jj 0 jj Physical and Interfacial Electrochemistry 2013 Lecture 4. Electrochemical Thermodynamics Module JS CH3304 MolecularThermodynamics and Kinetics Thermodynamics of electrochemical systems Thermodynamics, the science of possibilities is of general utility. The well established methods of thermodynamics may be readily applied to electrochemical cells. We can readily compute thermodynamic state functions such as G, H and S for a chemical reaction by determining how the open circuit cell potential Ecell varies with solution temperature. We can compute the thermodynamic efficiency of a fuel cell provided that G and H for the cell reaction can be evaluated. M Ox,Red Red',Ox' M ' We can also use measurements of equilibrium cell potentials to - + determine the concentration of Anode a redox active substance present Cathode Oxidation Reduction at the electrode/solution interface. e- loss This is the basis for potentiometric e- gain chemical sensing. LHS RHS 1 Standard Electrode Potentials Standard reduction potential (E0) is the voltage associated with a reduction reaction at an electrode when all solutes are 1 M and all gases are at 1 atm. Reduction Reaction - + 2e + 2H (1 M) 2H2 (1 atm) E0 = 0 V Standard hydrogen electrode (SHE) Measurement of standard redox potential E0 for the redox couple A(aq)/B(aq). electron flow Ee reference indicator H2 in electrode Pt electrode SHE P t A(aq) H2(g) H+(aq) B(aq) test redox couple salt bridge E0 provides a quantitative measure for the thermodynamic tendency of a redox couple to undergo reduction or oxidation. 2 Standard electrode potential • E0 is for the reaction as written •The more positive E0 the greater the tendency for the substance to be reduced • The half-cell reactions are reversible •The sign of E0 changes when the reaction is reversed • Changing the stoichiometric coefficients of a half-cell reaction does not change the value of E0 19.3 We should recall from our CH1101 The procedure is simple to apply. One determines electrochemistry lectures that the couple with the most positive standard any combination of two redox couples may reduction potential (or the most positive be used to fabricate a galvanic cell . This equilibrium potential Ee determined via the Nernst facility can then be used to obtain useful equation if the concentrations of the reactants -3 thermodynamic information about a cell differ from 1 mol dm ) . This couple will undergo reaction which would be otherwise difficult reduction at the cathode . The other redox couple to obtain. Herein lies the usefulness of will consequently undergo oxidation at the anode . electrochemical thermodynamics. This information can also be used to determine the direction of electron flow, for upon placing a Given any two redox couples A/B and P/Q load on the cell electrons will flow out of the we can readily use tables of standard anode because of the occurrence of a spontaneous reduction potentials to determine which of de-electronation (otherwise known as oxidation or the two couples is preferentially reduced. electron loss) reaction , through the external Once this is known the galvanic cell can be circuit and into the cathode causing a spontaneous constructed, the net cell potential can be electronation (aka reduction or electron gain) evaluated, and knowing this useful reaction to occur. Hence in a driven cell the anode thermodynamic information can be obtained will be the negative pole of the cell and the for the cell reaction. cathode the positive pole. Now according to the IUPAC convention if the cell reaction is spontaneous the resultant cell potential will be positive. We ensure that such is the case by writing the cathode reaction on the rhs , and the anode reaction on the lhs of the cell diagram . Then since Ee,rhs is more positive than Ee,lhs a positive cell potential Ve will be guaranteed 3 0 0 0 0 0 A P B Q Ecell ERHS ELHS Ecathode Eanode electron flow Ve Anode + - Oxidation Cathode M Reduction M P(aq) A(aq) Q(aq) B(aq) Ee,anode Ee,cathode A ne B Cathode salt bridge mA nP mB nQ mn PQmeAnode aaBQ QR mn redox couple aaAP E E(T ) G,H,S, • When a spontaneous reaction takes place in a Galvanic cell, electrons are deposited in one electrode (the site of oxidation or anode) and collected from another (the site of reduction or cathode), and so there is a net flow of current which can be used to do electrical work We. • From thermodynamics we note that Ecell maximum electrical work done at constant temperature and pressure We is equal to the change in Gibbs free energy G for the net cell reaction. • We use basic physics to evaluate the electrical work We done in moving n mole Electrons through a potential difference of Ecell . W q E e E 1 electron : e cell cell 1 mole electrons : We N Ae Ecell We n N A e Ecell n mole electrons : Relation between thermodynamics G We ne N A Ecell of cell reaction and observed G We cell potential n F Ecell 4 A ne B E0 A, B 0 0 P me Q E P, Q We assume that E A,B is more positive than E0 and so is assigned as the cathode reaction. mA mne mB P,Q nP nme nQ We subtract the two reactions to obtain the following result. mA nP mB nQ mA nQ mB nP To proceed we subtract the corresponding thermodynamic state functions In this case G0 00 0 0 0 00 0 GmGnGmnFEmFEnmFEEcell A,, B P Q A , B P , Q A ,, B P Q nmFE cell Note that nm denotes the number of electrons transferred per mole of reaction as written. mA nP mB nQ A ne B Cathode aamn Net Cell Reaction BQ QR mn P Q me Anode aaAP The establishment of equilibrium does not imply the cessation of redox activity at the interface . The condition of equilibrium implies an equality in the electrochemical potentials of the transferring species in the two phases and in the establishment of a compensating two way flow of charge across the interface resulting in a definite equilibrium potential difference e or Ee . A single equilibrium potential difference may not be measured. Instead a potential is measured between two electrodes (a test or indicator electrode and a reference electrode). This is a potentiometric measurement. The potential of the indicator electrode is related to the activities of one or more of the components of the test solution and it therefore determines the overall equilibrium cell potential Ee . Under ideal circumstances, the response of the indicator electrode to changes in analyte species activity at the indicator electrode/solution interface should be rapid, reversible and governed by the Nernst equation. The ET reaction involving the analyte species should be kinetically facile and the ratio of the analyte/product concentration should depend on the interfacial potential difference via the Nernst equation. 5 The potentiometric measurement. Potential reading Device (DVM) In a potentiometric measurement two electrodes are used. These consist of the indicator or sensing electrode, and a reference electrode. A Electroanalytical measurements relating potential to analyte B concentration rely on the response of one electrode only (the indicator electrode). Reference Indicator The other electrode, the reference electrode electrode electrode is independent of the Solution containing solution composition and provides analyte species A stable constant potential. The open circuit cell potential is measured using a potential measuring device such as a potentiometer, a high impedance voltameter or an electrometer. Equilibrium condition between phases: chemical potential. It is well known from basic chemical thermodynamics that if two phases and with a common uncharged species j, are brought together, then the tendency of species j to pass from phase to phase will be determined by the difference in the chemical Potential between the two phases. The condition for equilibrium is Phase Phase 0 ~ jj j j jj The standard thermodynamic definition of the chemical j potential is: G j n j nPTk ,, Alternatively we can view the chemical potential of a species j in a phase as a measure of the work that must be done for the reversible transfer of one mole of uncharged species j from the gaseous state of unit fugacity (the reference state) into the bulk of phase . In electrochemistry we deal with charged species and charged phases . 6 Electrochemical Activity We consider the work done W in transferring i i a a a species i from the interior of a standard i i i phase to the interior of the phase of interest. We also assume that the species i has a charge qi = zie. If two phases and contain a species i with different electrochemical i activities such that the Wi electrochemical activity of species i in phase is i 0 greater than that of phase then there is a tendency for species i to leave phase Standard Phase Destination Phase and enter phase . The driving force for the The electrochemical activity can be defined in the transport of species i is the following manner. difference in electrochemical activity qzFW iii00 between the two phases. aaiiexp a i exp exp kTBB RT kT In the latter expression ai represents the activity of species i. Hence the difference in electrochemical Now from the definition of electrochemical potential is split up into two distinct activity zF components. First, the difference in chemical aaexp i 0 ii potential i and second the difference in RT electrical potential . zF i 0 aaii exp Hence we note that the electrochemical RT potential is defined as the work required to Hence transfer 1 mole of charged species from infinity in vacuum into a material phase.