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
1
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
2
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
3
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)
4
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 °
5
Aqueous Complexes
• 2 main types
– Ion pairs
– Coordination compounds
6
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
7
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)
8
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
9
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°)
10
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
11
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
12
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
13
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
14
Complexation Example
• How much is Ca2+ decreased by complexation
with SO42-?
15
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
16
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”
17
Acids and Bases
18
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
19
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
20
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+ + ClSulfuric 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)
21
Alkali
Metals
Alkaline
Earths
22
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)
23
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
24
Dissociation of Silicic Acid
• H4SiO4 ↔ H+ + H3SiO4– 1st dissociation :
– Ka1 is small
– At pH 7:
• H3SiO4- ↔ H+ + H2SiO42– 2nd dissociation:
– Ka2 is very small
25
Dissociation of Silicic Acid (cont.)
• H2SiO42- ↔ H+ + HSiO43– 3rd dissociation:
– miniscule
• HSiO43- ↔ H+ + SiO44– 4th dissociation:
< miniscule
26
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
27
Example
• Assume 0.1 moles of acetic acid is
dissolved in 1 L H2O, determine fraction
(x) that dissociates…
– Assume γ = 1
28
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
29
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
30
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
31
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
32
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
33
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
34
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
35
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)
36
0
Dissociation and pH
–2
–4
++
Mg
–6
Diagram Mg , T = 25 °C , P = 1.013 bars, a [H2 O] = 1
–8
+
MgOH
–10
++
log a Mg
++
Brucite
25°C
0
2
4
6
8
pH
10
12
14
Walt Mon Feb 06 2006
37
Dissociation and pH
• Dissociation of weak acids/bases controlled by
pH
• Rewrite mass action equations for H2S
– H2S(aq)  H+ + HS-
38
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
39
Total S = 10-4 M
–2
--
Some species w/ SO4 (log activity)
–4
H2 S(aq)
HS
-
S
--
–6
pH = 12.9
pH = 7
–8
–10
–12
–14
–16
–18
–20
2
3
4
5
6
7
8
9
10
11
12
13
14
pH
Walt Tue Feb 14 2006
40
Total DIC = 10-1 M
0
-
CO2 (aq)
--
HCO3
CO3
pH = 10.33
pH = 6.35
–4
–6
-
Species with HCO3 (log molal)
–2
–8
–10
–12
–14
–16
2
3
4
5
6
7
8
9
10
11
12
pH
Walt Tue Feb 21 2006
41