Chapter 7 Electrochemistry
§7.7 Thermodynamics of reversible cell
7.7.1. Measurement of Electromotive forces (emf's)
What is electromotive forces?
Can voltameter be used to measure electromotive force?
U
E  ( Ro  Ri ) I
V
Ro
Ro  Ri
E
U
Ro
Ri
E
 1
U
Ro
E Ri
U
I
Ro
Discussion
High-impedance input
1) Poggendorff’s compensation method
Es
i = 0, thermodynamic reversibility.
Ew
A
A
B
C2
C1
Ex
Ex
K
G
EW: working cell
Ex: test cell
Es: standard cell
Es
Principle of potentiometer
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.
2) Weston standard cell
Cork sealed with
paraffin or wax
Saturated
CdSO4
solution
8
CdSO 4  H 2 O
3
Hg2SO4
Cd(Hg)x
Hg
Commercial Weston Standard cell
+
--
8
Cd(5%  12%)(Hg) xCdSO 4  H 2O(s)CdSO 4 (sat)
3
8
CdSO 4  H 2 O(s)HgSO 4 (s)Hg(l)+
3
Weston standard cell
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
Temperature-dependence of emf
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
2. Nernst equation and standard EMF of cell
1889, Nernst empirical equation
cC + dD = gG + hH
RT aGr aHh
EE 
ln c d
nF aC aD
Walther H.
1920
Noble Prize
Nernst
Germany
1864/06/25~1941/11/18
Studies on thermodynamics
physical meaning of E
Theoretical deduction of Nernst Equation:
For a general electrochemical reaction:
cC + dD = gG + hH
Van’t Horff equation
Δ r Gm  nFE
aGg aHh
Ka  c d
aC aD
aGg aHh
Δ r Gm  Δ r Gm  RT ln c d
aC aD
Δ r Gm  nFE
RT aGr aHh
EE 
ln c d
nF aC aD
7.7.3. Standard electromotive forces
RT aGr aHh
EE 
ln c d
nF aC aD
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.
E
2 RT
2 RTA
ln m  E 
m
F
F
Experimental determination of standard electromotive force
0.075
E/V
0.074
0.073
0.072
E
0.071
0.070
2.0x10-4
4.0x10-4
6.0x10-4
m / mol  kg 1
Cf. Levine, p. 430
7.7.4. Temperature-dependence of emf's
For Weston Standard Cell:
E/V = 1.018646 - 4.0510-5(T/℃-20) - 9.510-7 (T/℃-20)2 +
110-8(T/℃-20)3
Temperature coefficient:
 E 
5
-1

  10 V  K
 T  p
By differentiating the equation
- rGm = nFE
with respect to temperature, we obtain
 (Δ r Gm ) 
 E 


  ΔS  nF 

T

T

p

p
 E 
ΔS  nF 


T

p
 E 
Qre  TΔS  nFT 


T

p
  E 

 E 
Δ r H m  Δ r Gm  TΔ r S m  nFE  nFT 
  nF T 
  E
 T  p
  T  p

ΔG  nFE
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
1
1
H 2 ( p )  Cl2 ( p )  H  (aq)  Cl  (aq)
2
2
Δ r H m  Δ f H m [H + (aq)]  Δ f H m [Cl (aq)]  167kJ  mol 1
How to solve this deadlock?
The customary convention is to take the standard free energy of
formation of H+(aq) at any temperatures to be zero.
Δ f Gm [H + (aq)]  0
Δ r H m  Δ f H m [H + (aq)]  Δ f H m [Cl- (aq)]
 167kJ  mol 1
Δ f H m [H + (aq)]  0
Δ f H m [Cl- (aq)]  167kJ  mol1
Sm [H + (aq)]  0
1
Cl2 ( p )  e  Cl (aq)
2
K+
Na+
Cl
H+
Br
Mg2+
Ca2+
By definition
I
Standard free energies of formation of aqueous ions at 298.3 K
Ion
ΔGm / kJ·mol-1
Ion
ΔGm / 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
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.
Exercise-2
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.
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