George Mason University General Chemistry 212 Chapter 21 Electrochemistry Acknowledgements Course Text: Chemistry: the Molecular Nature of Matter and Change, 7th edition, 2011, McGraw-Hill Martin S. Silberberg & Patricia Amateis The Chemistry 211/212 General Chemistry courses taught at George Mason are intended for those students enrolled in a science /engineering oriented curricula, with particular emphasis on chemistry, biochemistry, and biology The material on these slides is taken primarily from the course text but the instructor has modified, condensed, or otherwise reorganized selected material. Additional material from other sources may also be included. Interpretation of course material to clarify concepts and solutions to problems is the sole responsibility of this instructor. 2/18/2015 1 Electrochemistry Redox Reactions and Electrochemical Cells Review of Oxidation Reduction Concepts Half-Reaction Method for Balancing Redox Reactions Electrochemical Cells Voltaic Cell: Using Spontaneous Reactions to Generate Electrical Energy Construction and Operation Cell Notation Why Does the Cell Work 2/18/2015 2 Electrochemistry Cell Potential: Output of a Voltaic Cell Standard Cell Potentials Strengths of Oxidizing and Reducing Agents Free Energy and Electrical Work Standard Cell Potential Effect of Concentration of Ecell Changes in Ecell During Cell Operation Concentration Cells Electrochemical Processes in Batteries Primary (Nonrechargeable Batteries) Fuel Cells 2/18/2015 3 Electrochemistry Corrosion: A case of Environmental Electrochemistry Corrosion of Iron Protecting Against Corrosion Electrolytic Cells: Using electrical energy to drive Nonspontaneous Reactions Construction and Operation Predicting Electrolysis Products Stoichiometry of Electrolytes 2/18/2015 4 Electrochemistry Electrochemistry The study of the relationship between chemical change (reactions) and the flow of electrons (electrical work) Electrochemical Systems Electrolytic – Work done by absorbing free energy from a source (passage of an electrical current through a solution) to drive a nonspontaneous reaction Voltaic/Galvanic – Release of free energy from a spontaneous reaction to produce electricity (Batteries) 2/18/2015 5 Electrochemistry Oxidation-Reduction Concepts Review Oxidation – Loss of Electrons Reduction – Gain of Electrons Oxidizing Agent – Species that causes another species to be oxidized (lose electrons) Oxidizing agent is reduced (gains e-) Reducing Agent – Species that cause another species to be reduced (gain electrons) Reducing agent is oxidized (loses e-) 2/18/2015 Oxidation (e- loss) always accompanies Reduction (e- gain) Total number of electrons gained by the atoms/ions of the oxidizing agent always equals the total number of electrons lost by the reducing agent 6 Electrochemistry 2/18/2015 7 Electrochemistry Oxidation Number A number equal to the magnitude of the charge an atom would have if its shared electrons were held completely by the atom that attracts them more strongly The oxidation number in a binary ionic compound equals the ionic charge The oxidation number for each element in a covalent compound (or polyatomic ion) are assigned according to the relative attraction of an atom for electrons See next slide for a summary of the rules for assigning oxidation numbers 2/18/2015 8 Electrochemistry Rules for Assigning an oxidation Number (O.N.) 2/18/2015 9 Electrochemistry Balancing Redox Reactions Oxidation Number Method Half-Reaction Method The balancing process must insure that: The number of electrons lost by the reducing agent equals the number of electrons gained by the oxidizing agent 2/18/2015 10 Electrochemistry Oxidation Number Method Assign oxidation numbers to all elements in the reaction From changes in oxidation number of given elements, identify oxidized and reduced species For each element that undergoes a change of oxidation number, compute the number of electrons lost in the oxidation and gained in the reduction from the oxidation number change (Draw tie-lines between these atoms) Multiply one or both these number by appropriate factors to make the electrons lost equal to the electrons gained Use factors as coefficients in reaction equation 2/18/2015 11 Practice Problem Balance equation with Oxidation Number method: Cu(s) + HNO3 (aq) Cu(NO3 )2 + NO2 (g) + H 2O(l) 0 +5 +1 -2 +5 +2 -2 -2 +4 +1 -2 Cu(s) + HNO3 (aq) Cu(NO3 )2 + NO2 (g) + H 2O(l) Loses 2e- Cu(s) + HNO3 (aq) Cu(NO3 )2 + NO2 (g) + H 2O(l) Gains 1e- Balance the Equation Accounts for the two electrons needed to balance the 2 electrons from the Copper oxidation Cu(s) + 2HNO3 (aq) Cu(NO3 )2 + 2NO2 (g) + H 2O(l) Cu(s) + 4HNO3 (aq) Cu(NO3 )2 + 2NO2 (g) + 2H 2O(l) 2/18/2015 12 Electrochemistry Half-Reaction Method Applicable to Acid or Base solutions Does not usually require Oxidation Numbers (ON) Procedure Divide the overall reaction into: Oxidation Half-Reaction Reduction Half-Reaction Balance each half-reaction for atoms & charge Multiply one or both reactions by some integer to make electrons gained equal to electrons lost Recombine to given balanced redox equation 2/18/2015 13 Electrochemistry Redox Half-Reaction Method – Example 26 Cr2 O7 (aq) + I- (aq) Cr 3 (aq) + I 2 (s) Divide steps into Half-Reactions 6 2 2Cr2 O7 Cr 3 (Cr gains e- - reduction) I - I 2 (Iodine loses e- - oxidation) 2/18/2015 14 Electrochemistry Balance Atoms & Charges for Cr2O72- / Cr3+ Cr O 2 6 Cr2 O7 6 2 14H 6e -6 + 2Cr 3+ 2- 7 + Add 7 Water molecules to balance Oxygen 2Cr 3+ + 7H 2O 2Cr26 O7 + 14H+ + + (+12 (+14) + 2Cr Cr26 O7 2- 3+ Add 14 H+ ions on left to balance 14 H on right + 7H 2O 2Cr 3+ + 7H 2O -14) = +6 Add 6 electrons (e-) on left to balance reaction charges (6 electrons gained this is the reduction reaction Balance Atoms & Charges for I- / I2 2I - I 2 2I 2/18/2015 - I 2 + 2e No need to add H2O or H+ - Add 2 electrons (e-) on right to balance reaction charges 15 Electrochemistry Redox Half-Reaction Method – Example (con’t) Multiply each half-reaction, if necessary, by an integer to balance electrons lost/gained 2 e- lost in oxidation reaction and 6 e- gained in reduction Multiply oxidation half-reaction by 3 3(2I- ) 3I 2 + 3(2e- ) 6I- 3I 2 + 6e Add 2 half-reactions together 6e - + 14H+ + Cr2O7 2- 2Cr 3+ + 7H 2O 6I - 6I 2/18/2015 + 14H+ + Cr2O7 2- 3I 2 + 6e3I 2 + 2Cr 3+ + 7H 2O 16 Electrochemistry Half-Reaction Method in a “Basic” solution Sodium Permanganate & Sodium Oxalate Mn 7 O42 NaMnO4 - (aq) + 3 2 2C2 O 4 Na2C2O4 Mn 4 O2 2 (s) 4 + C O3 2- (aq) Half-Reactions C2O42- MnO4- MnO2 CO32- MnO4- MnO2 + 2H2O 2 H 2O + C2O42- 2CO32- 4H+ + MnO4- MnO2 + 2H2O 2 H2O + C2O42- 2CO32- + 4H+ 3e- + 4H + + MnO 4- MnO 2 + 2H 2O 2 H 2O + C2O 4 2- 2CO 3 2- + 4H + + 2e - (reduction) (oxidation) Multiply each reaction by appropriate integer 6e- + 8H+ + 2MnO4- 2MnO2 + 4H 2O 2/18/2015 6H2O + 3 C2O42- 6CO32- + 12H + + 6e17 Electrochemistry Sodium Permanganate & Sodium Oxalate (con’t) Add reactions 6e- + 8H+ + 2MnO4- 2MnO2 + 4H 2O 6H2O + 3 C2O42- 6CO32- + 12H + + 6e2MnO4- + 2H2O + 3 C2O42- 2MnO2 + 6CO32- + 4H+ Add OH- to neutralize H+ , balance H2O, and form “basic” solution 2MnO4- + 2H2O + 3 C2O42- + 4OH- 2MnO2 + 6CO32- + 4H+ + 4OH2MnO4- + 2H2O + 3 C2O42- + 4OH- 2MnO2 + 6CO32- + 4H2O 2MnO4- + 3 C2O42- + 4OH- 2MnO2 + 6CO32- + 2H2O 2/18/2015 18 Electrochemistry Electrochemical Cells 2/18/2015 Voltaic (Galvanic) Cells Use spontaneous reaction (G < 0) to generate electrical energy Difference in Chemical Potential energy between higher energy reactants and lower energy products is converted to electrical energy to power electrical devices Thermodynamically - The system does work on the surroundings 19 Electrochemistry Electrochemical Cells 2/18/2015 Electrolytic Cells Uses electrical energy to drive nonspontaneous reaction (G > 0) Electrical energy from an external power supply converts lower energy reactants to higher energy products Thermodynamically – The surroundings do work on the system Examples – Electroplating and recovering metals from ores 20 Electrochemistry 2/18/2015 21 Electrochemistry Electrochemical Cells Cell notation is used to describe the structure of a voltaic (galvanic) cell For the Zn/Cu cell, the cell notation is: Zn(s) Zn2+(aq) Cu2+(aq) Cu(s) = phase boundary (solid Zn vs. Aqueous Zn2+) = salt bridge Anode reaction (oxidation) is left of the salt bridge Cathode reaction (reduction) is right of the salt bridge Half-cell components usually appear in the same order as in the half-reactions (Zn(s) + 2e- Zn2+). Zinc solid loses 2 e- (oxidized) to produce zinc(II) at the negative ANODE Copper(II) gains 2e- (reduced) to form copper metal at 22 positive CATHODE 2/18/2015 Electrochemistry Voltaic (Galvanic) Cells Zinc metal (Zn) in solution of Cu++ ions Cu 2+ (aq) + 2e- Cu(s) [reduction] Zn(s) Zn 2+ (aq) + 2e- [oxidation] Zn(s) + Cu 2+ (aq) Zn 2+ + Cu(s) Construction of a Voltaic Cell The oxidizing agent (Zn) and reducing agent (Cu2+) in the same beaker will not generate electrical energy Separate the half-reactions by a barrier and connect them via an external circuit (wire) Set up salt bridge between chambers to maintain neutral charge in electrolyte solutions 2/18/2015 23 Electrochemistry 2/18/2015 Oxidation Half-Cell Anode Compartment – Oxidation of Zinc (An Ox) Zinc metal in solution of Zn2+ electrolyte (ZnSO4) Zn is reactant in oxidation half-reaction Conducts released electrons (e-) out of its half-cell Reduction Half-Cell Cathode Compartment – Reduction of Copper (Red Cat) Copper bar in solution of Cu2+ electrolyte (CuSO4) Copper metal is product in reduction half-cell reaction Conducts electrons into its half-cell 24 Electrochemistry Zinc-Copper Voltaic Cell 2/18/2015 25 Electrochemistry Relative Charges on the Anode/Cathode electrodes Electrode charges are determined by the source of the electrons and the direction of electron flow Zinc atoms are oxidized (lose 2 e-) to form Zn2+ at the anode Anode – negative charge (e- rich) Released electrons flow to right toward cathode to be accepted by Cu2+ to form Cu(s) 2/18/2015 Cathode – positive charge (e- deficient) 26 Electrochemistry Purpose of Salt Bridge Electrons from oxidation of Zn leave neutral ZnSO4 solution producing net positive charge Incoming electrons to CuSO4 solution would produce net negative charge in solution as copper ions are reduced to copper metal Resulting charge imbalance would stop reaction Salt bridge provides “liquid wire” allowing ions to flow through both compartments completing circuit Salt bridge constructed of an inverted “U-tube” containing a solution of non-reacting Na+ & SO42- ions in a gel 2/18/2015 27 Electrochemistry Active vs Inactive Electrodes 2/18/2015 Active Electrodes Electrodes in Zn/Cu2+ cell are active Zinc & Copper bars are components of the cell reactions Mass of Zn bar decreases as Zn2+ ions in cell solution increase Mass of Copper bar increases as Cu2+ ions accept electron to form more copper metal 28 Electrochemistry Active vs Inactive Electrodes 2/18/2015 Inactive Electrodes In many Redox reactions, one or the other reactant/product is not capable of serving as an electrode Inactive electrodes - Graphite or Platinum Can conduct electrons into and out of halfcells Cannot take part in the half-reactions 29 Electrochemistry Voltaic Cell with Inactive Graphite Electrodes 2/18/2015 30 Practice Problem A mercury battery, used for hearing aids and electric watches, delivers a constant voltage (1.35 V) for long periods. The half reactions are given below. Which half reaction occurs at the Anode and which occurs at the Cathode? What is the overall cell reaction? HgO(s) + H2O(l) + 2e- Hg(l) + 2 OH-(aq) Zn(s) + 2 OH-(aq) Zn(OH)2(s) + 2eAns: Reduction occurs at Cathode (Red Cat) Hg2+ gains 2 e- (reduced) to form Hg Oxidation occurs at the Anode (An Ox) Zn loses 2 e- (oxidized) to form Zn2+ 2/18/2015 HgO(s) + Zn(s) + H 2O Zn(OH)2 + Hg(l) 31 Practice Problem Write the cell notation for a voltaic cell with the following cell reaction Ni(s) + Pb (aq) Ni (aq) + Pb(s) 2+ 2+ Ans: Pb 2+ (aq) + 2e- Pb(s) Ni(s) Ni 2+ + 2e- Reduction @ Cathode (Red Cat) Oxidation @ Anode (An Ox)) Ni(s) I Ni 2+ (aq) Anode (oxidation) is represented on left side of Cell notation 2/18/2015 Pb 2+ (aq) I Pb(s) Cathode (reduction) is represented on right side of cell notation 32 Practice Problem Write the cell reaction for the following voltaic cell Pt|H2(g) | H+(aq) ║ Br2(l) | Br-(aq)|Pt Note: Platinum (Pt) serves as a reaction site at the anode, but does not participate in the reaction Ans: Br2 (l) + 2e- 2Br - (aq) gain 2 e- Reduction @ Cathode (Red Cat) H2 (g) 2H+ (aq) + 2e- lose 2 e- Oxidation @ Anode (An Ox) PtIH2 (g) + Br2 (l) 2H + (aq) + 2Br - (aq)IPt 2/18/2015 33 Electrochemistry Cell Potential 2/18/2015 The movement of electrons is analogous to the pumping of water from one point to another Water moves from a point of high pressure to a point of lower pressure. Thus, a pressure difference is required The work expended in moving the water through a pipe depends on the volume of water and the pressure difference 34 Electrochemistry Cell Potential Movement of Electrons An electric charge moves from a point of high electrical potential (high electrical pressure) to one of lower electrical potential The work expended in moving the electrical charge through a conductor depends on the potential difference and the amount of charge Work(w) = Potential difference (E) Charge w = Ecell Charge 2/18/2015 35 Electrochemistry Cell Potential Purpose of a voltaic cell is to convert the free energy of a spontaneous reaction into the kinetic energy of electrons moving through an external circuit (electrical energy) Electrical energy is proportional to the difference in the electrical potential between the two cell electrodes Cell Potential 2/18/2015 36 Electrochemistry Cell Potential Positive Cell Potential – Electrons flow spontaneously from the negative electrode (Anode) to the positive electrode (Cathode) Ecell > 0 for a spontaneous process Negative cell potential is associated with a “nonspontaneous” cell reaction Ecell < 0 for a nonspontaneous process Cell potential for a cell reaction at equilibrium would be “0” Ecell = 0 for an equilibrium process 2/18/2015 As with Entropy, there is a clear relationship between Ecell , K, and G 37 Electrochemistry Units of Cell Potential The SI (metric) unit of electrical charge is the: Coulomb (C) The SI (metric) unit of current is the: Ampere (A) 1 coulomb 1 ampere = second 1A = 1 C / s The SI (metric) unit of electrical potential is the: “Volt (V)” By definition, the energy released by a potential difference of one volt moving between the anode and cathode of a voltaic cell releases 1 joule of work per coulomb of charge 1 volt = 2/18/2015 1J C 1C = 1J V 38 Electrochemistry The charge (F) that flows through a cell equals the number of moles of electrons (n) transferred times the charge of 1 mol of electrons charge Charge = moles of e mol e- Moles e- = n Charge Mol e - 96, 485 C = F = Faraday Constant = mol e - Charge = nF F = 96, 485 C mol e- F = 96, 485 × 2/18/2015 J C - Coulomb , SI unit of charge V J J 4 = 9.6×10 × V • mol eV • mol e 39 Electrochemistry The total amount of a substance undergoing a ReDox reaction in a cell depends on the total charge flowing through the cell, which is a function of the current (amperes) and the time (seconds) The ratio of the total charge and the charge per mole of electrons determines the number moles of substance that will react Thus, Moles of substance = Charge (C) moles e- (n) Charge / moles e - (F) Moles of substance = Current (i) × Time (t) = n×F Moles of substance = 2/18/2015 i ×t n×F amperes seconds moles e96, 485 Coulombs × moles substance mole e- n = total moles electrons 40 Electrochemistry How long in seconds would it take to deposit 38.93 g of Pb from an aqueous solution of Pb2+ with a current of 1.679 A? Moles = Time = Time = it nF = Current (Amperes) × Time (seconds) (moles e- ) × (Faradays (Coulombs / mole e - )) Moles mole e- Faradays Current 1 mol Pb 2 mol e 39.93 g Pb 207.2 g mol Pb 96, 485 C - mol e 1.679 A Time = 2.215 × 104 sec 2/18/2015 41 Electrochemistry Standard Cell Potential Eocell – The potential measured at a specific temperature (298 K) with no current flowing and all concentrations in their “Standard States” 1 atm for gases 1 M for solutions Pure solids for electrodes Zn(s) + Cu2+ (aq; 1M) Zn2+ (aq; 1M) + Cu(s) 2/18/2015 Eocell = 1.10V 42 Electrochemistry Standard Electrode Half-Cell Potentials o E half-cell – Potential associated with a given half-cell reaction (electrode compartment) when all components are in “Standard States” Standard Electrode Potential for a half-cell reaction, whether anode (oxidation) or cathode (reduction) is written and presented in Appendix D as a “reduction” 2+ Cu (aq) + 2e Cu(s) [reduction - cathode] Ex. Zn(s) Zn 2+ (aq) + 2e- [oxidation - anode] would be written in the table as: Cu2+ (aq) + 2e- Cu(s) EoCopper (Eocathode ) [reduction] Zn2+ (aq) + 2e- Zn(s) 2/18/2015 Eo Zinc (Eoanode ) [reduction] 43 Electrochemistry Standard Electrode Half-Cell Potentials Electrons flow spontaneously from Anode (negative) to Cathode (positive) Cathode must have a more “Positive” Eohalf-cell than the Anode For a “positive” Eocell ; i.e., a spontaneous reaction Eocell = (Eocathode (reduction) - Eoanode (oxidation) ) > 0 Eocell = Eocopper - Eo Zinc The standard cell potential is the difference between the standard electrode potential of the “Cathode” (reduction) half-cell and the standard electrode potential of the “Anode” (oxidation) half-cell Standard half-cell potentials are “intensive” properties, thus their values do NOT have to be adjusted for stoichiometry (# of moles) 2/18/2015 44 Practice Problem Write out the overall equation for the cell reaction and determine the standard cell potential for the following galvanic cell [Eo (Ag+/Ag) = 0.80 V; Eo (Ni2+/Ni) = - 0.26 V] Ni(s) I Ni 2+ (aq) Ag + (aq) I Ag(s) 2Ag + (aq) + 2e- 2Ag(s) Ni(s) Ni 2+ (aq) + 2e- [reduction (cathode)] [oxidation (anode)] Ni(s) + 2Ag + (aq) Ni 2+ + 2Ag(s) Write both reactions in "reduction" form 2Ag + (aq) + 2e- 2Ag(s) Ni 2+ (aq) + 2e- Ni(s) [reduction (cathode)] [reduction (anode)] Eocell = EoSilver(Red) - Eo Nickel(Ox) 2/18/2015 Eocell = 0.80 - (-0.26) = 1.06 V 45 Electrochemistry The Standard Hydrogen Electrode Half-cell potentials are not absolute quantities The values found in tables are determined relative to a “Standard” The Standard Electrode potential is defined as zero (Eoreference) = 0.00 The “standard reference half-cell” is a standard “Hydrogen” electrode Specially prepared Platinum electrode immersed in a 1 M aqueous solution of a strong acid through which H2 gas at 1 atm is bubbled 2H+ (aq; 1 M) + 2e- 2/18/2015 H2 (g); 1 atm) Eoreference = 0.00V 46 Electrochemistry Reference Half-Cell and Unknown Half-Cell The “Standard” electrode can act as either the “Anode” or the “Cathode” Oxidation of H (lose e-) at anode half-cell and 2 reduction of unknown at cathode half-cell Eocell = Eocathode - Eoanode Eounknown - Eoreference Eocell = Eounknown - 0.00 V = Eounknown Reduction of H+ (gain e-) at cathode half-cell and oxidation of unknown at anode half-cell Eocell = Eocathode - Eoanode Eoreference - Eounknown Eocell = 0.00 V - Eounknown 2/18/2015 = - Eounknown 47 Practice Problem Determine the standard electrode potential, Eozinc, using a voltaic cell consisting of the Zn/Zn2+ half-reaction and the H+/H2 half-reaction. Eocell = + 0.76 V Ans: Zinc is being oxidized (loses 2e-) producing electrons at the negative anode; H+ gains e- at positive cathode 2H+ (aq) + 2e- Zn(s) H2 (g) Zn2+ (aq) + 2e- Eoreference = 0.00 V Eo zinc = ? V Zn(s) + 2H+ (aq) Zn2+ (aq) + H2 (g) Eocell = Eocathode - Eoanode Eocell = 0.76V Eoreference - Eo Zinc Eo Zinc = Eoreference - Eocell = 0.00 V - 0.76 V = - 0.76 V 2/18/2015 48 Electrochemistry Relative Strength of Oxidizing and Reducing Agents Cu 2+ (aq) + 2e- = Cu(s) Eo = 0.34 V 2H+ (aq) + 2e- = H2 (g) Eo = 0.00 V Zn 2+ (aq) + 2e- = Zn(s) Eo = - 0.76 V The more positive the Eo value, the more readily the reaction occurs Strength of Oxidizing Agents – Cu2+ > H+ > Zn2+ Strength of Reducing Agents – Zn > H2 > Cu Oxidizing agents decrease in strength as the value of Eo decreases, while the strength of the reducing agents increases as the value of Eo decreases Cu2+ is the stronger Oxidizing agent Zn metal (not the ion) is the stronger Reducing agent 2/18/2015 49 Electrochemistry Table of Standard Electrode Potentials (The emf Series) Selected Standard Electrode Potentials (298oC) All Values are relative to the “standard hydrogen (reference) electrode All reactions are written as “reductions” 2/18/2015 50 Electrochemistry EMF Series All Values are relative to the “standard hydrogen (reference) electrode All reactions are written as “reductions” F2 is the strongest oxidizing agent (high, positive Eo) Fluorine is very electronegative with a high ionization potential (easily reduced by gaining electrons) By gaining e- it forms the weakest reducing agent, F- , which is very reluctant to lose electrons) Li metal is strongest reducing agent (low, more negative Eo) Lithium has a Low ionization energy and is easily oxidized by losing electrons By losing e- , Lithium forms the weakest oxidizing agent, Li+ 2/18/2015 51 Electrochemistry Similarities – Acid/Base vs Redox Acid Strength vs Base Strength using Ka & Kb values Redox (Oxidizing agent vs Reducing agent) using Standard Electrode Potential (Eo) values Appendix D (Table of Standard Electrode Potentials) The stronger oxidizing agent (species on left side of table) has a half-reaction with a larger more positive (less negative) Eo than a species lower in the list The stronger reducing agent (species on the right side of table) has a half-reaction with a smaller (less positive) Eo value than a species higher in the list A spontaneous reaction between a metal, acting as a reducing agent by losing electrons (oxidized) to be gained by the ion of another element (reduced) would occur if the Eo potential of the metal is less than that of the metal ion. 52 2/18/2015 Electrochemistry Writing Spontaneous Redox Reactions A spontaneous reaction (Eocell > 0) will occur between an oxidizing agent and any reducing agent that lies below it in the table Zn(s) (reducing agent (Eo = -0.76 V) will react spontaneously with Cu2+ (oxidizing agent) (Eo = +0.34 V), which lies above Zn in the table The Reduction of Cu2+ to Cu will occur at the Cathode The Oxidation of Zn to Zn2+ will occur at the Anode 2/18/2015 A spontaneous reaction will occur when the Eo of the reaction at the Cathode (reduction) minus the Eo of the reaction at the Anode (oxidation) is > 0 (Positive) Eocell = (Eocathode (reduction) - Eoanode (oxidation) ) > 0 53 Electrochemistry Writing Spontaneous Redox Reactions Combing half-cell reactions to form a “Net” reaction In the Standard Electrode Potential table (Appendix D), both reactions are written as “reductions” (e- gain) One of the reactions will have to be reversed so that the applicable reactants are on the left side of the net equation and the products on the right side The sign of Eo for the reversed reaction need not be reversed Which reaction to reverse? Scenario #1 - Net reaction is supplied Balanced equation clearly indicates which species is oxidized and which species is reduced Consult table to see which half-cell reaction (Con’t) was reversed 54 2/18/2015 Electrochemistry Writing Spontaneous Redox Reactions (con’t) Combing half-cell reactions to form a “Net” reaction Net reaction example Zn(s) + Cu 2+ (aq) Stronger Reducing Agent Stronger Oxidizaing Agent Zn 2+ (aq) + Cu(s) Weaker Oxidizing Agent Weaker Reducing Agent Cu2+ is reduced at Cathode - Cu2+ + 2e- Cu(s) Eo = + 0.34V Zn(s) is oxidized at Anode - Zn s Zn2+ + 2e- Eo = - 0.76 V Zinc metal is the stronger reducing agent (least positive Eo value) Zn(s) reaction was reversed Eocell = (Eocathode (reduction) - Eoanode (oxidation) ) Eocell = + 0.34 V - (-0.76V) = + 1.10 V > 0 2/18/2015 Reaction Spontaneous 55 Electrochemistry Writing Spontaneous Redox Reactions (con’t) Combing half-cell reactions to form a “Net” reaction Scenario #2 - Net reaction to be determined from half-cell reactions Ag + (aq) + e- = Ag(s) Sn 2+ (aq) + 2e- = Sn(s) Eo = + 0.80 V Eo = - 0.14 V Since the net reaction is not known, it is not clear which reaction occurs at a particular electrode For a spontaneous reaction, the cathode [reduction] potential minus the anode [oxidation] potential must be “positive” (Eocell > 0) To ensure this, the Anode Oxidation term in the Eocell equation must have an Eo value less than the Cathode Reduction term 2/18/2015 56 Electrochemistry Writing Spontaneous Redox Reactions (con’t) Combing half-cell reactions to form a “Net” reaction Scenario #2 - Net reaction to be determined from half-cell reactions (con’t) Since -0.14 < +0.80, the Sn2+ + 2 e- reaction must be reversed (converted to the Anode Oxidation term) Balance equations to account for reaction coefficients (e- lost = e- gained) 2Ag + (aq) + 2eSn(s) = = 2Ag(s) Sn 2+ (aq) + 2e- Sn(s) + 2Ag + (aq) Eo = + 0.80 V (Cathode Reduction) Eo = - 0.14 V (Anode Oxidaton) Sn 2+ (aq) + 2Ag(s) (overall reaction) Eocell = Eocathode reduction(Ag) - Eoanode oxidation(Sn) 2/18/2015 Eocell = 0.80 - (-0.14) = + 0.94 V (Spontaneous) 57 Practice Problem Consult the table of standard electrode potentials in your textbook in order to decide which one of the following reagents is capable of reducing I2(s) to I- (aq, 1 M) I2(s) + 2e- 2I-(aq) +0.53V Reduction Form a. Br-(aq) Br2(l) b. Ag(s) Ag+(aq) + e- Ag(s) +0.80V c. Sn(s) Sn2+(aq) + 2e- Sn(s) -0.14V d. Zn2+ (aq, 1 M) Zn2+ (aq) + 2e- Zn(s) -0.76V e. Sn4+ (aq,1 M) Sn4+ (aq) + 2e- Sn2+ (aq) +0.13V + 2e- 2Br-(aq) +1.07V (con’t) 2/18/2015 58 Practice Problem (con’t) The I2 is being reduced – gaining electrons – at Cathode (Red Cat) The other solution must be capable of being oxidized at Anode (AnOx) Only answers a, b, c reflect oxidizable elements, i.e., can lose electrons a. The Br- solution undergoes oxidation (lose e-) at the Anode Thus Eocell = Eocathode - Eoanode + 0.53 - (+1.07) = - 0.54Eo Neg Eocell Bromide (Br - ) will not reduce I 2 b. The Silver (Ag(s) undergoes oxidation (loses e-) to form Ag+ Thus: Eocell = Eocathode - Eoanode + 0.53 - (+0.80) = - 0.27o Neg Eocell Ag(s) will not reduce I 2 2/18/2015 (con’t) 59 Practice Problem (con’t) c. The Sn(s) will undergo oxidation to form Sn2+ Eocell = Eocathode - Eoanode + 0.53 - (-0.14) = + 0.67o Pos Eocell Sn(s) will reduce I 2 d. The Zn2+ solution is already oxidized (will not lose any more e-) Thus: Zn2+ will not reduce I 2 e. The Sn4+ solution is already oxidized Thus: Sn4 will not reduce I 2 2/18/2015 60 Practice Problem Combine the following 3 half-cell reactions into 3 balanced spontaneous reactions; Calculate Eocell for each; rank the relative strengths of the oxidizing & reducing agents (A) NO3- (aq) + 4H+ (aq) + 3 e- NO(g) + 2H2O(l) N2 (g) + 5H+ + 4e- N2 H5+ (B) (C) MnO2 (s) + 4H+ (aq) + 2e- Mn2+ (aq) + 2H2o (l) Eo = 0.96 V Eo = - 0.23 V Eo = 1.23V 1. Combine & Balance half-reactions A & B Eo in (A) is more positive than Eo in (B) Reverse B (A – cathode reduction; B – anode oxidation) + (A) 4NO3 (aq) + 16H (aq) + 12 e 4NO(g) + 8H2O(l) (B) 3N2 H5 + 3N2 (g) 15H+ + 12e- Eo = 0.96 V Eo = -0.23 V 3N2H5 +(aq) + 4NO3- (aq) + H + (aq) 3N2 (g) + 4NO(g) + 8H2O(l) Eocell (A + B) = 0.96 V - (-0.23 V) = 1.19 V 2/18/2015 Con’t 61 Practice Problem (con’t) 2. Combine & Balance half-reactions A & C Reverse half-reaction (A) (Eo 1.23 > Eo 0.96) (C – cathode reduction; A – anode oxidation) (C) 3MnO2 (s) + 12H+ (aq) + 6e- 3Mn2+ (aq) + 6H2o (l) Eo = 1.23 V (A) 2NO(g) + 4H2O(l) 2NO3- (aq) + 8H+ (aq) + 6 e3MnO2 (s) + 4H+ (aq) + 2NO(g) Eo = 0.96 V 3Mn2+ (aq) + 2H2O(l) + 2NO3 Eocell (A + C) = (1.23 V - 0.96 V) = 0.27 V 3. Combine and Balance half-reactions B & C Reverse half-reaction B (1.23 > -0.23) (C – cathode reduction; B – anode oxidation) (C) (B) 2MnO2 (s) + 8H+ (aq) + 4e- 2Mn2+ (aq) + 4H2o(l) N 2H5 + N2 (g) + 5H + + 4e- Eo = 1.23 V Eo = -0.23 V N2 H5 (aq) + 2MnO2 (s) + 3H+ (aq) N2 (g) + 2Mn2+ (aq) + 4H2O(l) 2/18/2015 Eocell (B + C) = 1.23 V - (-0.23) = 1.46 V Con’t 62 Practice Problem (con’t) Overall Ranking of Oxidizing & Reducing Agents (C) MnO2 (s) + 4H+ (aq) + 2e- Mn2+ (aq) + 2H2o (l) Eo = 1.23 V (A) NO3- (aq) + 4H+ (aq) + 3 e - NO(g) + 2H2O(l) Eo = 0.96 V (B) N2 (g) + 5H+ + 4e- N2H5 Oxidizing Agents : MnO2 > NO3- Reducing Agents : N2H5+ > NO Eo = -0.23 V > N2 > Mn2+ Rank Oxidizing & Reducing Agents Within Each Equation Equation 1 (A+B): Oxidizing Agent – Reducing Agent – Equation 2 (C+A): Oxidizing Agent – Reducing Agent – Equation 3 (C+B): Oxidizing Agent – Reducing Agent – 2/18/2015 NO3- > N2 N2H5+ > NO MnO2 > NO3NO > Mn+2 MnO2 > N2 N2H5+ > Mn+2 63 Electrochemistry Relative Reactivities of Metals Metals that displace H2 from acid If the Eocell for the reaction of H+ is more positive for metal A than it is for metal B, metal A is a stronger reducing agent than metal B and a more active metal 2H + (aq) + 2e- H 2 (g) Eo = 0.00 V (cathode - reduction) Fe(s) Fe+2 (aq) + 2eEo = - 0.44 V (anode - oxidation) Fe(s) + 2H + (aq) H 2 (g) + Fe 2+ (aq) Eocell = 0.00 - (-0.44) = 0.44 V Metals Li through Pb (includes Fe) in the standard electrode potential list (appendix D) lie below H+ and give positive Eocell when reducing H+ to H2, i.e., Hydrogen gas is released 2/18/2015 64 Electrochemistry Relative Reactivities of Metals Metals that cannot displace H2 from acid Metals that lie above the standard hydrogen reference half-reaction cannot reduce H+ from acids The Eocell for the reversed metal half-reaction is negative and the reaction does not occur 2H + (aq) + 2e- H 2 (g) Eo = 0.00 V (cathode - reduction) 2 Ag(s) 2Ag + (aq) + 2e- Eo = 0.80 V (anode - oxidation) 2Ag(s) + 2H + (aq) H 2 (g) + 2Ag + (aq) Eocell = 0.00 V - 0.80 V = - 0.80 V (not spontaneous) 2/18/2015 The higher the metal in the list, the more negative is its Eocell for the reduction of H+ to H2, thus its reducing strength (and reactivity) is less Thus, Gold (Au3+, Eo = +1.5V) is less active than Silver (Ag+, Eo = +0.8V) and does not release H2 gas 65 Electrochemistry Relative Reactivities of Metals Metals that displace H2 from water Metals that lie below the half-cell reaction potential for water can displace H2 from water In the reaction below the E value for water is not the standard state value listed in the table because in pure water, [OH-] is 1.0 x 10-7 M, not the standard state value of 1 M (-0.83 V) 2H 2O(l) + 2e- H 2 (g) + 2OH - E = -0.42V 2Na(s) Eo = -2.71 V 2Na+ (aq) + 2e- 2Na(s) + 2H 2O(l) 2Na + (aq) + H 2 + 2OH - Eocell = - 0.42 V - (-2.71 V) = + 2.29 V Ecell > 0 Sodium displaces Hydrogen from water 2/18/2015 66 Electrochemistry Relative Reactivities of Metals Metals that can displace other metals from solution Any metal that is lower in the standard electrode half-cell list can reduce the ion of a metal that is higher in the list, thus displacing that metal from solution (See next slide and slide #48) Fe2+ (aq) + 2e- Fe(s) Eo = -0.44V (cathod; reduction) Zn(s) Zn 2+ (aq) + 2e- Eo = -0.76V (anode; oxidation) Zn(s) + Fe2+ Zn 2+ (aq) + Fe(s) Eocell = - 0.44 V - (-0.76 V) = 0.32 V Ecell > 0 Zinc is the stronger reducing agent reducing Fe2+ to Fe and displacing it from solution 2/18/2015 67 Electrochemistry 2/18/2015 68 Electrochemistry Free Energy and Electrical Work Electrical Work Potential (Ecell, in volts) times the charge Work(w) = Potential difference (E) Charge w = Ecell charge 2/18/2015 Ecell measured with no current flowing No energy lost to heating Ecell voltage is maximum possible for cell Work is maximum possible Only reversible process can do maximum work Reversible process with no current flow: Forward reaction if opposing potential is smaller Reverse reaction if opposing potential is larger 69 Electrochemistry Spontaneous Reaction – G < 0 Spontaneous Reaction – Ecell > 0 ΔG - Ecell The voltaic cell loses energy as it does work on the surroundings; thus the work term (wmax) is negative w max = - Ecell charge ΔG = wmax Recall Slide 70 from Chapter 20 w max = - Ecell charge = G G = w max = - Ecell charge G = w max = - Ecell nF ΔG o = - Eocell n F Recall : (Recall slide # 39) (components in standard states) n = moles Coulombs J 4 F = 9.65 10 = 9.65 10 mole V • mol e 4 2/18/2015 70 Electrochemistry Electrical Work (con’t) Relate standard cell potential to equilibrium constant (K) of the redox reaction ΔG o = - RT lnK (Slide 82 from Chapter 20) ΔG o = - Eocell n F -Eocell n F = - RT lnK J 298.15 K RT mol rxn K = lnK = 2.303(log K) n mol e J nF (9.65 104 ) mol rxn V • mol e 8.314 Eocell E 2/18/2015 o cell 0.0592 V = log K n nEocell log K = 0.0592 V (at 298.15K) 71 Electrochemistry Summary Relationship between Go 2/18/2015 Eocell K 72 Electrochemistry Effect of Concentration on Cell Potential Most cells do not start with concentrations in their “standard” states (Slide 86 from Chapter 20) ΔG = ΔGo + RTlnQ Recall: G = - nF Ecell o ΔG o = - nF × Ecell (Standard State) o ΔG = - nF × Ecell = ΔGo + RTlnQ = - n F × Ecell + RTlnQ o -nF × Ecell = - n F × Ecell + RT lnQ nF RTlnQ o Ecell = Ecell (Nernst Equation) nF nF J 8.314 298.15 K o mol rxn K Ecell = Ecell 2.303 log Q n mol eJ (9.65 104 ) mol rxn V • mol e o Ecell = Ecell - 2/18/2015 0.0592 V × log Q n (at 298.15 K) 73 Electrochemistry Changes in Potential During Cell Operation The potential of a cell changes as the concentration of the cell components change Zn(s) + Cu 2+ (aq) Zn 2+ (aq) + Cu(s) 2+ [Zn ] o Ecell = 1.10 V Q = [Cu 2+ ] Ecell = E o cell 0.0592 V × log Q n Stage 1 When Q < 1 Ecell > Eocell Stage 2 When Q = 1 o Ecell = Ecell Stage 3 When Q > 1 o Ecell < Ecell (at 298.15 K) Stage 4 When Q = K Ecell = 0 (Equilibrium) If Q / K < 1, Ecell is positive (+) (cell does work) If Q / K = 1, Ecell = 0 2/18/2015 (equilibrium - cell no longer does work) If Q / K > 1, Ecell is negative (-) (reaction reverses until Q / K = 1) 74 Electrochemistry If Q / K < 1, Ecell is positive (+) (cell does work) If Q / K = 1, Ecell = 0 (cell no longer does work) If Q / K > 1, Ecell is negative (-) (reaction reverses until Q / K = 1) Ecell = E 2/18/2015 o cell 0.0592 V × log Q n 75 Electrochemistry Concentration Cells In a cell composed of the same substance, but differing concentrations in the two half-cells, the two concentrations move to equilibrate producing electrical energy The cell reaction is the “sum” of identical half-cell reactions written in opposite directions 2/18/2015 The Standard Electrode Potentials (Eocell) are both based on a 1 M solution (standard conditions), so they “cancel” each other, i. e., Eocell = 0 The non-standard cell potential, Ecell, depends on the ratio of the two concentrations [A]dil / [A]conc = Q 76 Electrochemistry How the Concentration Cell Works The dilute solution is in the Anode compartment (oxidation) and the concentrated solution is in the Cathode compartment (Reduction) Cu(s) Cu 2+ (aq;0.10M) + 2e- (Oxidation) Cu 2+( aq;1.0M) + 2e- Cu(s) Reduction In the Anode (dilute) half-cell, Cu atoms give up 2 electrons and the resulting Cu2+ ions enter the solution and make it more concentrated In the Cathode (conc) half-cell, Cu2+ ions gain 2 electrons and the resulting Cu atoms plate out on the electrode, making the solution less concentrated In this type of Voltaic cell, the dilution continues until equilibrium is attained, i.e., Ecell decreases until Ecell = 0 (Q = K) 2/18/2015 77 Electrochemistry Alkaline Battery MnO2 (s) + 2H2O(l) + 2e- Mn(OH)2 (s) + 2OH- (aq) Zn(s) + 2OH- (aq) ZnO(s) + H2O(l) + 2e- Zn(s) + MnO2 (s) + H 2O(l) ZnO(s) + Mn(OH)2 (s) Ecell = 1.5 V [Anode (Oxidation] Overall Cell Reaction Nickel-Metal Hydride (Ni-MH) Battery NiO(OH)(s) + H2O(l) + e- Ni(OH)2 (s) + OH- (aq) MH(s) + OH- (aq) M(s) + H2O(l) + e- MH(s) + NIO(OH)(s) M(s) + Ni(OH)2 (s) [Cathode (Reduction] Ecell = 1.4 V [Cathode (Reduction] [Anode (Oxidation] Overall Cell Reaction Lithium Ion Battery Li1-xMn2O4 (s)(s) + xLi + + xe- LiMn2O4 (s) + OH- (aq) Li xC6 xLi + + xe- + C6 (s) Li xC6 + Li1-xMn 2O4 (s) LiMn 2O4 (s) + C6(s) 2/18/2015 [Cathode (Reduction] [Anode (Oxidation] Ecell = 3.7 V Overall Cell Reaction 78 Practice Problem Calculate Ecell for a voltaic cell containing the following halfcells: Zn(s) I Zn2+ (aq) II H+ I H (g) 2 [Zn2+] = 0.010 M Construct Eo [H+] = 2.5 M PH2 = 0.30 atm cell 2H+ (aq) + 2e- H2 (g) Zn(s) Zn 2+ (Eo = 0.00 V) (red; cathode) + 2e - (Eo = - 0.76 V) (ox; anode) 2H+ (aq) + Zn(s) H2 (g) + Zn2+ (aq) Eocell = 0.00 V - (-0.76 V) = 0.76 V 2+ Calculate Q Q = PH2 [Zn ] = 0.30 0.010 = 4.8 10-4 + 2 2 [H ] Ecell = Eocell - 2.303 × 2/18/2015 2.5 RT 0.0592 V log Q = Eocell log Q nF n 0.0592 V Ecell = 0.76V - log(4.8 10-4 ) = 0.76V - (-0.0982 V = 0.86 V 2 79 Practice Problem What is the equilibrium constant for the following reaction [Eo(Ce4+/Ce3+) = 1.72 V Eo(Cl2/Cl-) = 1.36 V 2 Cl-(aq) + 2 Ce4+(aq) Cl2(g) + 2 Ce3+(aq) Cl - (aq) I Cl 2 (g) II Ce4+ (aq) I Ce3+ (aq) 2Ce4+ (aq) + 2e- 2Cl - (aq) Cl 2 2Ce3+ (aq) (Eo = 1.36 V) (ox; anode) + 2e - 2Ce4+ (aq) + 2Cl - (Eo = 1.72 V) (red; cathode) Cl 2 (g) + 2Ce3+ (aq) Eocell = 1.72V - 1.36 V = 0.36 V E o cell 0.0592 V = log K n nEocell 2 0.36 V log K = = = 12.2 0.0592 V 0.0592 V 2/18/2015 (at 298.15 K) 80 Practice Problem Write out the overall equation for the cell reaction and determine the standard cell potential for the following galvanic cell. [Eo (Ag+/Ag) = 0.80 Eo (Ni2+/Ni) = -0.26] Ni(s)|Ni2+(aq)║Ag+(aq)|Ag(s) 2Ag + (aq) + 2e- 2Ag + (aq) Ni(aq) Ni 2+ (Eo = 0.80 V) (red; cathode) + 2e - (Eo = - 0.26 V) (ox; anode) 2Ag + (aq) + Ni(aq) Ni 2+ (aq) + 2Ag + (aq) Eocell = 0.80V - (- 0.26) = 1.06 V 2/18/2015 81 Practice Problem What is the maximum work you can obtain from 15.0 g of Ni in the galvanic cell shown in the previous problem when the Ecell is 0.97 V? [Eo (Ag+/Ag) = 0.80 Eo (Ni2+/Ni) = -0.26] Ni(s)|Ni2+(aq)║Ag+(aq)|Ag(s) 2Ag + (aq) + Ni(aq) Ni 2+ (aq) + 2Ag + (aq) w max = - Ecell charge w max charge = nF F = 96,485 C J = 96,485 mol eV • mol e - mol eJ 5 = -Ecell n F = -0.97 V × 2 × 96,485 = 1.87 10 J / mol mol Ni V • mol e Mass 15.0g mol(Ni) = = = 0.256 mol Mol Wgt 58.69 g / mol wmax = 0.256 mol ×(-1.87×105 J / mol = -4.78×104 J 2/18/2015 wmax = - 4.78 ×104 J = - 4.78 kJ 82 Practice Problem What is the cell voltage (Ecell) for the following galvanic cell? Cd(s)|Cd2+(0.026 M)║Ni2+(0.00420 M)|Ni(s) Ni 2+ (aq) + 2e- Ni(s) Cd(s) Cd 2+ + 2e- Cd(s) + Ni 2+ (aq) Eo = - 0.25 V Eo = - 0.40 V (Reduction) (Oxidation) Cd 2+ + Ni(s) Eocell = - 0.25 V - (-0.40 V) = 0.15 V [Cd 2+ ] 0.026M Q = = = 6.19 2+ 0.00420M [Ni ] o Ecell = Ecell - Ecell = 0.15 V 2/18/2015 0.0592 V × log Q n (at 298.15 K) 0.0592 V × log 6.19 = 0.15 V - (0.0296 0.79) = 0.13 V 2 83 Practice Problem Construct a Voltaic Cell to determine the pH of an Unknown Solution Compartment #1 – Cathode consisting of Standard Hydrogen Electrode based on H2/H+ half-cell reaction at standard conditions (H+ – 1 M; H2 – 1 atm) Compartment #2 – Anode consisting of same apparatus but dipping into a solution of unknown H+(pH) Although Eocell = 0, the individual half-cells differ in [H+] and Ecell is not = 0 2H+ (aq; 1 M) + 2e- H 2 (g; 1 atm) [cathode; reduction] H2 (g; 1atm) 2H+ (aq; unknown) + 2e- [anode; oxidation] 2H + (aq; 1M) 2H + (aq; unknown) 2/18/2015 Ecell = ? Con’t 84 Practice Problem (Con’t) Ecell = E o cell 2 0.0592 V 0.0592 V [H + ]unknown o × log Q = Ecell × log + 2 n n ]H ]standard Substituting 1M for [H+ ]standard and 0 V for Eocell gives : Ecell 2 0.0592 V [H + ]unknown 0.0592 V + 2 = 0V × log = log[H ]unknown 2 2 1 2 0.0592 V × 2 log [H + ]unknown = - 0.0592V log[H + ]unknown 2 Ecell -log[H + ]unknown = 0.0592 Ecell = - Since pH = - log[H + ] pH = Ecell 0.0592 Measure the cell potential with a Voltmeter and calculate pH 2/18/2015 85 Practice Problem What is the pH of the test solution when Ecell = 0.612 V at 25 oC? Pt|H2(g)(1 atm)|H+(test sol’n)║AgCl(s),Ag(s)|Cl-(2.80 M) AgCl(s) + e- Ag(s) + Cl - (aq) Eo = 0.22V [cathode; reduction] H2 (g; 1atm) 2H+ (aq; unknown) + 2e- Eo = 0.0V [anode; oxidation] H2 (g;1atm) + 2AgCl(s) 2Ag(s) + 2Cl - (aq) + 2H+ (aq, unknown) [Cl - ]2 [H + ]2 Q = H 2 (g;1atm) Ecell = E o cell Eocell = 0.22 V - 0.0 V = 0.22 V 0.0592 V 0.0592 V [Cl - ]2 [H + ]2 o × log Q = Ecell × log n 2 H 2 (g;1atm) 0.0592 V (2.80)2 [H + ]2 0.612 V = 0.22 V × log = 0.22 V - 0.0296(log(7.84) + 2log[H + ]) 2 1 -0.0296 2log[H + ] = 0.612 - 0.22 + 0.0296 0.894 -log[H + ] = pH = 7.07 2/18/2015 86 Summary Equations charge Charge = moles of e mol eCharge = nF F - Faraday Constant - F = 96, 485 C mol e- (C - coulomb, SI unit of charge) Eocell = Eocathode (reduction) - Eoanode (oxidation) 2H + (aq) + 2e- H 2 (g) Eo = 0.00 V (cathode - reduction) Ag(s) Ag + (aq) + e- Eo = 0.80 V (anode - oxidation) 2Ag(s) + 2H + (aq) H 2 (g) + 2Ag + (aq) Eocell = 0.00 V - 0.80 V = - 0.80 V 2/18/2015 87 Summary Equations G = w max = - Ecell charge G = w max = - Ecell nF o ΔG o = - Ecell nF (components in standard states) ΔG o = - RT lnK -Eocell n F = - RT lnK ΔG = ΔGo + RTlnQ -nF Ecell = - n F Eocell + RTlnQ o Ecell = Ecell - o Ecell = Ecell - 2/18/2015 RTlnQ nF (Nernst Equation) 0.0592 V × log Q n (at 298.15 K) 88