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ACTIVITY

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Activity Coefficients No direct way to measure the effect of a single ion in solution (charge balance) Mean Ion Activity Coefficients – determined for a salt (KCl, MgSO 4, etc.) ±KCl = [( K )( Cl )] 1/2 K sp = ±KCl 2 (mK + )(mCl - ) MacInnes Convention K = Cl = ±KCl –Measure other salts in KCl electrolyte and substitute ±KCl in for one ion to measure the other ion w.r.t. ±KCl and ±salt

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Mean Ion Activity Coefficients versus Ionic Strength

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Debye-Hückel Assumes ions interact coulombically, ion size does not vary with ionic strength, and ions of same sign do not interact A, B often presented as a constant, but: A=1.824928x10 6 0 1/2 ( T) -3/2, B=50.3 ( T) -1/2 Where is the dielectric constant of water and is the density

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Higher Ionic Strengths Activity coefficients decrease to minimal values around 1 - 10 m, then increase –the fraction of water molecules surrounding ions in hydration spheres becomes significant –Activity and dielectric constant of water decreases in a 5 M NaCl solution, ~1/2 of the H2O is complexed, decreasing the activity to 0.8 –Ion pairing increases, increasing the activity effects

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Adds a correction term to account for increase of i after certain ionic strength Truesdell-Jones (proposed by Huckel in 1925) is similar: Extended Debye-Hückel

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Davies Equation Lacks ion size parameter –only really accurate for monovalent ions Often used for Ocean waters, working range up to 0.7 M (avg ocean water I)

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Specific Ion Interaction theory Ion and electrolyte-specific approach for activity coefficients Where z is charge, i, m(j) is the molality of major electrolyte ion j (of opposite charge to i). Interaction parameters, (i,j,I) describes interaction of ion and electrolyte ion Limited data for these interactions and assumes there is no interaction with neutral species

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Pitzer Model At ionic strengths above 2-3.5, get +/+, -/- and ternary complexes Terms above describe binary term, f y describes interaction between same or opposite sign, terms to do this are called binary virial coefficients Ternary terms and virial coefficients refine this for the activity coefficient

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Setchenow Equation log i =K i I For molecular species (uncharged) such as dissolved gases, weak acids, and organic species K i is determined for a number of important molecules, generally they are low, below 0.2 activity coefficients are higher, meaning mi values must decline if a reaction is at equilibrium “salting out” effect

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Half Reactions Often split redox reactions in two: –oxidation half rxn e- leaves left, goes right Fe 2+ Fe 3+ + e- –Reduction half rxn e- leaves left, goes right O 2 + 4 e - 2 H 2 O SUM of the half reactions yields the total redox reaction 4 Fe 2+ 4 Fe 3+ + 4 e- O 2 + 4 e - 2 H 2 O 4 Fe 2+ + O 2 4 Fe 3+ + 2 H 2 O

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ELECTRON ACTIVITY Although no free electrons exist in solution, it is useful to define a quantity called the electron activity: The pe indicates the tendency of a solution to donate or accept a proton. If pe is low, there is a strong tendency for the solution to donate protons - the solution is reducing. If pe is high, there is a strong tendency for the solution to accept protons - the solution is oxidizing.

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THE pe OF A HALF REACTION - I Consider the half reaction MnO 2 (s) + 4H + + 2e - Mn 2+ + 2H 2 O(l) The equilibrium constant is Solving for the electron activity

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DEFINITION OF Eh Eh - the potential of a solution relative to the SHE. Both pe and Eh measure essentially the same thing. They may be converted via the relationship: Where = 96.42 kJ volt -1 eq -1 (Faraday’s constant). At 25°C, this becomes or

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Free Energy and Electropotential Talked about electropotential (aka emf, Eh) driving force for e - transfer How does this relate to driving force for any reaction defined by G r ?? G r = - n E –Where n is the # of e-’s in the rxn, is Faraday’s constant (23.06 cal V -1 ), and E is electropotential (V) pe for an electron transfer between a redox couple analagous to pK between conjugate acid- base pair

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Nernst Equation Consider the half reaction: NO 3 - + 10H + + 8e - NH 4 + + 3H 2 O(l) We can calculate the Eh if the activities of H +, NO 3 -, and NH 4 + are known. The general Nernst equation is The Nernst equation for this reaction at 25°C is

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Let’s assume that the concentrations of NO 3 - and NH 4 + have been measured to be 10 -5 M and 3 10 -7 M, respectively, and pH = 5. What are the Eh and pe of this water? First, we must make use of the relationship For the reaction of interest r G° = 3(-237.1) + (-79.4) - (-110.8) = -679.9 kJ mol -1

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O2/H2O C 2 HO

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UPPER STABILITY LIMIT OF WATER (Eh-pH) To determine the upper limit on an Eh-pH diagram, we start with the same reaction 1/2O 2 (g) + 2e - + 2H + H 2 O but now we employ the Nernst eq.

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As for the pe-pH diagram, we assume that p O 2 = 1 atm. This results in This yields a line with slope of -0.0592.

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LOWER STABILITY LIMIT OF WATER (Eh-pH) Starting with H + + e - 1/2H 2 (g) we write the Nernst equation We set p H 2 = 1 atm. Also, G r ° = 0, so E 0 = 0. Thus, we have

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Construction of these diagrams For selected reactions: Fe 2+ + 2 H 2 O FeOOH + e - + 3 H + How would we describe this reaction on a 2-D diagram? What would we need to define or assume?

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How about: Fe 3+ + 2 H 2 O FeOOH (ferrihydrite) + 3 H + K sp =[H + ] 3 /[Fe 3+ ] log K=3 pH – log[Fe 3+ ] How would one put this on an Eh-pH diagram, could it go into any other type of diagram (what other factors affect this equilibrium description???)

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INCONGRUENT DISSOLUTION Aluminosilicate minerals usually dissolve incongruently, e.g., 2KAlSi 3 O 8 + 2H + + 9H 2 O Al 2 Si 2 O 5 (OH) 4 + 2K + + 4H 4 SiO 4 0 As a result of these factors, relations among solutions and aluminosilicate minerals are often depicted graphically on a type of mineral stability diagram called an activity diagram.

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ACTIVITY DIAGRAMS: THE K 2 O-Al 2 O 3 -SiO 2 -H 2 O SYSTEM We will now calculate an activity diagram for the following phases: gibbsite {Al(OH) 3 }, kaolinite {Al 2 Si 2 O 5 (OH) 4 }, pyrophyllite {Al 2 Si 4 O 10 (OH) 2 }, muscovite {KAl 3 Si 3 O 10 (OH) 2 }, and K-feldspar {KAlSi 3 O 8 }. The axes will be a K + /a H + vs. a H 4 SiO 4 0. The diagram is divided up into fields where only one of the above phases is stable, separated by straight line boundaries.

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Activity diagram showing the stability relationships among some minerals in the system K 2 O-Al 2 O 3 -SiO 2 -H 2 O at 25°C. The dashed lines represent saturation with respect to quartz and amorphous silica.

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Seeing this, what are the reactions these lines represent?

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