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

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 = -5.708 log Keq at 25°C

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

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)

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 °

Aqueous Complexes 2 main types Ion pairs Coordination compounds

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

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)

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

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°)

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

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

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

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

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

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

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”

Acids and Bases

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

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

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)

Alkali Metals Alkaline Earths

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)

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

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

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

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

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

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

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

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

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

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

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

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

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)

Dissociation and pH

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

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

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

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