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Oxidation and Reduction Lecture 9

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Redox in Aqueous Solutions Redox reactions occur over a wide range of conditions: from groundwaters to magma. They are approached differently. We begin with aqueous solutions.

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Electrochemical Cells A simple redox reaction would be: o We want to know ∆G of the reaction. Measuring energy of it in electrochemical cell might be good approach. o However, such a cell can only measure exchange of electrons (e.g., between Zn and Cu) o We really want to know are energies for individual redox reactions such as:

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Hydrogen Scale Potential We assign a potential of 0 for the reaction: ½H 2(g) = H aq + + e - o in practice one side has Pt electrode in H 2 gas, the other acid with a H+ = 1. Then for the reaction The potential is assigned to Potentials measured in this way are called hydrogen scale potentials, written E H and have units of volts.

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Table 3.3 E H ˚ and pe˚ for half-cell reactions

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E H and ∆G Electrochemical energy is a form of free energy. E H is related to ∆G r by: ∆G r = -z F E H where F is the Faraday constant (96,485 coulombs) and converts volts to joules. and ∆G˚ = -z F E˚ o Values of E˚ available in compilations (e.g., Table 3.3) Since then This is known as the Nernst Equation.

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pe Consider again the reaction: The equilibrium constant expression for this reaction is ? In log form: We define pe as: So

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Standard State pe and Relation to E H Continuing with the reaction In an aqueous solution, the standard state activities are? Thereforepe˚ = log K More generally, o So for this reaction: pe is related to E H as:

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What pe is really telling us We have defined pe as the negative log of the activity of the electron. So a high pe means a low activity and concentration of electrons in our system. A low concentration of electrons implies an oxidized system; a high concentration (and low pe) implies a reduced system. Same is true of E H. So these are parameters that tell us about the redox state of our system (just as pH tells us about acidity).

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Speaking of pe and pH… A commonly used diagram to illustrate chemical variation in aqueous solutions is the pe- pH diagram (or E H -pH) Water only stable over limited range, so we start by setting boundaries. ½O 2(g) + 2e - + 2H + = H 2 O o In the standard state: pe = pH o The is a line with intercept of and slope of -1. Similarly: H + + e - = ½H 2(g) and pe = -pH

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pe-pH Diagrams To construct the diagrams 1.Write a reaction relating species of interest. 2.Redox reactions should contain e - 3.pH dependent reactions should contain H + 4.Write the equilibrium constant expression. 5.Get in log form, solve for pe with equation of the form pe = a + bpH 5.Find or calculate value of log K.

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Drawing stability boundaries Now consider: For equal activities of the two species, pe = log K o (horizontal line with intercept = K) Next Fe 3+ –Fe(OH) 2+: Fe 3+ + H 2 O = Fe(OH) 2+ + H + Use H + rather than OH - !

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Fe 2+ –Fe(OH) 2+ Our reaction is: Equilibrium constant expression is: In the form we want: We can write it as as the sum of two reactions, o we sum o to yield The log equilibrium constant of the net reaction is the sum of the equilibrium constants of the two.

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Line 5 has a slope of -1 and an intercept of log K. We can also use pe-pH diagrams to illustrate stability of solid phases in presence of solution. In this case, we must choose concentration.

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More about pe-pH diagrams pe-pH diagrams are a kind of stability or predominance diagram. They differ from phase diagrams because lines indicate not phase boundaries, but equal concentrations. o There is only 1 phase in this this diagram – an aqueous solution. Regions are regions of predominance. o The aqueous species continue to exist beyond their fields, but their concentrations drop off exponentially.

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Environmental Interpretation of pe-pH

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Redox in Magmas

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Oxygen Fugacity Igneous geochemists use oxygen fugacity ƒ O 2 to represent the redox state of the system. Hence, the oxidation of ferrous to ferric iron would be written as: 2FeO + O 2(g) = Fe 2 O 3 For example, oxidation of magnetite to hematite: 2Fe 3 O 4 + ½O 2(g) = 3Fe 2 O 3 (Actually, there isn’t much O 2 gas in magmas. Reaction more likely mediated by water and hydrogen).

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Redox in Magmatic Systems For magnetite-hematite 2Fe 3 O 4 + ½O 2(g) = 3Fe 2 O 3 assuming the two are pure solids At a temperature such as 1000K

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Oxygen Fugacity Buffers The log ƒ O 2 – T diagram is a phase diagram illustrating boundaries of phase stability. The two phases coexist only at the line. Reactions such as magnetite-hematite (or iron- wüstite or fayalite- magnetite-quartz) are buffers. For example, if we bleed O 2 into a magma containing magnetite, the ƒ O 2 cannot rise above the line until all magnetite is converted to hematite (assuming equilibrium!)

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