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Gibbs Free Energy Gibbs Free Energy (G) is a measure of enthalpy (heat) taking entropy (randomness) into account ΔG R ° is a measure of the driving force.

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Presentation on theme: "Gibbs Free Energy Gibbs Free Energy (G) is a measure of enthalpy (heat) taking entropy (randomness) into account ΔG R ° is a measure of the driving force."— Presentation transcript:

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

2 Gibbs Free Energy Two ways to calculate – G R = ΔH R - T ΔS R – G R = n i G fi (products) – n i G fi (reactants) G R and K eq are related: – G R = -RT ln K eq – G R = -5.708 log K eq at 25°C 2

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

4 Activity Activity coefficients ( ) are a function of ionic strength – I = ½ m i z i 2 Use Debye-Hückel or extended Debye-Hückel equation (unless saline solution) – log = -Az 2 I ½ (1 - aBI ½ ) 4

5 Aqueous Complexes Complex: chemical association of 2 or more dissolved species to form a 3 rd dissolved species Some examples: – Al 3+ + OH - Al(OH) 2+ – Al(OH) 2+ + OH - Al(OH) 2 + – Ca 2+ + SO 4 2- CaSO 4(aq) – Ca 2+ + HCO 3 - CaHCO 3 + (aq) Note: ΣCa in solution = Ca 2+ (ion) + CaSO 4 ° + CaHCO 3 + + any other Ca-containing complexes Aqueous complex distinguished from solid of same composition by subscript (aq) or superscript ° 5

6 Aqueous Complexes 2 main types – Ion pairs – Coordination compounds 6

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 7

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) 8

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 Σm Ca = m Ca2+ + m CaHCO3+ + m CaSO4° + … – Σm Ca = measured amount – m Ca2+ used in thermodynamic calculations – We cant directly measure m CaHCO3+, m CaSO4° : must calculate 9

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., As 5+ usually exists as an oxyanion (H 2 AsO 4 - ) and As 3+ usually exists as an uncharged species (H 3 AsO 3 ° ) 10

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 CH 3 Hg + most toxic form; elemental Hg much less toxic 11

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 12

13 Complexes and Thermodynamics The presence and stability of complexes can be predicted using thermodynamics – Ca 2+ + SO 4 2- CaSO 4(aq) – K assoc = association constant (also K a ); also called stability constant – The larger the K assoc, the more stable the complex K assoc have smaller ranges compared to K eq, probably because bonds are weak As with K eq, K assoc values have been determined in the lab and are included in thermodynamic databases of geochemical models 13

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 14

15 Complexation Example How much is Ca 2+ decreased by complexation with SO 4 2- ? 15

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 16

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 17

18 Acids and Bases 18

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., H 2 CO 3 HCO 3 - + H + – H 2 CO 3 donates a proton when it dissociates = Acid HCO 3 - + H + H 2 CO 3 – HCO 3 - accepts a proton = Base 19

20 Definitions Some species can act as both acid and base, depending on reaction HCO 3 - + H + H 2 CO 3 – HCO 3 - accepts a proton = Base HCO 3 - CO 3 2- + H + – HCO 3 - donates a proton = Acid 20

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 K a HCl H + + Cl - Sulfuric acid: H 2 SO 4 – acid rain (burning fossil fuels), AMD Nitric acid: HNO 3 – acid rain, nitrification (NH 4 + NO 3 - ) 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

22 Alkali Metals Alkaline Earths 22

23 Acid/Base Strength Weak acids/bases release only a small fraction of available H + /OH - – Acetic acid (CH 3 COOH), H 2 CO 3, H 3 PO 4, H 4 SiO 4 Small K a – Ammonium hydroxide (NH 4 OH), nickel hydroxide (Ni(OH) 2 ) In real world geochemistry, were 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

24 Important Acids in Groundwater Carbonic acid: H 2 CO 3 – CO 2 – Dominant source of H + in most groundwater Silicic acid: H 4 SiO 4 – mineral weathering Acetic acid: CH 3 COOH – natural and anthropogenic (landfills); organic acid Other organic acids (formic, oxalic) Phosphoric: H 3 PO 4 24

25 Dissociation of Silicic Acid H 4 SiO 4 H + + H 3 SiO 4 - – 1 st dissociation : – K a1 is small – At pH 7: H 3 SiO 4 - H + + H 2 SiO 4 2- – 2 nd dissociation: – K a2 is very small 25

26 Dissociation of Silicic Acid (cont.) H 2 SiO 4 2- H + + HSiO 4 3- – 3 rd dissociation: – miniscule HSiO 4 3- H + + SiO 4 4- – 4 th dissociation: < miniscule 26

27 Dissociation Reactions Dissociation reactions reach equilibrium very quickly – e.g. CH 3 COOH CH 3 COO - + H + – K a = 1.76 x 10 -5 at 25°C, 1 atm Very small number, most remains undissociated – Knowing K a and the initial concentration of CH 3 COOH, we can calculate how much dissociates 27

28 Example Assume 0.1 moles of acetic acid is dissolved in 1 L H 2 O, determine fraction (x) that dissociates… – Assume γ = 1 28

29 Dissociation of Water H 2 O H + + OH - (or H 2 O + H + H 3 O + ) – K w = [H + ] [OH - ] = 1 x 10 -14 at 25°C Remember that [H 2 O] = 1 Small dissociation constant, but nearly unlimited source of H + or OH - – For pure H 2 O at 25°C, [H + ] = [OH - ] = 10 -7 mol/L 29

30 Dissociation of Water H 2 O 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

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 31

32 Calculating pH of Acids and Bases What is the pH of 0.1 M acetic acid? – CH 3 COOH CH 3 COO - + 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

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 – H 2 S (aq) H + + HS - – HS - H + + S 2- – Note that 1 st reaction contributes much more H + (K 1 >> K 2 ) – Other examples: H 2 CO 3, H 2 SO 4, H 3 PO 4 33

34 Determining concentrations of species for polyprotic acids/bases Dissolve 0.1 moles of H 2 S in pure water at 25°C; what are the concentrations of all the aqueous species? – Again, well assume γ = 1 34

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 - : K eq = 10 -8.6 – Lets calculate the concentrations of species as a function of pH 35

36 Brucite solubility Plot activity of Mg species vs. pH to get an Activity Diagram – log [Mg(OH) + ] = 5.4 – pH – log [Mg 2+ ] = 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 – Mg 2+ dominates at pH < 11.4 (most geologic environments) 36

37 Dissociation and pH 37

38 Dissociation and pH Dissociation of weak acids/bases controlled by pH Rewrite mass action equations for H 2 S – H 2 S (aq) H + + HS - 38

39 Dissociation and pH – Can do same for HS - vs. S 2- – HS - H + + S 2- – 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

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

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


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