out-class extensive reading - shandong university

§7.7 Thermodynamics of reversible cell

Out-class extensive reading:

Ira N. Levine, pp. 294-310

Section 10.10 standard-state thermodynamic properties of solution components

pp. 426

Section 14.6 thermodynamics of galvanic cells

Goals of this class:


(1) Understand the principle for determining EMF: high input voltmeter and

compensation.

(2) Demonstrate the component of Weston standard cell;

(3) Nernst equation: theoretical deduction and application;

(4) Apply the principle for determining thermodynamic quantities from

electrochemical measurements;

(5) Understand the principles of relative standard;

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 voltameter


(1) Poggendorff’s compensation method i = 0, thermodynamic reversibility.

EW: working cell

Ex: test cell

Es: standard cell

A

Es

Ex

Principle of potentiometer

G

Ew

Ex

Es

K

A B

C1 C2



(2) Weston 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.



http://en.wikipedia.org/wiki/File:Westoncell_Volt.png

http://en.wikipedia.org/wiki/File:Westoncell_Volt.png

Hg

Hg2SO4

4 2

8CdSO H O

3

Saturated

CdSO4 solution

Cd(Hg)x

+ --

Cork sealed with paraffinor wax

Commercial Weston Standard cell

4 2 4 4 2 4

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

3 3x




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

Temperature-dependence of emfThe 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




7.7.2 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

cC + dD = gG + hH

Walther H. Nernst

1920 Noble Prize

Germany

1864/06/25~1941/11/18

Studies on thermodynamics

What is the 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

r mΔ G nFE r mΔ G nFE

G H

C D

lnr h

c d

a aRTE E

nF a a

Theoretical deduction of Nernst Equation:

7.7.2 Nernst equation and standard EMF of cell


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.

7.7.3. Standard electromotive forces


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

Experimental 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) -

9.510-7 (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 Δ

p p

H G T S

E EnFE nFT nF T E

T T

re Δp

EQ T S nFT

T

ΔG nFE

Δp

ES nF

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.

7.7.5. Thermodynamic quantities of ions

2 2

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

2 2p p

+

r m f m f m

1

Δ Δ [H (aq)] Δ [Cl (aq)]

167kJ mol

H H H

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

+

f mΔ [H (aq)] 0H

+

m [H (aq)] 0S

How to solve this deadlock?

- 1

f mΔ [Cl (aq)] 167kJ molH

2

1Cl ( ) e Cl (aq)

2p


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

mΔGmΔG

7.7.5. Thermodynamic quantities of ions


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


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