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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, MgSO4, etc.) g±KCl = [(gK)(gCl)]1/2 Ksp= g±KCl2(mK+)(mCl-) • MacInnes Convention gK = gCl= g±KCl • Measure other salts in KCl electrolyte and substitute g±KCl in for one ion to measure the other ion w.r.t. g±KCl and g±salt**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=1.824928x106r01/2(T)-3/2, B=50.3 (T)-1/2 Where is the dielectric constant of water and r is the density**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**Extended Debye-Hückel**• Adds a correction term to account for increase of gi after certain ionic strength • Truesdell-Jones (proposed by Huckel in 1925) is similar:**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)**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**Pitzer Model**• At ionic strengths above 2-3.5, get +/+, -/- and ternary complexes • Terms above describe binary term, fy 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**Setchenow Equation**log gi=KiI • For molecular species (uncharged) such as dissolved gases, weak acids, and organic species • Ki 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**Half Reactions**• Often split redox reactions in two: • oxidation half rxn e- leaves left, goes right • Fe2+ Fe3+ + e- • Reduction half rxn e- leaves left, goes right • O2 + 4 e- 2 H2O • SUM of the half reactions yields the total redox reaction 4 Fe2+ 4 Fe3+ + 4 e- O2 + 4 e- 2 H2O 4 Fe2+ + O2 4 Fe3+ + 2 H2O**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.**THE pe OF A HALF REACTION - I**Consider the half reaction MnO2(s) + 4H+ + 2e- Mn2+ + 2H2O(l) The equilibrium constant is Solving for the electron activity**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**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 DGr ?? DGr = - nE • 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**Nernst Equation**Consider the half reaction: NO3- + 10H+ + 8e- NH4+ + 3H2O(l) We can calculate the Eh if the activities of H+, NO3-, and NH4+ are known. The general Nernst equation is The Nernst equation for this reaction at 25°C is**Let’s assume that the concentrations of NO3- and NH4+ have**been measured to be 10-5 M and 310-7 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 rG° = 3(-237.1) + (-79.4) - (-110.8) = -679.9 kJ mol-1**O2/H2O**C2HO**UPPER STABILITY LIMIT OF WATER (Eh-pH)**To determine the upper limit on an Eh-pH diagram, we start with the same reaction 1/2O2(g) + 2e- + 2H+ H2O but now we employ the Nernst eq.**As for the pe-pH diagram, we assume that pO2 = 1 atm. This**results in This yields a line with slope of -0.0592.**LOWER STABILITY LIMIT OF WATER (Eh-pH)**Starting with H+ + e- 1/2H2(g) we write the Nernst equation We set pH2 = 1 atm. Also, Gr° = 0, so E0 = 0. Thus, we have**Construction of these diagrams**• For selected reactions: Fe2+ + 2 H2O FeOOH + e- + 3 H+ How would we describe this reaction on a 2-D diagram? What would we need to define or assume?**How about:**• Fe3+ + 2 H2O FeOOH(ferrihydrite) + 3 H+ Ksp=[H+]3/[Fe3+] log K=3 pH – log[Fe3+] 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???)**INCONGRUENT DISSOLUTION**• Aluminosilicate minerals usually dissolve incongruently, e.g., 2KAlSi3O8 + 2H+ + 9H2O Al2Si2O5(OH)4 + 2K+ + 4H4SiO40 • 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.**ACTIVITY DIAGRAMS: THE K2O-Al2O3-SiO2-H2O SYSTEM**We will now calculate an activity diagram for the following phases: gibbsite {Al(OH)3}, kaolinite {Al2Si2O5(OH)4}, pyrophyllite {Al2Si4O10(OH)2}, muscovite {KAl3Si3O10(OH)2}, and K-feldspar {KAlSi3O8}. The axes will be aK+/aH+ vs. aH4SiO40. The diagram is divided up into fields where only one of the above phases is stable, separated by straight line boundaries.**Activity diagram showing the stability relationships among**some minerals in the system K2O-Al2O3-SiO2-H2O at 25°C. The dashed lines represent saturation with respect to quartz and amorphous silica.