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Chemistry 232 Electrochemistry

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Chemistry 232. Electrochemistry. A Schematic Galvanic Cell. Galvanic cells – an electrochemical cell that drives electrons through an external circuit spontaneous redox reaction occurring inside cell. . e -. Porous Disk. e -. e -. Oxidizing Agent. Reducing Agent. Anode. Cathode. - PowerPoint PPT Presentation

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Page 1: Chemistry 232

Chemistry 232

Electrochemistry

Page 2: Chemistry 232

A Schematic Galvanic Cell

Galvanic cells – • an electrochemical

cell that drives electrons through an external circuit

• spontaneous redox reaction occurring inside cell.

Anode Cathode

e-

Reducing Agent

e-

e-

Oxidizing Agent

Porous Disk

Page 3: Chemistry 232

The Zinc/Copper galvanic cell.

e-

1.10 V

a(Zn2+) = 1.00e-

e-

Anode Cathode

Porous Disk or Salt BridgeZn(s) Cu(s)

e-

a(Cu2+) = 1.00

The Zn/Cu Galvanic Cell

Cu2+ (aq) + 2 e- Cu (s) (cathode, RHS)

Zn2+ (aq) + 2 e- Zn (s) (anode, LHS)

Page 4: Chemistry 232

Cell Reactions The difference in the RHS and the LHS reaction

Cu2+ (aq) + Zn (s) Cu (s) + Zn2+ (aq) For each half reaction, we can write the reaction

quotient as followsCu2+ (aq) + 2 e- Cu (s) Q = 1/ a(Cu2+) Zn2+ (aq) + 2 e- Zn (s) Q = 1/ a(Zn2+)

Overall Qcell = a(Zn2+) / a(Cu2+)

Page 5: Chemistry 232

Cell Diagrams A shorthand way of expressing what

takes place in an electrochemical cell. For the above electrochemical cell.

Pt Cu (s) Cu2+ (aq) Zn2+ (aq) Zn (s) Pt

Note phase boundary liquid junction

salt bridges

Page 6: Chemistry 232

Another Example The cell reaction

H2 (g) + Cu2+ (aq) 2 H+ (aq) + Cu (s)

Pt H2 (g) H+ (aq) Cu2+ (aq) Cu (s) Pt

Electrochemical cells a cell that has not reached equilibrium can

do electrical work by driving electrons through an external wire.

Page 7: Chemistry 232

Reversible Electrochemical Cells In order for us to make measurements on

an electrochemical cell, it must be operating reversibly. • Place an opposing source of potential in the

external circuit • Cell operates reversibly and at a constant

composition.

we,max = G

Page 8: Chemistry 232

The Measurement of Cell Potentials Measure the potential of an electrochemical cell

when the cell is at equilibrium, i.e., the state between the galvanic and the electrolytic cell.

e-

Reducing Agente-

e-

Oxidizing Agent

Anode Cathode

Porous Disk

Counter potential (load)

Page 9: Chemistry 232

Derivation of the Nernst Equation Consider an electrochemical cell that

approaches the equilibrium state by an infinitesimal amount d

d GddG rxnJJ

J Reminder

PTJ

JJr d

dG G,

Page 10: Chemistry 232

The Work in Transporting Charge The maximum work

d Gdw rxne max,

F = Faraday’s constant = e NA = 96485 C/mole

For the passage d electrons from the anode (LHS) to the cathode (RHS)

d Fd eN A

Page 11: Chemistry 232

The Cell Potential The work to transport charge

celle E d F dw max,

Gd

dwrxn

e

max,

cellrxn E- F G

Page 12: Chemistry 232

Standard Cell Potentials From the reaction Gibbs energy

cellcello

rr E F QRTGG ln

cellcell

orr E

F QRT

F G

F G

ln

We define

F GE

or

cell

Page 13: Chemistry 232

The Nernst Equation

E represents the standard cell potential, the potential of the cell when all cell components are under standard conditions. • f (all gases) = 1 • a (solutes) = 1• T = 298.15 K• P = 1.00 bar pressure

cellcell QF

RTEE ln

Page 14: Chemistry 232

Cells at Equilibrium When the electrochemical cell has

reached equilibrium

cellcellcell KQV 0E

Kcell = the equilibrium constant for the cell reaction.

RTFE KK

F RTE cellcell

lnln

Knowing the E° value for the cell, we can estimate the equilibrium constant for the cell reaction.

Page 15: Chemistry 232

Equilibrium Constant Calculations from Cell Potentials Examine the following cell.

Pt Sn2+ (aq), Sn4+ (aq) Fe3+ (aq) Fe2+ (aq) Pt

Half-cell reactions.Sn4+ (aq) + 2 e- Sn2+ (aq) E(Sn4+/Sn2+) = 0.15 VFe3+ (aq) + e- Fe2+ (aq) E (Fe3+/Fe2+) = 0.771 V

Cell ReactionSn2+ (aq) + 2 Fe3+ (aq) Sn4+ (aq) + 2 Fe2+ (aq)

Ecell = (0.771 - 0.15 V) = 0.62 V

Page 16: Chemistry 232

Standard Reduction Potentials Standard reduction potentials are

intensive properties. We cannot measure the potential of an

individual half-cell! We assign a particular cell as being our

reference cell Assign values to other electrodes on that

basis.

Page 17: Chemistry 232

a (H+) = 1.00

H2 (g)

e-

Pt gauze

The Standard Hydrogen Electrode Eo (H+/H2) half-cell = 0.000 V

f{H2(g)} = 1.00

Page 18: Chemistry 232

A Galvanic Cell With Zinc and the Standard Hydrogen Electrode.

e-

Zn2+, SO42-

a (H+) = 1.00

Anode Cathode

Porous Disk or Salt Bridge

Source of H+ (e.g.,HCl (aq), H2SO4 (aq))

a(Zn2+) = 1.00

H2 (g)

0.763 Ve-

Zn(s)

Pt gauze

Page 19: Chemistry 232

The Cell Equation for the Zinc-Standard Hydrogen Electrode. The cell reaction 2 H+ (aq) + Zn (s) H2 (g) + Zn2+ (aq)

Pt Zn (s) Zn2+ (aq),a=1 H+ (aq), a=1 H2 (g), f=1 Pt

When we measure the potential of this cell Ecell = ERHS - ELHS

but ERHS = E(H+/H2) = 0.000 V Ecell = E(Zn2+/Zn) = 0.763 V

Page 20: Chemistry 232

The Spontaneous Direction of a Cell Reaction Examine the magnitude the of the

standard cell potential!

F GE

orxn

cell

If the standard cell potential is positive, the rG is negative!

Page 21: Chemistry 232

The Composition Dependence of the Cell Potential Nonstandard cell potential (Ecell) will be a

function of the activities of the species in the cell reaction.

cellcell QF

RTEE ln

To calculate Ecell, we must know the cell reaction and the value of Qcell.

Page 22: Chemistry 232

Example For the following system

Pt H2 (g) H+ (aq) Cu2+ (aq) Cu (s) Pt

Calculate the value of the cell potential when the f (H2) = 0.50, a(Cu2+) = 0.20, and a(H+) = 0.40.

Page 23: Chemistry 232

Concentration Cells Electrolyte concentration cell

• the electrodes are identical; they simply differ in the concentration of electrolyte in the half-cells.

Page 24: Chemistry 232

Concentration Cells (II) Electrode concentration cells

• the electrodes themselves have different compositions. This may be due to.• Different fugacities of gases involved in

electrode reactions (e.g., The H+ (aq)/H2 (g) electrode).

• Different compositions of metal amalgams in electrode materials.

Page 25: Chemistry 232

Applications of Electrochemistry

Measurement of activities and activity coefficients.

Electrochemical series.

Equilibrium constants and thermodynamic functions of cell reactions

Page 26: Chemistry 232

Obtaining Standard Cell Potentials Look at the following cell

Pt H2 (g) HCl (aq) AgCl (s) Ag (s) Pt

)(ln2

cellcell HfCla Ha

FRTEE

Ecell = E(AgCl/Ag) - E (H+/H2) = E(AgCl/Ag)

Page 27: Chemistry 232

Ecell Values and Activity Coefficients In dilute solution, using the DHLL

21

cell mF

RT3442AgAgClEmF

RT6064E .)(log.

Plot LHS vs. m1/2

Once Ecell is known, we can obtain experimental estimates of the mean activity coefficients.

Page 28: Chemistry 232

The Calculation of Standard Cell Potentials

y = 0.0582x + 0.2222R2 = 0.9836

0.220

0.222

0.224

0.226

0.228

0.230

0.232

0.234

0.236

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Page 29: Chemistry 232

Electrochemical Series Look at the following series of reactions

Cu2+ (aq) + 2 e- Cu (s) E(Cu2+/Cu) = 0.337 VZn2+ (aq) + 2 e- Zn (s) E(Zn2+/Zn) = -0.763 V

Zn has a thermodynamic tendency to reduce Cu2+ (aq)

Pb2+ (aq) + 2 e- Pb (s) E(Pb2+/Pb) = -0.13 VFe2+ (aq) + 2 e- Fe (s) E(-Fe2+/Fe) = -0.44 V

Fe has a thermodynamic tendency to reduce Pb2+ (aq)

Page 30: Chemistry 232

Thermodynamic Information Note

GFEGr

PT

,

And GFE r

Page 31: Chemistry 232

Entropy Changes To obtain the entropy change for the cell

reaction

PPTPTrxn T

EFGT

SS

,,

P

PTrxnrxn TEFG

TS

,

Page 32: Chemistry 232

Enthalpy Changes To obtain the enthalpy change for the cell reaction

PTPTPTrxn

STGHH,,,

PTEFTFE

Prxn T

EFTFEH

Page 33: Chemistry 232

The Liquid Junction Potential Examine the following electrochemical

cell Activity difference of the HCl between

compartment 1 and compartment 2 There should be a transport of matter

from one cell compartment to the other!

Page 34: Chemistry 232

A Concentration Cell

e-

a (Cl -) = 0.0010

Left Right

Porous Disk or Salt Bridge

a(Cl-) = 0.010

0.0592Ve-

Ag(s) Ag(s)

Page 35: Chemistry 232

The Development of Liquid Junction Potentials The cell

compartments are identical except for the activities of the electrolyte solutions.

HCl (a1)

HCl (a2)

Ag/AgCl electrode

Page 36: Chemistry 232

Note that we now have the migration of both cations and anions through the liquid junction.

Cl-

Ag/AgCl electrode

H+

Page 37: Chemistry 232

After a period of time

------------ - - - -

Ag/AgCl electrode

+ + + + +

Page 38: Chemistry 232

Choose the lower compartment as our LHS electrode.

Ag AgCl Cl- (aq) a1 Cl- (aq), a2 AgCl (s) Ag (s)

Note: liquid junction

For the passage of one mole of charge through the cell

-F Ecell = GJ

Page 39: Chemistry 232

The Cell Reactions For the LHS and RHS electrodes

AgCl (s) + e- Ag (s) + Cl- (a1) LHSAgCl (s) + e- Ag (s) + Cl- (a2) RHS

Net changeCl- (a1) Cl- (a2)

Note that the charge at the interface is transported by the anions and cations in the cell reaction!

Page 40: Chemistry 232

The Transport Numbers How is the charge carried at the interface of the

cells?• t+ moles of charge carried by the H+ (cation).

• t- moles of charge carried by the Cl- (anion). Passage of one mole of “+” charge through the

interface • requires the passage of t+ moles of H+ (aq) from the LHS

RHS, and the passage of t- mole of Cl- charge from the RHS LHS.

Page 41: Chemistry 232

At the boundary t+ H+(a1) + t- Cl-(a2) t+ H+(a2) + t- Cl-(a1)

For the entire cellCl- (a1) t+ H+(a1) + t- Cl-(a2) Cl- (a2) t+ H+(a2) +

t- Cl-(a1) The cell reaction involves the transport of t+

moles of HCl from the LHS to the RHs of the cell.

Page 42: Chemistry 232

The Gibbs Energy Changes For the above cell reaction, we can write

the Gibbs energy expressions as follows

11

22

ClaRTClHaRTHtClaRTClHaRTHtG

)(ln)()(ln)()(ln)()(ln)(

1

2

ClaHaClaHaRTtG )()(

)()(ln

Page 43: Chemistry 232

Cells With Transference Note a(H+) a (Cl-) = {a (HCl)}2

1

2

HClaHClaRTt2G )(

)(ln

1

2wt HCla

HClaF

RTt2E )()(ln

Note that the cell potential with transference, Ewt is determined as follows

Page 44: Chemistry 232

Cells without Transference What if we were able to set up a cell so that the

transport at the interface did not contribute to the overall G?

The potential of this cell would be the cell potential without transference, Ewot.

Cl- (a1) Cl- (a2)

1

2

HClaHClaRTG )(

)(ln

1

2wot HCla

HClaF

RTE )()(ln

Page 45: Chemistry 232

The Liquid Junction Potential The liquid junction potential is the

difference in the cell potentials with and without transference!

wotwtLJ EEE

1

2LJ HCla

HClaF

RTt21E )()(ln

Page 46: Chemistry 232

L.J. Potentials Depend on Transport Numbers What is the following were true? t+ t- 0.5 ELJ would be very small

and would only make a small contribution to the overall cell potential !

Page 47: Chemistry 232

L.J. Potentials Depend on Transport Numbers ELJ a potential problem any time we

measure the cell potential whose electrodes have different electrolytes

How does the salt bridge help?• e.g., for species with t+ t- 0.5, the ELJ

values are small and are readily established!