Types of potentials at electrode/solution interface

Transcription

1 Types of potentials at electrode/solution interface

2 Volta potential () or outer potential is the part of total potential difference across metal- electrolyte interface Defined as the work required to bring a unit point charge from infinity to a point just outside the surface of the phase by a distance of about cm from surface outer potential is a measurable quantity

3 Galvani potential () or inner is the electrostatic potential which is actually experienced by a charged particle inside the phase Defined as the work required to bring a unit point charge from infinity to a point inside the phase Inner potential is not measurable

4 The inner and outer potential differ by the surface potential () is caused by an inhomogeneous charge distribution at the surface can not be measured

5 Physical chemistry, Atkins

6 If is not measurable then can not be measured too Electrode potential (E) is its relative to another reference E= - ref which reference to use and at what conditions?

7 Metal electrode is an excellent conductor; its excess charge is restricted to a surface region about 1 A thick charge in the solution extends over a larger region of space, typically 5 20 A thick charge distribution in two narrow regions of equal and opposite charge is known as the electric double layer

8 It can be viewed as a capacitor with an extremely small plate separation, and therefore has a very high capacitance Many models for DL (Helmholtz, Gouy Chapman, Stern, Grahame) voltage drop between the metal and the solution is typically of the order of 1 V potential drop extends over such a narrow region, creates extremely high fields of up to 10 9 Vm 1

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10 Interfacial Electrochemistry, W. Schmickler, E. Santos, 2 nd edition

11 Why electron transfer? Electronic levels in metals are not discrete like in an atom or molecule Neighboring atoms have overlapped orbitals forming continuum energy levels available electrons fill these levels from bottom upwards The Fermi-level (E F ) corresponds to the energy at which the top electrons sit Each metal has its characteristic E F

12 See this website for more details

13 E F is not fixed and can be moved by supplying electrical energy (potential) Value of E F to Lowest Unoccupied Molecular Orbital (LUMO) and Highest Occupied Molecular Orbital (HOMO) on the reactant, can tell if electrons transfer from electrode to reactant or vice versa

14 Types of (electro)chemical reactions Electrochemical reaction is electrode reaction Electron transfer is evolved Chemical changes occur as a result General electrode reaction is represented by O + ne R O and R may be soluble in solution

15 Electrode reactions are oxidation-reduction reactions represented as oxidation is the removal of electrons from a species reduction is the addition of electrons to a species Cathode - where reduction occurs Anode - where oxidation occurs Redox reaction is a reaction in which there is a transfer of electrons from one species to another oxidant + ne = reductant Redox reaction takes place in an electrochemical cell An electrochemical cell consists of two electrodes An electrode is metallic conductors, in contact with an electrolyte (ionic conductor)

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17 Examples of electrode reactions

18 Types of electrodes Various kinds of electrode are shown below

19 Physical chemistry, Atkins & Paula

20 Electrochemical cell can be: Galvanic cell produces electricity as a result of the spontaneous reaction occurring in it Electrolytic cell in which a non-spontaneous reaction is driven by an external source of current A redox reaction is expressed as the sum of two reduction half-reactions; each one defines a redox couple

21 Examples for anodic reactions 2H 2Cl 2 O O Cl 2 2( g ) 4H 2e 4e Fe 2 Fe 3 e

22 Examples for cathodic reactions Ag e Ag ( s) 2H 2e H 2( g ) NO 3 10H 8e NH 4 3H 2 O

23 Homework (1) Calculate the standard free energy ( r G o ) of the reaction: 2 2H( aq) Fe( s) H Fe 2( g) ( aq) All the required data can be found at Answer must be sent by before October 11 th, 2:00 pm. Any answer sent after that is not accepted.

24 reduction and oxidation processes responsible for the overall reaction in a cell are separated in space oxidation takes place at one electrode and reduction takes place at the other electrons released in oxidation Red 1 Ox 1 + n e at anode travel through the external circuit and reenter cell through cathode, i.e where reduction Ox 2 + n e Red 2 occur

25 In galvanic cell Cathode has higher potential and anode has lower potential What about electrolytic cell? Physical chemistry, Atkins & Paula

26 Expressing equilibrium for electrochemical reactions Recalling that r G r G o RT ln Q Then for the reaction Cu 2+ (aq) + 2e Cu(s) (metal/metal ion electrode) Activity of metallic Cu is assumed to be unity, then r r G G r r G G o o RT ln RT ln a a 1 Cu reaction quotient a Cu Cu 2 2

27 For the reaction 2H + (aq) + 2e H 2 (g) (gas electrode) r G r G o RT ln a a H 2 2 H a H 2 P H 2 r G r G o RT ln a p H 2 H 2

28 For the reaction AgCl(s)+e Ag(s) +Cl - (aq) (metal/insoluble salt) r G r G o RT ln a Ag a a Cl AgCl Activities of solids are unity, then r G r G o RT ln a Cl

29 For the reaction Fe 3+ (aq) +e Fe 2+ (aq) (Redox electrode) r G r G o RT ln a a Fe Fe 2 3

30 All equations for half reaction How to write it for complete cell reaction? Try to do that for 2H Fe H Fe 2 ( aq) ( s) 2( g) ( aq) Remember that r G=0 at equilibrium, and r G o = -RT ln K

31 Express the formation of H 2 O from H 2 and O 2 in acidic solution (a redox reaction) as the difference of two reduction half-reactions: 4 H + (aq) + 4 e 2 H 2 (g), O 2 (g) + 4 H + (aq) + 4 e 2 H 2 O(l) Write the relation between r G and r G o

32 Cell/electrode reaction spontaneous or non spontaneous?? Spontaneous reactions have r G < 0 So will electrode/cell with r G < 0 has positive or negative potential?

33 Gibbs Function and Work Start with the First Law of Thermodynamics and some standard thermodynamic relations. We find du dq dw dq = T ds dw PdV dw electrical du T ds PdV dw electrical dh P du P PdV dg T dh T T ds du T,P PdV T ds T ds PdV dw electrical PdV T ds dg T,P dw electrical Gibbs function is at the heart of electrochemistry. It identifies the amount of work we can extract electrically from a system.

34 Gibbs and the Cell Potential Here we can easily see how this Gibbs function relates to cell potential w electrical = E Q Q= nf w electrical = n F E Negative work means that work is being done by the system on the surroundings. G T,P w electrical n F E cell potential is used to directly calculate r G Maximum non-expansion work

35 This leads to that a negative reaction Gibbs energy, corresponding to a spontaneous cell reaction, corresponds to a positive cell (electrode) potential driving power of a cell (that is, its potential) is proportional to the slope of the Gibbs energy with respect to the extent of reaction reaction that is far from equilibrium (when the slope is steep) has a strong tendency to drive electrons through an external circuit

36 Physical chemistry, Atkins & Paula

37 If r G for a reaction in a galvanic cell is -100kJ/mol, then cell potential can be calculated as E E E cell cell cell rg nf 5 1x10 J/mol 1x C/mol 1V Note that 1J = 1C V

38 Consider a cell with a maximum cell potential of 2.50 V. If 1.33 mol of e passes through the cell at an average potential E = 2.10 V. What is the efficiency of the cell? w = Q E = nfe. = 1.33 mol C/mol 2.10 V (V = J/C) w = J = 269 kj w max = nfe max = 1.33 mol C/mol 2.50 V = 321 kj efficiency = w/w max 100% = 269/ % = 83.8 % Of course, since w max is only achievable if the work is done reversibly (infinitely slowly), we can never reach 100% efficiency in any system in the real world. tte/firstyrchem/electro/index.htm

39 Nernst equation E E E r G cell o cell cell E r G o cell o rg nf rg nf o RT RT nf ln Q ln Q Nernst equation relates cell potential to activities E o cell is the cell standard potential

40 Cell potential varies with Q according to the figure shown. Standard cell potential when Q=1 Physical chemistry, Atkins & Paula

41 Typical example on Nernst equation Daniell cell

42 Electrodes and cell reactions RHE Cu 2 aq 2e Cu s LHE Zn s Zn 2 aq 2e Note that n=2 Cu 2 aq Zn s Zn 2 aq Cu s E E RT nf ln a Cu a Zn 2 =1 a Cu 2 a Zn If ions activity is assumed to be equal to concentration, then E E RT 2F 2 Zn ln Cu ln Zn 2 Cu 2

43 cell potential can be calculated according to values of ions concentration When [Zn 2+ ] = 1.00 M and [Cu 2+ ] = 0.01 M, then E ln V ln 100 When [Zn 2+ ] = 1.00 M and [Cu 2+ ] = 1.00 M, then E= 1.10 V!

44 Cell at equilibrium If cell reaction reaches equilibrium, then Q=K Chemical reaction at equilibrium can not do work Cell potential would be zero ln K nfe RT o cell This equation predicts equilibrium constant from measured standard cell potential

45 standard electrode potential The potential assigned to electrode with respect to another electrode with zero potential The electrode with zero potential (assumed to be) is the standard hydrogen electrode (SHE) designated as Pt/H 2 (g)/h + (aq) E o = 0 V at all temp. Standard conditions mean: hydrogen ion activity=1 Hydrogen gas pressure =1 bar temperature = 298K Standard cell potential with (SHE) as LHE and the other electrode as RHE equals E o of RHE All electrodes reaction are assumed to REDUCTION reactions

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47 Harned cell Consists from Hydrogen electrode as LHE and sliver/sliver chloride as RHE Pt H 2 (g) HCl(aq) AgCl(s) Ag(s) Cell reaction AgCl(s) + ½ H 2 (g) H + (aq) + Cl! (aq) + Ag(s) E o cell = E o (AgCl/Ag,Cl-) E o SHE = E o (AgCl/Ag,Cl-)

48 Using Debye-Huckel limiting law for 1:1 electrolyte Cl H o Cl Ag AgCl cell H H Cl H o Cl Ag AgCl cell a a F RT E E a a a a F RT E E ln 1 ln, /, / / 2 2 ln 2 ln 2 ln 2 ln 2 ln ln b RT F E b F RT E F RT E b F RT E F RT b F RT E E b a o cell o cell o cell

49 left can be evaluated at a range of molalities, plotted against b 1/2 and extrapolated to b = 0 The intercept at b 1/2 = 0 is the value of E o for the silver/silverchloride electrode Physical chemistry, Atkins & Paula

50 The extrapolated value of E o = V Physical chemistry, Atkins & Paula

51 List of standard potentials A list of standard potentials can be complied for other electrodes. It is called electrochemical series. More reducing Element Reaction E æ (V) Gold Au + + e - Au Chlorine Cl 2 (g) + 2 e - 2 Cl Platinum Pt e - Pt 1.18 Palladium Pd e - Pd Silver Ag + + e - Ag Copper Cu+ + e - Cu Copper Cu e - Cu Iron Fe e - Fe Lead Pb e - Pb Tin Sn e - Sn Nickel Ni e - Ni Cobalt Co e - Co Cadmium Cd e - Cd Iron Fe e - Fe Zinc Zn e - Zn Manganes e Mn e - Mn Aluminum Al e - Al Magnes ium Mg e - Mg Sodium Na + + e - Na Calcium Ca e - Ca Potassium K + + e - K More oxidizing

52 More questions electrochemical series can be found on this website Applications of Electrochemical Series hemistry-iii/redox-reactions/electrochemicalseries-applications.php

53 Cell notation phase boundaries are represented by a vertical bar Pt(s) H 2 (g) HCl(aq) AqCl(s) Ag(s) A liquid junction is represented by Zn(s) ZnSO 4 (aq) CuSO 4 (aq) Cu(s) Physical chemistry, Atkins & Paula

54 A double vertical line,, represents an interface for which it is assumed that the junction potential has been eliminated Physical chemistry, Atkins & Paula

55 Electrochemical methods, fundamentals and applications, A. Bard and L. Faulkner, 2 nd ed. 2001

56 Cell potential Cell potential is calculated from cathode and anode potential assuming: Cathode is RHE and its reaction is reduction Anode is LHE and its reaction is oxidation Cell potential is the difference between cathode potential and anode potential i.e. In standard state E cell = E R E L E o cell = E o R E o L

57 Using the table of E o for electrodes calculate E o cell for a cell composed from copper and nickel electrodes Cu 2+ /Cu Ni 2+ /Ni Cu 2+ (aq) + 2e Cu(s) Ni 2+ (aq) + 2e Ni(s) V V Potential of Ni electrode is more negative that Cu Ni will be anode (LHE) and Cu (RHE) will be cathode E o cell = E o Cu2+/Cu E o Ni2+/Ni = (-0.257) = V Cell reaction is spontaneous as E o cell is positive Ni(s) + Cu 2+ (aq) Cu(s) + Ni 2+ (aq)

58 What would be the potential of a cell composed of Zn electrode and Pb electrode Zn 2+ /Zn Pb 2+ /Pb Zn 2+ (aq) + 2e Zn(s) Pb 2+ (aq) + 2e Pb(s) V V Write the cell spontaneous reaction and find the anode and cathode. Calculate the standard potential for the reaction Sn Fe 2+ Sn + 2Fe 3+

59 determination of equilibrium constants Equilibrium constant can be calculated from E o cell according to the equation ln K nfe RT For example Daniell cell has standard potential of +1.1 V, so o cell ln ln K 2x96500x1.1 K 8.314x298 K x10 37 Comment on the value of K!

60 A disproportionation is a reaction in which a species is both oxidized and reduced. To study the disproportionation 2 Cu + (aq) Cu(s) + Cu 2+ (aq) we combine the following electrodes: The standard potential of the cell is therefore The corresponding equilibrium constant is K = Which oxidation state for Cu is more stable in aqueous solution?

61 Answer questions 6.23(a), 6.23(b) and 6.24(a)

62 Uses of Electrochemical Series A species with a low standard reduction potential has a thermodynamic tendency to reduce a species with a high standard reduction potential, or low reduces high Metals can be arranged according to their activity

63 increasing reactivity Activity Series of Metals potassium sodium React violently with cold water calcium React slowly with cold water magnesium aluminum zinc chromium React very slowly with steam but quite reactive in acid 63 iron nickel tin lead copper silver platinum gold React moderately with high levels of acid Un-reactive in acid hydrogen

64 can acidified dichromate (Cr 2 O 7 2- ) oxidize Hg to Hg 2 2+? Answer: E o are V for Cr 2 O 7 2- Cr 3+ and V for Hg 2 2+ Hg and since high oxidizes low, then Cr 2 O 7 2- will oxidize Hg to Hg 2 2+

65 Can Pb displaces Fe 2+ ions, and Cu 2+ ions from their solution? Answer: Values for E o are: V for Pb Pb V for Fe Fe V for Cu Cu 2+ Because Lead is NOT lower than Fe 2+ then it can not displace it i.e. Pb + Fe 2+ Pb 2+ + Fe But Lead is lower than Cu 2+, so it can displace it from its solution i.e. Pb + Cu 2+ Pb 2+ + Cu

66 determination of thermodynamic functions from galvanic cell standard potential of a cell is related to the standard reaction Gibbs energy by Since ( G/ T)= -S r G o = -nf E o cell Then o de ( dt cell ) P r nf (de o cell /dt) P is the temperature coefficient of standard cell Finally the standard enthalpy of cell reaction can be calculated as r H o r G o T r S o S o nf( E o cell T o de dt cell )

67 The Pt,H 2 (g)/hcl(aq)/hg 2 Cl 2 (s)/hg has a potential of V at 20 o C and a potential of V at 30 o C. Calculate r G o, r S o, r H o for the cell reaction at 25 o C. RHE: LHE: ½ Hg 2 Cl 2 (s)+e Hg(l) + Cl - (aq) ½ H 2 (g) H + (aq)+e Cell reaction: ½ Hg 2 Cl 2 (s)+ ½ H 2 (g) Hg(l) + HCl(aq) r G o = -nf E o cell r G(293K) = kj r G(303K) = kj r G o (298K)=( r G(293K)+ r G(303K))/2= kj

68 (de o cell /dt) P = (E 293 -E 303 )/( ) =( )/( ) = -3x10-4 V/K r S o = nf (de o cell /dt) P = -29 J/K r H o = (298x-0.029)= kj

69 Question: If the potential and temperature coefficient of Harned cell are 0.002V and x10-5 V/K respectively, calculate r G, r S and r H for the cell reaction. See also Example 6.5 in Physical chemistry by Atkins & Paula

70 Determination of mean activity coefficient If E o value for a cell is known, then its possible to find mean activity coefficient of an electrolyte by measuring the cell s potential at a specific concentration. For example for Harned cell, ± for HCl ions can be evaluated by rearrangement of the equation to be E cell 2RT F ln b E o 2RT F ln ln o F( Ecell E 2RT cell ) ln b

71 the potential of Harned cell Pt/H 2 (1atm)/HCl(0.0134m)/AgCl(s)/Ag(s) was found to be 0.45V, calculate ± for HCl at this molality. E o cell equals V ln ln 96500( ) 2x8.314x ln.0134

72 Ion selective electrodes an electrode that generates a potential in response to presence of specific ions in solution is called ionselective electrode. Hydrogen electrode is a typical example. Is sensitive to hydrogen ion activity Its potential is proportional to ph E o = 0 If P H2 = 1, Q = 1/a H+ and E = (RT/F) ln(a H+ ) E = E ø - (RT/nF) lnq ph=-loga H so E = (RT/F)pH At 25 C, E= mVpH

73 Glass electrode is sensitive to hydrogen ion activity because of the complex processes that take place at inner and outer glass membrane and the solution. The glass used is permeable to Li + and Na + ions but not H +. Other ion selective electrode sensitive to many ions are available. Physical chemistry, Atkins & Paula

74 Reference electrodes Primary reference electrode (SHE) Secondary reference electrodes Calomel Sliver/sliver chloride Mercury/ mercury sulphate Lead/ lead sulphate Mercury/mercury oxide Other reference electrodes

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