11

CELL POTENTIAL, ECELL POTENTIAL, E

• Electrons are “driven” from anode to cathode by Electrons are “driven” from anode to cathode by an electromotive force or an electromotive force or emfemf..

• For Zn/Cu cell, this is indicated by a voltage of For Zn/Cu cell, this is indicated by a voltage of 1.10 V at 25 ˚C and when [Zn1.10 V at 25 ˚C and when [Zn2+2+] and [Cu] and [Cu2+2+] = 1.0 M.] = 1.0 M.

Zn and ZnZn and Zn2+2+,,anodeanode

Cu and CuCu and Cu2+2+,,cathodecathode

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons1.10 V1.10 V

1.0 M1.0 M 1.0 M1.0 M

22

CELL POTENTIAL, CELL POTENTIAL, EE

• For Zn/Cu cell, For Zn/Cu cell, potentialpotential is is +1.10 V+1.10 V at 25 ˚C at 25 ˚C and when [Znand when [Zn2+2+] and [Cu] and [Cu2+2+] = 1.0 M.] = 1.0 M.

• This is the This is the STANDARD CELL STANDARD CELL POTENTIAL, EPOTENTIAL, Eoo

• ——a quantitative measure of the tendency of a quantitative measure of the tendency of reactants to proceed to products when all reactants to proceed to products when all are in their standard states at 25 ˚C. are in their standard states at 25 ˚C.

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

33

Calculating Cell VoltageCalculating Cell Voltage

• Balanced half-reactions can be added Balanced half-reactions can be added together to get overall, balanced together to get overall, balanced equation. equation.

Zn(s) ---> ZnZn(s) ---> Zn2+2+(aq) + 2e-(aq) + 2e-CuCu2+2+(aq) + 2e- ---> Cu(s)(aq) + 2e- ---> Cu(s)----------------------------------------------------------------------------------------CuCu2+2+(aq) + Zn(s) ---> Zn(aq) + Zn(s) ---> Zn2+2+(aq) + Cu(s)(aq) + Cu(s)

Zn(s) ---> ZnZn(s) ---> Zn2+2+(aq) + 2e-(aq) + 2e-CuCu2+2+(aq) + 2e- ---> Cu(s)(aq) + 2e- ---> Cu(s)----------------------------------------------------------------------------------------CuCu2+2+(aq) + Zn(s) ---> Zn(aq) + Zn(s) ---> Zn2+2+(aq) + Cu(s)(aq) + Cu(s)

If we know EIf we know Eoo for each half-reaction, we for each half-reaction, we could get Ecould get Eoo for net reaction. for net reaction.

44

CELL POTENTIALS, ECELL POTENTIALS, Eoo

Can’t measure 1/2 reaction Eo directly. Therefore, measure it relative to a

STANDARD HYDROGEN CELL, SHE.STANDARD HYDROGEN CELL, SHE.

2 H2 H++(aq, 1 M) + 2e- <----> H(aq, 1 M) + 2e- <----> H22(g, 1 atm)(g, 1 atm)2 H2 H++(aq, 1 M) + 2e- <----> H(aq, 1 M) + 2e- <----> H22(g, 1 atm)(g, 1 atm)

EEoo = 0.0 V = 0.0 V

55

Zn/Zn2+ half-cell hooked to a SHE.Eo for the cell = +0.76 V

Zn/Zn2+ half-cell hooked to a SHE.Eo for the cell = +0.76 V

Volts

ZnH2

Salt Bridge

Zn2+ H+

Zn Zn2+ + 2e- OXIDATION ANODE

2 H+ + 2e- H2REDUCTIONCATHODE

- +

Volts

ZnH2

Salt Bridge

Zn2+ H+

Zn Zn2+ + 2e- OXIDATION ANODE

2 H+ + 2e- H2REDUCTIONCATHODE

- +

Negative Negative electrodeelectrode

Supplier Supplier of of

electronselectrons

Acceptor Acceptor of of

electronselectrons

Positive Positive electrodeelectrode

2 H2 H++ + 2e- --> H + 2e- --> H22

ReductionReductionCathodeCathode

Zn --> ZnZn --> Zn2+2+ + 2e- + 2e- OxidationOxidation

AnodeAnode

66

Reduction of HReduction of H++ by Zn by Zn

Figure 20.10Figure 20.10

77

Volts

ZnH2

Salt Bridge

Zn2+ H+

Zn Zn2+ + 2e- OXIDATION ANODE

2 H+ + 2e- H2REDUCTIONCATHODE

- +

Volts

ZnH2

Salt Bridge

Zn2+ H+

Zn Zn2+ + 2e- OXIDATION ANODE

2 H+ + 2e- H2REDUCTIONCATHODE

- +

Overall reaction is reduction of HOverall reaction is reduction of H++ by Zn metal. by Zn metal.

Zn(s) + 2 HZn(s) + 2 H++ (aq) --> Zn (aq) --> Zn2+2+ + H + H22(g)(g) E Eoo = +0.76 V = +0.76 V

Therefore, Therefore, EEoo for for Zn ---> ZnZn ---> Zn2+2+ (aq) + 2e- (aq) + 2e- is is +0.76 V+0.76 V

Zn is a Zn is a (better) (poorer)(better) (poorer) reducing agent than H reducing agent than H22..

88

Volts

CuH2

Salt Bridge

Cu2+ H+

Cu2+ + 2e- Cu REDUCTION CATHODE

H2 2 H+ + 2e-OXIDATION ANODE

-+

Volts

CuH2

Salt Bridge

Cu2+ H+

Cu2+ + 2e- Cu REDUCTION CATHODE

H2 2 H+ + 2e-OXIDATION ANODE

-+

Cu/CuCu/Cu2+2+ and H and H22/H/H++ Cell Cell

EEoo = +0.34 V = +0.34 V

Acceptor Acceptor of of

electronselectrons

Supplier Supplier of of

electronselectrons

CuCu2+2+ + 2e- --> Cu + 2e- --> CuReductionReductionCathodeCathode

HH22 --> 2 H --> 2 H++ + 2e- + 2e-

OxidationOxidationAnodeAnode

PositivePositive NegativeNegative

99

Cu/CuCu/Cu2+2+ and H and H22/H/H++ Cell Cell

Overall reaction is reduction of CuOverall reaction is reduction of Cu2+2+ by H by H22 gas. gas.

CuCu2+2+ (aq) + H (aq) + H22(g) ---> Cu(s) + 2 H(g) ---> Cu(s) + 2 H++(aq)(aq)

Measured Measured EEoo = +0.34 V = +0.34 V

Therefore, Therefore, EEoo for Cu for Cu2+2+ + 2e- ---> Cu + 2e- ---> Cu is is

Volts

CuH2

Salt Bridge

Cu2+ H+

Cu2+ + 2e- Cu REDUCTION CATHODE

H2 2 H+ + 2e-OXIDATION ANODE

-+

Volts

CuH2

Salt Bridge

Cu2+ H+

Cu2+ + 2e- Cu REDUCTION CATHODE

H2 2 H+ + 2e-OXIDATION ANODE

-+

+0.34 V+0.34 V

1010

Zn/Cu Electrochemical CellZn/Cu Electrochemical Cell

Zn(s) ---> ZnZn(s) ---> Zn2+2+(aq) + 2e-(aq) + 2e- EEoo = +0.76 V = +0.76 VCuCu2+2+(aq) + 2e- ---> Cu(s)(aq) + 2e- ---> Cu(s) EEoo = +0.34 V = +0.34 V------------------------------------------------------------------------------------------------------------------------------CuCu2+2+(aq) + Zn(s) ---> Zn(aq) + Zn(s) ---> Zn2+2+(aq) + Cu(s) (aq) + Cu(s)

EEoo (calc’d) = +1.10 V (calc’d) = +1.10 V

Cathode, Cathode, positive, positive, sink for sink for electronselectrons

Anode, Anode, negative, negative, source of source of electronselectrons

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons ++

1111

Uses of EUses of Eoo Values ValuesUses of EUses of Eoo Values Values

• Organize half-Organize half-reactions by reactions by relative ability to relative ability to act as oxidizing act as oxidizing agentsagents

• Table 20.1Table 20.1

• Use this to predict Use this to predict cell potentials and cell potentials and direction of redox direction of redox reactions.reactions.

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

Zn

Zn2+ ions

Cu

Cu2+ ions

wire

saltbridge

electrons

1212

TABLE OF STANDARD TABLE OF STANDARD REDUCTION POTENTIALSREDUCTION POTENTIALS

TABLE OF STANDARD TABLE OF STANDARD REDUCTION POTENTIALSREDUCTION POTENTIALS

2

Eo (V)

Cu2+ + 2e- Cu +0.34

2 H+ + 2e- H 0.00

Zn 2+ + 2e- Zn -0.76

oxidizingability of ion

reducing abilityof element

1313

Potential Ladder for Reduction Half-ReactionsPotential Ladder for Reduction Half-ReactionsFigure 20.11Figure 20.11

1414

1515

Using Standard Potentials, EUsing Standard Potentials, Eoo

Table 20.1Table 20.1

• Which is the best oxidizing agent:

O2, H2O2, or Cl2? _________________

• Which is the best reducing agent:

Hg, Al, or Sn? ____________________

1616

Standard Redox Potentials, EStandard Redox Potentials, Eoo

Cu2+ + 2e- Cu +0.34

+2 H + 2e- H2 0.00

Zn2+ + 2e- Zn -0.76

Northwest-southeast rule:Northwest-southeast rule: product-favored product-favored reactions occur between reducing agent at reactions occur between reducing agent at

southeast corner (anode) and oxidizing agent southeast corner (anode) and oxidizing agent at northwest corner (cathode). at northwest corner (cathode).

Any substance on the right will reduce any Any substance on the right will reduce any substance higher than it on the left.substance higher than it on the left.

1717

Standard Redox Potentials, EStandard Redox Potentials, Eoo

Any substance on the right Any substance on the right will reduce any substance will reduce any substance higher than it on the left.higher than it on the left.

• Zn can reduce HZn can reduce H++ and and CuCu2+2+..

• HH22 can reduce Cu can reduce Cu2+2+ but but

not Znnot Zn2+2+

• Cu cannot reduce HCu cannot reduce H++ or or ZnZn2+2+..

Eo (V)

Cu2+ + 2e- Cu +0.34

2 H+ + 2e- H2 0.00

Zn2+ + 2e- Zn -0.76

oxidizingability of ion

reducing abilityof element

Eo (V)

Cu2+ + 2e- Cu +0.34

2 H+ + 2e- H2 0.00

Zn2+ + 2e- Zn -0.76

oxidizingability of ion

reducing abilityof element

1818

Using Standard Potentials, EUsing Standard Potentials, Eoo

Table 20.1Table 20.1

• In which direction do the following reactions In which direction do the following reactions

go?go?

• Cu(s) + 2 AgCu(s) + 2 Ag++(aq) ---> Cu(aq) ---> Cu2+2+(aq) + 2 Ag(s)(aq) + 2 Ag(s)

• 2 Fe2 Fe2+2+(aq) +(aq) + Sn2+(aq) ---> 2 Fe3+(aq) + Sn(s)

• What is Eonet for the overall reaction?

1919

Standard Redox Standard Redox Potentials, EPotentials, Eoo

E˚E˚netnet = “distance” from “top” half-reaction = “distance” from “top” half-reaction

(cathode)(cathode) to “bottom” half-reaction to “bottom” half-reaction (anode)(anode)

E˚E˚netnet = E˚ = E˚cathodecathode - E˚ - E˚anodeanode

EEoonetnet for Cu/Ag+ reaction = +0.46 V for Cu/Ag+ reaction = +0.46 V

2020

Volts

Cd Salt Bridge

Cd2+

Fe

Fe2+

Volts

Cd Salt Bridge

Cd2+

Fe

Fe2+

Cd --> CdCd --> Cd2+2+ + 2e- + 2e-oror

CdCd2+2+ + 2e- --> Cd + 2e- --> Cd

Fe --> FeFe --> Fe2+2+ + 2e- + 2e-oror

FeFe2+2+ + 2e- --> Fe + 2e- --> Fe

EEoo for a Voltaic Cell for a Voltaic Cell

All ingredients are present. Which way does All ingredients are present. Which way does reaction proceed?reaction proceed?

2121

From the table, you see From the table, you see

•• Fe is a better reducing Fe is a better reducing agent than Cdagent than Cd

•• CdCd2+2+ is a better is a better oxidizing agent than oxidizing agent than FeFe2+2+

Volts

Cd Salt Bridge

Cd2+

Fe

Fe2+

Volts

Cd Salt Bridge

Cd2+

Fe

Fe2+

EEoo for a Voltaic Cell for a Voltaic Cell

Overall reactionOverall reactionFe + CdFe + Cd2+2+ ---> Cd + Fe ---> Cd + Fe2+2+

EEoo = E˚ = E˚cathodecathode - E˚ - E˚anodeanode

= (-0.40 V) - (-0.44 V) = (-0.40 V) - (-0.44 V) = +0.04 V= +0.04 V

2222More About More About Calculating Cell VoltageCalculating Cell Voltage

Assume IAssume I-- ion can reduce water. ion can reduce water.

2 H2O + 2e- ---> H2 + 2 OH- Cathode2 I- ---> I2 + 2e- Anode-------------------------------------------------2 I- + 2 H2O --> I2 + 2 OH- + H2

2 H2O + 2e- ---> H2 + 2 OH- Cathode2 I- ---> I2 + 2e- Anode-------------------------------------------------2 I- + 2 H2O --> I2 + 2 OH- + H2

Assuming reaction occurs as written, Assuming reaction occurs as written,

E˚E˚netnet = E˚ = E˚cathodecathode - E˚ - E˚anodeanode

= (-0.828 V) - (+0.535 V) = = (-0.828 V) - (+0.535 V) = -1.363 V-1.363 V

Minus E˚ means rxn. occurs in opposite Minus E˚ means rxn. occurs in opposite

directiondirection

2323

Is E˚ related to ∆G?Is E˚ related to ∆G? YES!YES!

2424

Michael FaradayMichael Faraday1791-18671791-1867

Originated the terms anode, Originated the terms anode, cathode, anion, cation, cathode, anion, cation, electrode.electrode.

Discoverer of Discoverer of

• electrolysiselectrolysis

• magnetic props. of mattermagnetic props. of matter

• electromagnetic inductionelectromagnetic induction

• benzene and other organic benzene and other organic chemicalschemicals

Was a popular lecturer.Was a popular lecturer.

2525

EEoo and ∆G and ∆Goo

EEoo is related to ∆G is related to ∆Goo, the free , the free energy change for the reaction.energy change for the reaction.

∆∆GGoo = - n F E = - n F Eoo where F = Faraday constant where F = Faraday constant

= 9.6485 x 10= 9.6485 x 1044 J/V•molJ/V•mol

and n is the number of moles of and n is the number of moles of electrons transferredelectrons transferred

Michael FaradayMichael Faraday1791-18671791-1867

2626

EEoo and ∆G and ∆Goo

∆∆GGoo = - n F E = - n F Eoo

For a For a product-favoredproduct-favored reaction reaction

Reactants ----> ProductsReactants ----> Products

∆∆GGo o < 0 and so E < 0 and so Eo o > 0 > 0

EEoo is positive is positive

For a For a reactant-favoredreactant-favored reaction reaction

Reactants <---- ProductsReactants <---- Products

∆∆GGo o > 0 and so E > 0 and so Eo o < 0 < 0

EEoo is negative is negative

2727E at Nonstandard E at Nonstandard ConditionsConditions

• The The NERNST EQUATIONNERNST EQUATION• E = potential under nonstandard conditionsE = potential under nonstandard conditions

• n = no. of electrons exchangedn = no. of electrons exchanged

• ln = “natural log”ln = “natural log”

• If [P] and [R] = 1 mol/L, then E = E˚If [P] and [R] = 1 mol/L, then E = E˚

• If [R] > [P], then E is ______________ than E˚If [R] > [P], then E is ______________ than E˚

• If [R] < [P], then E is ______________ than E˚If [R] < [P], then E is ______________ than E˚

E EÞ - 0.0257 V

n ln

[Products][Reactants]

E EÞ - 0.0257 V

n ln

[Products][Reactants]