Oxidation and Reduction Lecture 9 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. Electrochemical Cells • A simple redox reaction would be: Feaq3+ + e- 2+ Feaq 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: Zns 2+ Znaq + 2e- Hydrogen Scale Potential • We assign a potential of 0 for the reaction: ½H2(g) = Haq+ + e- o in practice one side has Pt electrode in H2 gas, the other acid with aH+ = 1. • Then for the reaction Zn2+ aq + H 2(g) Zn s + 2H+ • The potential is assigned to 2+ Znaq + 2e- Zns • Potentials measured in this way are called hydrogen scale potentials, written EH and have units of volts. Table 3.3 EH˚ and pe˚ for half-cell reactions EH and ∆G • Electrochemical energy is a form of free energy. EH is related to ∆Gr by: ∆Gr = -zFEH • where F is the Faraday constant (96,485 coulombs) and converts volts to joules. • and ∆G˚ = -zFE˚ o Values of E˚ available in compilations (e.g., Table 3.3) • Since ∆ G = ∆ G˚+RT ln Õ aini • then • This is known as the Nernst Equation. pe • Consider again the reaction: Feaq3+ + e- 2+ Feaq • The equilibrium constant expression for this reaction is aq aFe ? K = aq 2+ aFe3+ ae- • In log form: logK = logaFe2+ - logaFe3+ - logae- • We define pe as: • So pe = - log ae- log K = log aFe2+ aFe3+ + pe Standard State pe and Relation to EH • Continuing with the reaction log K = log aFe2+ aFe3+ Feaq3+ + e- 2+ Feaq + pe • In an aqueous solution, the standard state activities are? • Therefore pe˚ = log K 1 • More generally, pe˚= log K z o So for this reaction: pe = pe˚- log • pe is related to EH as: pe = aFe2+ aFe3+ FEH 5039EH = 2.303RT T 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 EH. • So these are parameters that tell us about the redox state of our system (just as pH tells us about acidity). Speaking of pe and pH… • • A commonly used diagram to illustrate chemical variation in aqueous solutions is the pepH diagram (or EH-pH) Water only stable over limited range, so we start by setting boundaries. ½O2(g) + 2e- + 2H+ = H2O 1 log K = log aH 2O - log PO2 + 2 pe + 2 pH = 41.56 2 o o • • In the standard state: pe = 20.78-pH The is a line with intercept of 20.78 and slope of -1. Similarly: H+ + e- = ½H2(g) and pe = -pH pe-pH Diagrams • To construct the diagrams 1. Write a reaction relating species of interest. 2. Redox reactions should contain e3. 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. Drawing stability boundaries • Now consider: Feaq3+ + elog K = log 2+ Feaq aFe2+ aFe3+ + pe • For equal activities of the two species, • pe = log K o (horizontal line with intercept = K) • Next Fe3+–Fe(OH)2+: • Fe3+ + H2O = Fe(OH)2+ + H+ log K = log aFe(OH )2+ aFe3+ - pH Use H+ rather than OH-! 2+ 2+ Fe –Fe(OH) Fe(OH )aq + e + H • Our reaction is: • Equilibrium constant expression is: 2+ log K = log • In the form we want: aFe2+ aFe(OH )2+ - + 2+ Feaq + H 2O - pe - pH pe = log K - pH • We can write it as as the sum of two reactions, o we sum Feaq3+ + e+ Fe(OH )2+ aq + H o to yield + Fe(OH)2+ aq + e + H 2+ Feaq Feaq3+ + H 2O 2+ Feaq + H 2O • The log equilibrium constant of the net reaction is the sum of the equilibrium constants of the two. 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. 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. Environmental Interpretation of pe-pH Redox in Magmas Oxygen Fugacity • Igneous geochemists use oxygen fugacity ƒO2 to represent the redox state of the system. Hence, the oxidation of ferrous to ferric iron would be written as: 2FeO + O2(g) = Fe2O3 • For example, oxidation of magnetite to hematite: 2Fe3O4+ ½O2(g) = 3Fe2O3 • (Actually, there isn’t much O2 gas in magmas. Reaction more likely mediated by water and hydrogen). Redox in Magmatic Systems • For magnetite-hematite • 2Fe3O4+ ½O2(g) = 3Fe2O3 • assuming the two are pure solids K MH = 1 ƒ1/2 O 2 K=e -∆ G of /RT • At a temperature such as 1000K æ 6∆ G of ( Fe O ,1000 ) - 4∆ G of ( Fe O ,1000 ) ö 2 3 3 4 - log K = log ƒO2 = ç ÷ 2.303RT è ø Oxygen Fugacity Buffers • The log ƒO2 – 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 ironwüstite or fayalitemagnetite-quartz) are buffers. • For example, if we bleed O2 into a magma containing magnetite, the ƒO2 cannot rise above the line until all magnetite is converted to hematite (assuming equilibrium!)