2

pH

So

me

sp

eci

es

w/ S

O4--

(lo

g a

ctiv

ity)

H2S(aq) HS

-

S--

pH = 7 pH = 12.9

Total S = 10-4 M

41Walt Tue Feb 21 2006

2 3 4 5 6 7 8 9 10 11 12–16

–14

–12

–10

–8

–6

–4

–2

0

pH

Sp

eci

es

with

HC

O3- (

log

mo

lal)

CO2(aq) CO

3--

HCO3-

Total DIC = 10-1 M

pH = 6.35 pH = 10.33