Lecture 5: EquilibriumLecture 5: Equilibrium Electrochemistry

17-11-2009

• Lecture plan:Lecture plan:– representing redox reactions in terms of half-

reactionsreactions– electrochemical cells– the Nernst equation– standard potentials and electrode calibrationsta da d pote t a s a d e ect ode ca b at o– problems

Equilibrium electrochemistry

2 2( ) ( ) ( ) ( )Zn s Cu aq Zn aq Cu s+ ++ +

2

2

( ) ( ) 2( ) 2 ( )

Zn s Zn aq eC C

+

+

+

+

• Any redox reaction can be expressed as difference of two half reactions

( ) 2 ( )Cu aq e Cu s+

as difference of two half-reactions, which are conceptual reactions showing gain of electrons

Ox Redeν −+ →

Equilibrium electrochemistry

• Two half-reactions will run in the opposite directions in two half cells

1 1Ox Redeν −+ →Cathode

2 2Red Ox eν −→ +Anode

The electrode where oxidation occurs isThe electrode where oxidation occurs is called anode, the electrode where reduction occurs is called cathode.

Electrolyte

Electrochemical cells

Notation:

4 4( ) | ( ) ( ) | ( )Zn s ZnSO aq CuSO aq Cu s 4 4( ) | ( ) || ( ) | ( )Zn s ZnSO aq CuSO aq Cu s

Li id j ti Liquid junction potentialPh b d Liquid junction Liquid junction potential assumed eliminated

Phase boundary

Types of half-cells

M t l i t t ith it• Metal in a solution of

it’s ions

• Metal in contact with its insoluble salt

( ) ( )AgCl s e Ag s Cl− −+ → +2 2Zn e Zn+ −+ →

• Two different oxidation • Gas in contact with a

solution of it’s ionsstates of the same species

3 2Fe e Fe+ − ++ →2 2H e H+ −+ → Fe e Fe+ →22 2H e H+ →

The Nernst equation• A cell where overall cell reaction hasn’t reached chemical

equilibrium can do electrical work as the reaction drives electrons through an external circuitelectrons through an external circuit

,maxe rw GFE G

= Δ

ΔrFE Gν− = ΔFaraday constant AF eN=

Cell emf:rGEFν

Δ= −

Cell emf:

Fν0

0ln lnrG RT RTE Q E QΔ= =ln lnE Q E Q

F F Fν ν ν= − − = −

• As there is no potential difference at equilibrium:0

ln FEKRT

ν=

Standard potentials and SHE• Although it’s not possible to measure potentials of electrodes separately,

we can define a particular electrode as having zero potential at all temperaturestemperatures.

Standard Hydrogen Electrode (SHE) at aH+=1 (pH=0) and p=1bar

02( ) | ( ) | ( ) 0Pt s H g H aq E+ =

22 2H e H+ −+

Standard potentials and SHE• All other electrodes can be calibrated using SHE:

(“Harned cell” – calibration of Ag/AgCl electrode)

2( ) | ( ) | ( ) | ( ) | ( ) | ( )1 ( ) ( ) ( ) ( )

Pt s H g H aq HCl aq AgCl s Ag s

l l

+

21 ( ) ( ) ( ) ( )2

H g AgCl s HCl aq Ag s+ → +

2

01/ 2( / , ) ln H Cl

H

a aRTE E AgCl Ag ClF a

+ −−= −

0 0 2 2ln ln lnH Cl

RT RT RTE E a a E bF F F

γ+ − ±= − = − −

1202 lnRTE b E Cb+ = +For experimental calibration:

Fp

Standard efm can be found from the offset

Adding electrochemical reaction (Hess law)• Hess law

“Standard enthalpy of an overall chemical reaction is the sum of the standard enthalpies of the individual reactions it can be divided into”standard enthalpies of the individual reactions it can be divided into is applicable to the thermodynamic functions (∆G, ∆H etc.)

2 0

0

( ) 2 ( ) 0.340( ) ( ) 0.522

Cu aq e Cu s ECu aq e Cu s E

+ −

+ −

+ → = +

+ → = +

0

0

2*0.340 /

1*0.522 /r

r

G F

G F

Δ = −

Δ = −( ) ( )q r

2 0( ) ( ) ???Cu aq e Cu aq E+ − ++ → =0 00.158 (2*0.340 0.522) /E G F= + Δ = − −( ) ( ) ???Cu aq e Cu aq E+ → 0.158 (2 0.340 0.522) /rE G F+ Δ

Electrochemical series• Cell emfs are convenient source for data on equilibrium constants, Gibbs

energies etc.

0 0 00 0 01 1 2 2 2 1Red ,Ox ||Red ,Ox E E E= −

0 0Red1 has thermodynamic tendency to reduce Ox2 if: 0 02 1E E>

low reduces highlow reduces high

Species selective electrodes

• Ion-selective electrode is an electrode that generates t ti l i t th f l tia potential in response to the presence of a solution

of specific ions

Determination of thermodynamic functions by emf

• By measuring emf Gibbs energy can be determined:0 0G FEνΔrG FEνΔ = −

• The temperature coefficient of standard emf gives p gstandard entropy of the reaction:

doesn’t depend on pressure

00rSdE Δ

=

doesn t depend on pressure

dT Fν• and therefore provides non-calorimetric way to

00 0 0 0 dEH G T S F E Tν

⎛ ⎞Δ = Δ + Δ = − −⎜ ⎟

measure enthalpy

r r rH G T S F E TdT

νΔ = Δ + Δ = ⎜ ⎟⎝ ⎠

Application: Batteries• Lead-acid rechargeable battery (inv. 1859)

2 04 ( ) ( ) 2 ( ) 2 1 685PbO H SO PbSO H O E+ − −+ + + → +2 02 4 4 2

2 04 4

4 ( ) ( ) 2 ( ) 2 1.685

( ) ( ) ( ) 2 0.356

PbO H aq SO aq e PbSO s H O E

Pb s SO aq PbSO s e E

+

− −

+ + + → + =

+ → + = −

D i th h i th ti d• During the charging, the reactions are reversed• Life time is limited due to mechanical stress due to formation

and dissolution of solid materialand dissolution of solid material

• Alkaline cell:0

20

( ) 2 ( ) ( ) 2 1.1

2 ( ) 2 ( ) 2 ( ) 0 76

Zn s OH aq ZnO s H O e E

M O H O M O OH E

− −

− −

+ → + + =0

2 2 2 32 ( ) 2 ( ) 2 ( ) 0.76MnO s H O e Mn O s OH aq E+ + → + = −

Structure of metal-electrolyte interface• Formation of electrical double layer due to

specifically and non-specifically adsorbed ionsp y p y

Measuring absolute half-cell potential• The energy diagram of the cell:

k f ti

double layer

work function in solution

Fermi levels of two metals should be offset by the Gibbs energy

Measuring absolute half-cell potential• Gomer and Tryson experiment (J.Chem.Phys 66(1977), 4413):

variable DC voltage is applied to the gold-electrode capacitor with a vibrating plate, AC voltage is measured p , g

Vdc=0

Vdc=Vm2Au

E V φ• Absolute half cell potential for gold air electrode can be measured

2Au M Au AuE V φ= −

• Absolute SHE potential 0 4.73SHEE V= −

New problems

• Atkins 7.15(a) Devise cells in which the following are the reactions and calculate the standard emf in each case:reactions and calculate the standard emf in each case:(a) Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s)(b) 2 AgCl(s) + H2(g) → 2 HCl(aq) + 2 Ag(s)(c) 2 H2(g) + O2(g) → 2 H2O(l)

• Atkins 7.16(a) Use the Debye-Huckel limiting law and the ( ) y gNernst equation to estimate the potential of the cell

Ag|AgBr(s)|KBr(aq,0.050mol/kg)||Cd(NO3)2(aq, 0.010mol/kg) |CdAg|AgBr(s)|KBr(aq,0.050mol/kg)||Cd(NO3)2(aq, 0.010mol/kg) |Cd

at 25°C.• Atkins 7 18(a) The emf of the cellAtkins 7.18(a) The emf of the cell

Ag|AgI(s)|AgI(aq)|Ag is +0.9509 V at 25°C. Calculate (a) the solubility product of AgI and (b) its solubility.

Last lecture problems

• Atkins 6.9b: sketch the phase diagram of th t NH /N H i th t th tthe system NH3/N2H4 given that the two substances do not form a compound and NH3 freezes at -78C, N2H4 freezes at 3 , 2 4+2C, eutectic formed with mole fraction of N2H4 0.07 and melts at -80C.Atki 6 10b D ib th di d• Atkins 6.10b Describe the diagram and what is observed when a and b are cooled down

Assignment V• P7.16. Consider the cell

Zn(s)|ZnCl2(aq, 0.005 mol/kg)|Hg2Cl2(s)|Hg(l)f hi h th ti ifor which the reaction is

22 2 ( ) ( ) 2 ( ) 2 ( ) ( )Hg Cl s Zn s Hg l Cl aq Zn aq− ++ → + +

• Given that 0 2 02 2( , ) 0.7628; ( , ) 0.2676E Zn Zn E Hg Cl Hg+ = − = +

• and the measured emf E=+1.2272a) write the Nernst equation for the cellb) determine the standard emfc) find ∆ G ∆ G0 and K for the cell reactionc) find ∆rG, ∆rG0 and K for the cell reactiond) the mean ionic activity and activity coefficient for ZnCl2 from the

measured cell potential e) the mean ionic activity and activity coefficient for ZnCl2 from the

Debye-Huckel limiting lawf) given the emf temperature coefficient 4 52·10-4 V/K calculate ∆Sf) given the emf temperature coefficient -4.52·10 4 V/K calculate ∆S,

∆H.