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Equilibrium and the Driving Forces for Electrochemical Processes

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Equilibrium and the Driving Forces for Electrochemical Processes Part I Electrochemical Thermodynamics and Potentials: Equilibrium and the Driving Forces for Electrochemical Processes Prof. Shannon Boettcher Department of Chemistry University of Oregon 1 Chemical Thermodynamics Consider a chemical reaction: , , aA + bB cC + dD ∆ = ∆ ∆ − What criteria do⇆ we use to determine if the reaction goes forward or • Gibbs free energy can be used to calculate the backwards? maximum reversible work that may be performed by system at a constant temperature and pressure. • Gibbs energy is minimized when a system reaches chemical equilibrium at constant pressure and temperature. 2 Chemical Thermodynamics If not at standard state, then: = ∆ + ln ap is the activity of product p ∆ ar is the activity of reactant r vi is the stoichiometric number of i = = 0 γi is the activity coefficient of i ∏ γ ∏ c is the concentration of i i 0 ∏ ci is the standard state concentration of i ∏ γ 0 • Activity coefficients are “fudge” factors that all for the use of ideal thermodynamic equations with non-ideal solutions. • For dilute solutions, γi goes to 1 3 Chemical Thermodynamics Consider that the Gibbs energy can be written as a sum of enthalpy and entropy terms: = irreversible heat maximum ∆reversible ∆total heat− ∆ released/gained by the work released/gained reaction by reaction 4 Electrochemical Thermodynamics Consider the following thought experiment Zn + 2AgCl Zn2+ + 2Ag + 2Cl- do chemical reaction in do electrochemical reaction in do electrochemical reaction in B C in second calorimeter A calorimeter: calorimeter:⇆ calorimeter, resistor - e- e Q Zn + 2AgCl → r Zn2+ + 2Ag + 2Cl- Zn Ag/AgCl Zn Ag/AgCl Zn2+ - Cl 2+ Zn Qc Cl- Qc = = -233 kJ/mol Qc = = -233 kJ/mol = lim = -43 kJ/mol ∆ ∆ all species at standard state, extent of reaction small = lim ∆ →∞ = -190 kJ/mol ∆ →∞ Qc + Qr = = -233 kJ/mol Example from Bard and Faulkner 5 ∆ Electrochemical Thermodynamics Gibbs energy change is the maximum reversible work the system can do. nF is the number of charges per mole of reaction, = Ecell is the voltage… charge × voltage = energy ∆ − = + ln 0 = + ln − = − ln 0 0 log ∆ ∆ = − Remember Q includes ALL species in the log balanced reaction, including ions, solids, 0 − etc. 2.302 = log 0 . … and at 298.15 K, = − log 6 0 0 0592 V − Electrochemical Thermodynamics – Consider a electrochemical O + ne R reaction: ⇌ activity of R = ln activity of O 0 − = ln 0 γ − = ln γ ln 0 γ − − γ 7 Electrochemical Thermodynamics = ln ln 0 γ − E0' − O + ne– R γ What happened⇌ to the = ln “electrons” in our Nernst equation? 0′ − the formal potential… this depends on the identity and concentration of all species present in solution 8 Nernst Equation and Reference Electrodes In this form we actually mean: ( . ) = ( . ) ln ′ 0 Which is (when the reference is the hydrogen electrode): − n+ + O + (n/2)H2 R + nH ⇌ = ln at standard state, = =1. / + + H H 2 − 2 2 Key point: anytime you write the Nernst equation for a “half” reaction you are in fact using a short hand to represent the full reaction including the reference electrode/reaction 9 Equilibrium and the Chemical Potential Gibbs energy is minimized when a system reaches chemical aA + bB cC + dD equilibrium at constant pressure and temperature. How does the Gibbs energy change with amount of a substance? ⇆ mixture or pure figs. from substance solution Mark Lonergan (amount in mol) (amount in mol) = = 10 Chemical potential = j is the species , , α is the phase (e.g. metal, electrolyte, ionomer, etc.) α these are held constant ⁄ ≠ = + ln α o α chemical potential increases with concentration… (arbitrary) standard activity term state reference although we call it a “potential” units are energy, J 11 Chemical Reactions and μ Q 12 Electrochemical potential When we quantify for a charged particle, it is useful to define a new quantity,⁄ , that partitions the “quantum mechanical” internal free energy̅ and the “classical” electrostatic energy fig. from Mark Lonergan φ =−⋅∫ Ed path in electrochemistry, electrochemical potential determines equilibrium (other sources of free energy could be included, e.g. gravitational, but these are not generally important) 13 Properties of the electrochemical potential 14 Other Potentials in Electrochemistry term symbol unit brief definition significance / example of use defines criteria for equilibrium; differences in drive the electrochemical J/mol partial molar Gibbs free energy of a given species j in phase transport, transfer, and reactivity of both charged andα uncharged potential species ̅ � α partial molar free energy of a given species j in phase neglecting differences in describe driving force for reactions between chemical potential J/mol electrostatic contributionsa uncharged speciesα and the direction of diffusive transport α electric work needed to move a test charge to a specific point in space defines direction of electron transport in metals; gradient gives electric potential φ V from a reference point (often at infinite distance) divided by the value of electric field; used to calculate electric potential energy the charge free-energy change divided by the electron charge associated with moving an electron (and any associated ions/solvent indicates oxidizing or reducing power of an electrode; related to electrode potential V movement/rearrangement) from a reference state (often a reference the Fermi level of electrons in electrode electrode) to the working electrode free-energy change divided by the electron charge associated with indicates oxidizing or reducing power of electrons involved in moving an electron (and any associated ions/solvent electrochemical redox equilibria; related to “Fermi level” of the solution potential V movement/rearrangement) from a reference state (often a reference electrons in solution and equivalent to the solution reduction electrode) into the bulk of a solution via a redox reaction potential generally, the difference between the applied electrode potential and F gives the heat released, above that required by overpotential V the electrode potential when in equilibrium with the target thermodynamics, per mole of electrons to drive an electrochemical reaction electrochemical � process at a given rate; F = 96485 C·mol-1 a that is, no ‘long-range’ electrostatic interactions due to uncompensated charge, as would be described by the Poisson equation in classical electrostatics. The electrostatic terms that describe electron-nucleus and electron-electron interactions and dictate Coulombic potentials in the Schrödinger equation are included. 15 What does a voltmeter measure? Voltage, but what is voltage? φ =−⋅ ∫ Ed ? Not in this case α β path If the resistor/wire is the same material, then: = = +α β = ∆̅ ̅ − ̅ α α β β − − −∆ 16 Changes in total free energy drive transport = -2-1 − ̅ flux (mol cm s ) gradient in electrochemical potential = + = + ln α α α α o α j The electrochemical potential̅ is usually the proper measure of free energy in electrochemical systems, though other terms might be added in special cases u is mobility i 17 Changes in total free energy drive transport In one dimension, the gradient of leads to the drift diffusion equation. ̅ ui is mobility 18 Consider the electrode potential • units of V • given by the difference in , per charge, in the working electrode, relative to in a second electrode • second electrode is usually ̅reversible electrochemical half reaction (i.e. a reference̅ electrode): ( ) (vs. ) = we re − ̅ − ̅ we re • and are each themselves defined relative to an arbitrary reference (that cancel in the difference). The cell voltage is usually written = we reor ( ) cell we − re cathode − anode 19 Summary of Key Points • Measurements of “potential differences” are necessarily of the total free-energy difference. Decomposing into differences in activity, electric potential, and other terms requires a model and assumptions. • Transport of any species is governed by the spatial gradient in the electrochemical potential. • At equilibrium, the electrochemical potential of any given species must be the same throughout the system • For any chemical reaction, the sum of the electrochemical potentials of the reactants must equal those of the products. Processes with very slow kinetics are typically ignored. • The use of the word ‘potential’ alone should be avoided; the type of should be clear. 20 Part II Electrochemical Thermodynamics and Potentials: Applications Prof. Shannon Boettcher Department of Chemistry University of Oregon 21 Review of Key Points • Measurements of “potential differences” are necessarily of the total free-energy difference. Decomposing into differences in activity, electric potential, and other terms requires a model and assumptions. • Transport of any species is governed by the spatial gradient in the electrochemical potential. • At equilibrium, the electrochemical potential of any given species must be the same throughout the system • For any chemical reaction, the sum of the electrochemical potentials of the reactants must equal those of the products. Processes with very slow kinetics are typically ignored. • The use of the word ‘potential’ alone should be avoided; the type of should be clear. 22 Equilibration at a metal/redox-electrolyte solution interface consider O + R ⇌ We define even though How do these equilibrate? = there are “practically”s no s s ̅ m s electrons in the solution ̅ − ̅ shows no surface charge̅ initially,
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