Chapter 7 Electrochemistry

§7.7 Thermodynamics of reversible cell

7.7.1. Measurement of Electromotive forces (emf's)

Can voltameter be used to measure electromotive force?

IRRE io )( oR

UI

UR

RRE

o

io

o

i

R

R

U

E1

V

E Ri

Ro

U

Discussion

What is electromotive forces?

High-impedance input

1) Poggendorff’s compensation method

i = 0, thermodynamic reversibility.

Principle of potentiometer

EW: working cell

Ex: test cell

Es: standard cell

A

Es

Ex G

Ew

Ex

Es

K

A B

C1 C2

2) Weston standard cell

Drawing from Edward Weston's US Patent 494827 depicting the standard cell

The Weston cell, is a wet-chemical cell that produces a highly stable voltage suitable as a laboratory standard for calibration of voltmeters. Invented by Edward Weston in 1893, it was adopted as the International Standard for EMF between 1911 and 1990.

Hg

Hg2SO4

4 2

8CdSO H O

3

Saturated CdSO4 solution

Cd(Hg)x

+ --

Cork sealed with paraffin or wax

Commercial Weston Standard cell

2) Weston standard cell

4 2 4

4 2 4

8Cd(5% 12%)(Hg) CdSO H O(s) CdSO (sat)

38

CdSO H O(s) HgSO (s) Hg(l)+3

x

E(T) /V = 1.01845 – 4.05 10-5(T/K –293.15)

– 9.5 10-7(T/K –293.15)2 + 1 10-8 (T/K –293.15)3

Weston standard cell

Temperature-dependence of emf

The original design was a saturated cadmium cell producing a

convenient 1.018638 Volt reference and had the advantage of having

a lower temperature coefficient than the previously used Clark cell

2. Nernst equation and standard EMF of cell

1889, Nernst empirical equation

G H

C D

lnr h

c d

a aRTE E

nF a a y

cC + dD = gG + hH

Walther H. Nernst1920 Noble Prize

Germany1864/06/25~1941/11/18Studies on thermodynamics

physical meaning of E

For a general electrochemical reaction:

cC + dD = gG + hH G H

C D

g h

a c d

a aK

a a

Van’t Horff equation G Hr m r m

C D

Δ Δ lng h

c d

a aG G RT

a a y

r mΔ G nFE r mΔ G nFEy y

G H

C D

lnr h

c d

a aRTE E

nF a a y

Theoretical deduction of Nernst Equation:

7.7.3. Standard electromotive forces

G H

C D

lnr h

c d

a aRTE E

nF a a y

EӨ equals E when the activity of any chemical species is unit.

For cell: Pb(s)-PbO(s)|OH–(c)|HgO(s)-Hg(l)

Write out the cell reaction and Nernst equation.

For: Pt(s), H2 (g, p)|HCl(m) |AgCl(s)-Ag(s)

Write out the cell reaction and Nernst equation.

2 2ln

RT RTAE m E m

F F y

2.0x10-4 4.0x10-4 6.0x10-40.070

0.071

0.072

0.073

0.074

0.075

E

1/ mol kgm

E /

VExperimental determination of standard electromotive force

Cf. Levine, p. 430

7.7.4. Temperature-dependence of emf's

Temperature coefficient:

For Weston Standard Cell:

E/V = 1.018646 - 4.0510-5(T/ -20) - 9.5℃ 10-7 (T/ -20)℃ 2 +

110-8(T/ -20)℃ 3

By differentiating the equation

- rGm = nFE

with respect to temperature, we obtain

r m(Δ )Δ

pp

G ES nF

T T

1-5 KV 10

pT

E

r m r m r mΔ Δ Δp p

E EH G T S nFE nFT nF T E

T T

By measuring E and (E/T)p, thermodynamic quantities of the

cell reaction can be determined.

Because E and (E/T)p can be easily measured with high

accuracy, historically, the thermodynamic data usually measured

using electrochemical method other than thermal method.

re Δp

EQ T S nFT

T

ΔG nFE

Δp

ES nF

T

7.7.5. Thermodynamic quantities of ions

2 2

1 1H ( ) Cl ( ) H (aq) Cl (aq)

2 2p p y y

+ 1r m f m f mΔ Δ [H (aq)] Δ [Cl (aq)] 167kJ molH H H y y y

The customary convention is to take the standard free energy of formation of H+(aq) at any temperatures to be zero.

+f mΔ [H (aq)] 0G y

+f mΔ [H (aq)] 0H y

+m [H (aq)] 0S y

How to solve this deadlock?

- 1f mΔ [Cl (aq)] 167kJ molH y

2

1Cl ( ) e Cl (aq)

2p y

+ -r m f m f m

1

Δ Δ [H (aq)] Δ [Cl (aq)]

167kJ mol

H H H

y y y

Ion / kJ·mol-1 Ion / kJ·mol-1

H+ 0.000 OH -157.3

Li+ -298.3 Cl -276.5

Na+ -261.87 Br -131.2

K+ -282.3 SO42 -742.0

Ag+ 77.1 CO32 -528.1

Standard free energies of formation of aqueous ions at 298.3 K

mΔGymΔGy

H+

Cl

Br

I

K+

Na+

Mg2+

Ca2+

By definition

Exercise-1

At 298 K, for cell

Ag(s)-AgCl(s)|KCl(m)|Hg2Cl2(s)-Hg(l),

E = 0.0455V, (E/T)p = 3.38 10-4 V·K-1. Write the cell

reaction and calculate rGm, rSm, rHm, and Qre.

At 198 K, for cell

Pt(s), H2(g, p)|KOH(aq)|HgO(s)-Hg(l)

E = 0.926 V, product of water Kw=10-14. Given fGm of

HgO(s) is –58.5 kJ· mol-1, calculate fGm of OH.

Exercise-2

Self reading:

Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002.

pp. 294-310

Section 10.10 standard-state thermodynamic properties of solution components

pp. 426

Section 14.6 thermodynamics of galvanic cells

Section 14.7 standard electrode potentials

Section 14.8 concentration cells

Section 14.9 liquid-junction potential