Lecture 17. Thermodynamics of Galvanic (Voltaic) Cells.

Transcription

1 Lecture 17 Thermodynamics of Galvanic (Voltaic) Cells

2 Ballard PEM Fuel Cell. 53 Electrochemistry Alessandro Volta, , 1827, Italian scientist t and inventor. nt Luigi Galvani, , 1798, Italian scientist and inventor. 54 2

3 The Voltaic Pile Drawing done by Volta to show the arrangement of silver and zinc disks to generate an electric current. What voltage does a cell generate? 55 Operation of a Galvanic cell. In a Galvanic cell a spontaneous cell reaction produces electricity. Galvanic cells form the basis of energy storage and energy conversion devices (battery systems and fuel cells). Electrons leave a Galvanic cell at the anode (negative electrode), travel through the external circuit, and re-enter the cell at the cathode (positive electrode). The circuit is completed inside the cell by the electro-migration of ions through the salt bridge. We need to answer the following questions regarding Galvanic cells. Can we devise a quantitative measure for the tendency of a specific redox couple to undergo oxidation or reduction? Is the net cell reaction energetically feasible? Can we compute useful thermodynamic quantities such as the change in Gibbs energy ΔG or the equilibrium constant for the cell reaction? The answer is yes to all of these questions. We now discuss the thermodynamics of Galvanic cells. 56 3

4 The difference in electrical potential between the anode and cathode is called: cell voltage electromotive force (emf) cell potential Electrochemical Cells Cell Diagram Zn (s) +Cu 2+ (aq) Cu (s) +Zn 2+ (aq) [Cu 2+ ] = 1 M & [Zn 2+ ] = 1 M Zn (s) Zn 2+ (1 M) Cu 2+ (1 M) Cu (s) anode cathode Galvanic cell movie. 58 4

5 A Voltaic Cell Based on the Zinc-Copper 59 Reaction Electrochemical Cells anode oxidation cathode reduction spontaneous redox reaction

6 Electron flow in a Galvanic Cell. 61 Notation for a Voltaic Cell components of anode compartment (oxidation halfcell) components of cathode compartment (reduction half-cell) phase of lower oxidation state phase of higher oxidation state phase of higher oxidation state phase of lower oxidation state phase boundary between half-cells Examples: Zn(s) ) Zn 2+ (aq) Cu 2+ (aq) Cu (s) () Zn(s) Zn 2+ (aq) + 2e - Cu 2+ (aq) + 2e - Cu(s) graphite I - (aq) I 2 (s) H + (aq), MnO 4- (aq) Mn 2+ (aq) graphite inert electrode 62 6

7 Figure 21.6 A voltaic cell using inactive electrodes Oxidation half-reaction 2I - (aq) I 2 (s) + 2e - Reduction half-reaction MnO 4- (aq) + 8H + (aq) + 5e - Mn 2+ (aq) + 4H 2 O(l) Overall (cell) reaction 2MnO 4- (aq) + 16H + (aq) + 1I - (aq) 2Mn 2+ (aq) + 5I 2 (s) + 8H 2 O(l) 63 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 21.2: Diagramming Voltaic Cells PROBLEM: Diagram, show balanced equations, and write the notation for a voltaic cell that consists of one half-cell with a Cr bar in a Cr(NO 3 ) 3 solution, another half-cell with an Ag bar in an AgNO 3 solution, and a KNO 3 salt bridge. Measurement indicates that the Cr electrode is negative relative to the Ag electrode. PLAN: Identify the oxidation and reduction reactions and write each halfreaction. Associate the (-)(Cr) pole with the anode (oxidation) and the (+) pole with the cathode (reduction). SOLUTION: Voltmeter salt bridge Oxidation half-reaction Cr Ag Cr(s) Cr 3+ (aq) + 3e - K + e - Reduction half-reaction Ag + (aq) + e - Ag(s) Overall (cell) reaction Cr(s) + Ag + (aq) Cr 3+ (aq) + Ag(s) NO 3 - Cr 3+ Ag + Cr(s) Cr 3+ (aq) Ag + (aq) Ag(s) 64 7

8 Why Does a Voltaic Cell Work? The spontaneous reaction occurs as a result of the different abilities of materials (such as metals) to give up their electrons and the ability of the electrons to flow through the circuit. E cell > for a spontaneous reaction 1 Volt (V) = 1 Joule (J)/ Coulomb (C) 65 Table 21.1 Voltages of Some Voltaic Cells Voltaic Cell Voltage (V) Common alkaline battery Lead-acid car battery (6 cells = 12V) Calculator battery (mercury) Electric eel (~5 cells in 6-ft eel = 75V) Nerve of giant squid (across cell membrane)

9 Standard redox potentials. Given a specific redox couple we would like to establish a way by which the reducibility or the oxidizibility of the couple can be determined. This can be accomplished by devising a number scale, expressed in units of volts of standard electrode potentials E. Redox couples exhibiting highly negative E values are readily oxidised. Redox couples exhibiting highly positive E values are readily reduced. Hence the more positive the E value of a redox couple, the greater the tendency for it to be reduced. The electrode potential of a single redox couple A/B is defined with respect to a standard zero of potential. This reference is called the standard hydrogen reference electrode (SHE). E (A,B) is called the standard reduction potential for the reduction process A+ne - -> B, and it is defined as the measured cell potential obtained for the Galvanic cell formed by coupling the A/B electrode system with a hydrogen reference electrode. The cell configuration is + Pt H H ( aq) A( aq), B( aq) M, 2 E Cell = E Cathode E anode 67 Standard Reduction Potential E E (measured in volts V) is for the reaction as written. The more positive ii E the greater the tendency for the substance to be reduced. The half-cell reactions are reversible. The sign of E changes when the reaction is reversed. Changing the stoichiometric ometr c coefficients of a half-cell reaction does not change the value of E. Table 21.2 Selected Standard Electrode Potentials (298K) Half-Reaction E (V) F 2 (g) + 2e - 2F - (aq) Cl 2 (g) + 2e - 2Cl - (aq) MnO 2 (g) + 4H + (aq) + 2e - Mn 2+ (aq) + 2H 2 O(l) NO 3- (aq) + 4H + (aq) + 3e - NO(g) + 2H 2 O(l) +.96 Ag + (aq) + e - Ag(s) +.8 Fe 3+ (g) + e - Fe 2+ (aq) +.77 O 2 (g) + 2H 2 O(l) + 4e - 4OH - (aq) +.4 Cu 2+ (aq) + 2e - Cu(s) H + (aq) + 2e - H 2 (g). N 2 (g) + 5H + (aq) + 4e - N 2 H 5+ (aq) -.23 Fe 2+ (aq) + 2e - Fe(s) H 2 O(l) + 2e - H 2 (g) + 2OH - (aq) -.83 Na + (aq) + e - Na(s) Li + (aq) + e - Li(s)

10 69 Best oxidizing agents Kotz Figure 2.14 Best reducing agents Potential Ladder for Reduction Half-Reactions 7 1

11 Standard Redox Potentials, E o oxidizing ability of ion E o (V) Cu e- Cu H + + 2e- H 2. Zn e- Zn -.76 reducing ability of element Any substance on the right will reduce any substance higher than it on the left. Zn can reduce H + and Cu 2+ H 2 can reduce Cu 2+ but not Zn 2+ Cu cannot reduce H + or Zn Standard Electrode Potentials Standard reduction potential (E ) 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) 2H 2 (1 atm) E = V Standard hydrogen electrode (SHE)

12 Standard Redox Potentials, E o Ox. agent Cu e- --> Cu H + + 2e- --> H 2. Zn e- --> Zn -.76 Red. agent Any substance on the right will reduce any substance higher than it on the left. Northwest-southeast rule: productfavored reactions occur between reducing agent at southeast corner oxidizing agent at northwest corner 73 Standard Redox Potentials, E o CATHODE Cu e- --> Cu H + + 2e- --> H 2. Zn e- --> Zn -.76 ANODE Northwest-southeast rule: reducing agent at southeast corner = ANODE oxidizing agent at northwest corner = CATHODE 74 12

13 Standard Redox Potentials, E o E net = distance from top half-reaction (cathode) to bottom half-reaction (anode) E net = E cathode -E anode E o net for Cu/Ag + reaction = +.46 V 75 Standard cell potentials. The standard potential E cell developed by a Galvanic cell reflects the values of the standard potentials associated with the two component half reactions. This can be computed using the following simple procedure. The two half reactions are written as reduction processes. For any combination of two redox couples to form a Galvanic cell, the half reaction exhibiting the more positive E value occurs as a reduction process and is written on the RHS of the cell diagram, as the positive pole of the cell. In contrast, the half reaction which has the more negative E value is written on the LHS of the cell diagram as the negative pole of the cell, and will occur as an oxidation process. The overall cell reaction is given as the sum of the two component redox processes and the net cell potential is given by the expression presented across. E cell = E RHS E LHS = E cathode E M Ox, Red Red',Ox' M ' - Anode Oxidation e - loss LHS + anode Cathode Reduction e - gain RHS 76 13

14 electron flow Anode E e Cathode reference electrode SHE Pt H 2 in Pt indicator electrode H 2 (g) H + (aq) A(aq) B(aq) salt bridge test redox couple + Pt H H ( aq) A( aq), B( aq) M, 2 77 Figure 21.7 Determining an unknown E half-cell with the standard reference (hydrogen) electrode Oxidation half-reaction Zn(s) Zn 2+ (aq) + 2e - ( ) ( q) Overall (cell) reaction Zn(s) + 2H 3 O + (aq) Zn 2+ (aq) + H 2 (g) + 2H 2 O(l) Reduction half-reaction 2H 3 O + (aq) + 2e - H 2 (g) + 2H 2 O(l) 78 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 14

15 Sample Problem 21.3: Calculating an Unknown E half-cell from E cell PROBLEM: PLAN: SOLUTION: A voltaic cell houses the reaction between aqueous bromine and zinc metal: Br 2 (aq) + Zn(s) Zn 2+ (aq) + 2Br - (aq) E cell = 1.83V Calculate E bromine given E zinc = -.76V The reaction is spontaneous as written since the E cell is (+). Zinc is being oxidized and is the anode. Therefore the E bromine can be found using E cell = E cathode -E anode. anode: Zn(s) Zn 2+ (aq) + 2e - E = +.76 E Zn as Zn 2+ (aq) + 2e - Zn(s) is -.76V E cell = E cathode -E anode = 1.83 = E bromine - (-.76) E bromine = = 1.7V 79 By convention, electrode potentials are written as reductions. When pairing two half-cells, you must reverse one reduction halfcell to produce an oxidation half-cell. Reverse the sign of the potential. The reduction half-cell potential and the oxidation half-cell potential are added to obtain the E cell. When writing a spontaneous redox reaction, the left side (reactants) must contain the stronger oxidizing and reducing agents. Example: Zn(s) + Cu 2+ (aq) Zn 2+ (aq) + Cu(s) stronger reducing agent stronger oxidizing agent weaker oxidizing agent weaker reducing agent 8 15

16 Relationship between the change in Gibbs energy for the cell reaction and the cell potential. Transferring 1 electron : W = qe e cell = ee cell Transferring 1 mole electrons : W = N e A ee cell Transferring n mole electrons : 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 perform electrical work W e. From thermodynamics we note that the maximum electrical work W e done at constant temperature and pressure is equal to the change in Gibbs energy ΔG for the net cell reaction. We apply basic physics to evaluate the electrical work W e done in moving n mole electrons through a potential difference given by E cell. Relationship between thermodynamics of cell reaction and observed cell potential. ΔG = We = nen AEcell W = nn e A ee cell = nfe cell 81 What is the standard emf of an electrochemical cell made of a Cd electrode in a 1. M Cd(NO 3 ) 2 solution and a Cr electrode in a 1. M Cr(NO 3 ) 3 solution? Cd 2+ (aq) + 2e - Cd (s) E = -.4 V Cd is the stronger oxidizer Cr 3+ (aq) + 3e - Cr (s) E = -.74 V Cd will oxidize Cr Anode (oxidation): Cr (s) Cr 3+ (1 M) + 3e - x 2 Cathode (reduction): 2e - + Cd 2+ (1 M) Cd (s) x 3 2Cr (s) + 3Cd 2+ (1 M) 3Cd (s) + 2Cr 3+ (1 M) E cell = E cathode - E anode E = -.4 (-.74) cell Ecell =.34 V

17 Thermodynamics of cell reactions. Faraday constant : 96,5 C mol -1 The change in Gibbs energy for the overall cell reaction is related to the observed net cell potential generated. When the standard cell potential E cell is positive, the Gibbs energy ΔG is negative and vice versa. Once ΔG for a cell reaction is known, then the equilibrium constant K for the cell reaction can be readily evaluated. These expressions are valid for standard conditions : T = 298 K, p = 1 atm (or 1 bar); c = 1 mol L -1. ΔG Δ ΔG K = exp RT G = nfe cell # electrons transferred in cell reaction = RT ln K nfe = exp RT cell Gas Constant : J mol -1 K -1 Temperature (K) 83 A. Any one of these thermodynamic parameters can be used to find the other two. B Th i f ΔG o d E o determine the reaction direction at standard-state conditions. B. The signs of ΔG o and E o cell 84 17

18 Sample Problem 21.5: Calculating K and ΔG from E cell PROBLEM: Lead can displace silver from solution: Pb(s) + 2Ag + (aq) Pb 2+ (aq) + 2Ag(s) As a consequence, silver is a valuable by-product in the industrial extraction of lead from its ore. Calculate K and ΔG at 25 C for this reaction. PLAN: Break the reaction into half-reactions, find the E for each half-reaction and then the E cell. SOLUTION: Pb 2+ (aq) + 2e - Pb(s) Ag + (aq) + e - Ag(s) Pb(s) Pb 2+ (aq) + 2e - 2X Ag + (aq) +e - Ag(s) E = -.13V E =.8V E =.13V E =.8V E cell =.93V E cell =.592V log K n ΔG = -nfe cell = -(2)(96.5kJ/mol*V)(.93V) log K = n x E cell = (2)(.93V) K = 2.6x1 31 ΔG = -1.8x1 2 kj.592v.592v 85 The Nernst equation. The potential developed by a Galvanic cell depends on the composition of the cell. From thermodynamics the Gibbs energy change for a chemical reaction ΔG G varies with composition of the reaction mixture in a well defined manner. We use the relationship between ΔG and E to obtain the ΔG = ΔG + Nernst equation. Nernst eqn.holds for single redox couples and net cell reactions. RT ln Q ΔG nfe nfe = nfe E = E RT nf ΔG + ln Q T = 298K = nfe RT ln Q E = E.592 n logq Reaction quotient Q [ products] [ reactants] 86 18

19 2+ 2+ Zn ( s) + Cu ( aq) Zn ( aq) + Cu( s) E cell 2+ [ Zn ] [ ] 2 Cu.59 = Ecell log + 2 Equilibrium ΔG = E cell = W = Dead cell Q = K Q <1 W large Q = = 1 E cell Ecell As cell operates [ Zn ] [ Cu ] Q E cell Q 2+ [ Zn ] 2+ + [ Cu ] = 2 Q >1 W small 87 Sample Problem 21.6: Using the Nernst Equation to Calculate E cell PROBLEM: In a test of a new reference electrode, a chemist constructs a voltaic cell consisting of a Zn/Zn 2+ half-cell and an H 2 /H + half-cell under the following conditions: [Zn 2+ ] =.1M 1M [H + ] = 25M 2.5M P =.3atm H 2 Calculate E cell at 25 C. PLAN: Find E cell and Q in order to use the Nernst equation. SOLUTION: Determining E cell : 2H + (aq) + 2e - H 2 (g) E =.V Zn 2+ (aq) + 2e - Zn(s) E = -.76V Zn(s) Zn 2+ (aq) + 2e - E = +.76V.592V E cell = E cell - n log Q E cell =.76 - (.592/2)log(4.8x1-4 ) =.86V Q = P x [Zn 2+ ] H 2 [H + ] 2 Q = (.3)(.1) (2.5) 2 Q = 4.8x

20 Figure A concentration cell based on the Cu/Cu 2+ half-reaction Oxidation half-reaction Reduction half-reaction Cu(s) Cu 2+ (aq,.1m) + 2e - Cu 2+ (aq, 1.M) + 2e - Cu(s) Overall (cell) reaction Cu 2+ (aq,1.m) Cu 2+ (aq,.1m) 89 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 21.7: Calculating the Potential of a Concentration Cell PROBLEM: A concentration cell consists of two Ag/Ag + half-cells. In half-cell A, electrode A dips into.1m AgNO 3 ; in half-cell B, electrode B dips into 4.x1-4 M AgNO 3. What is the cell potential at 298K? Which electrode has a positive charge? PLAN: E cell will be zero since the half-cell potentials are equal. E cell is calculated from the Nernst equation with half-cell A (higher [Ag + ]) having Ag + being reduced and plating out, and in half-cell B Ag(s) will be oxidized to Ag +. SOLUTION: Ag + (aq,.1m) half-cell A Ag + (aq, 4.x1-4 M) half-cell B E cell = E cell -.592V [Ag + log ] dilute 1 [Ag + ] concentrated E cell = V log 4.x1-2 =.828V Half-cell A is the cathode and has the positive electrode. 9 2

21 Determination of thermodynamic parameters from E cell vs temperature data. Measurement of the zero current cell potential E as a function n of temperature t T enables thermodynamic quantities such as the reaction enthalpy ΔH and reaction entropy ΔS to be evaluated for a cell reaction. Gibbs-Helmholtz eqn. Δ ΔG ΔH = ΔG T T G = nfe P E = a + b E T ΔH = nfe T T E = nfe + nft T 2 ( T T ) + c( T ) + P T a, b and c etc are constants, which can be positive or negative. T is a reference temperature (298K) ( nfe) E ΔH = nf E T T P P Temperature coefficient of zero current cell potential obtained from experimental E=E(T) data. Typical values lie in range VK Once ΔH and ΔG are known then ΔS may be evaluated. ΔG = ΔH TΔS ΔH ΔG Δ S = T 1 E ΔS = nfe + nft T T E ΔS = nf T P P + nfe Electrochemical measurements of cell potential conducted under conditions of zero current flow as a function of temperature provide a sophisticated method of determining useful thermodynamic quantities

22 Figure The processes occurring during the discharge and recharge of a lead-acid battery VOLTAIC(discharge) ELECTROLYTIC(recharge) 93 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure The tin-copper reaction as the basis of a voltaic and an electrolytic cell voltaic cell electrolytic cell Oxidation half-reaction Sn(s) Sn 2+ (aq) + 2e - Reduction half-reaction Cu 2+ (aq) + 2e - Cu(s) Overall (cell) reaction Sn(s) + Cu 2+ (aq) Sn 2+ (aq) + Cu(s) Oxidation half-reaction Cu(s) Cu 2+ (aq) + 2e - Reduction half-reaction Sn 2+ (aq) + 2e - Sn(s) Overall (cell) reaction Sn(s) + Cu 2+ (aq) Sn 2+ (aq) + Cu(s) 94 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 22