Chemical equilibrium:
electrochemistry
자연과학대학 화학과
박영동 교수
Examples
In distilled water
Hg2(IO3)2 ⇄ Hg22+ + 2IO3
Ksp = 1.3 × 10-18
Ksp = [Hg22+][IO3]2 = x(2x)2 → x = [Hg22+] = 6.9 × 107
In 0.050 M KNO3
[Hg22+] = 1.0 × 106
→ 이온세기가 커지면 Hg22+ 와 IO3-간의 인력
은 순수한 물에서보다 줄어듦
→ 서로 합치려는 경향이 줌
→ Hg2(IO3)2 의 용해도가
!
Typical aqueous solution
𝑞
ϕ =
4𝜋𝜀𝑟
q1
q2
Examples
The activities of ions in solution
-
-
+
+
-
+
+
+
-
-
+
Fig. 5.33 The picture underlying the Debye-Hückel
theory is of a tendency for anions to be found around
cations, and of cations to be found around anions (one
such local clustering region is shown by the circle). The
ions are in ceaseless motion, and the diagram
represents a snapshot of their motion. The solutions to
which the theory applies are far less concentrated than
shown here.
Mean activity coefficients
Debye-Hückel limiting law.
where A = 0.509 for an aqueous solution
at 25°C and I is the dimensionless ionic
strength of the solution:
extended Debye-Hückel law
ionic strength of the solution:
Fig. 5.34 An experimental test
of the Debye-Hückel limiting
law.
Fig.5.35 The extended Debye-Hückel
law gives agreement with experiment
over a wider range of molalities.
The variation of the activity coefficient with ionic strength according
to the extended Debye–Hückel theory. (a) The limiting law for a 1,1electrolyte. (b) The extended law with B = 0.5. (c) The extended law,
extended further by the addition of a term CI; in this case with C =
0.2. The last form of the law reproduces the observed behaviour
reasonably well.
where A = 0.509 for an aqueous solution
at 25°C and I is the dimensionless ionic
strength of the solution:
Calculate the ionic strength and the mean activity
coefficient of 5.0×10-3 mol kg-1 KCl(aq) at 25°C.
I =½(b+ + b_)/bo= b/ bo
where b is the molality of the solution (and b+ = b_ = b).
log γ±= -0.509 × (5.0 × 10-3)1/2 = -0.036
Hence, γ± = 0.92. The experimental value is 0.927.
Self-test 5.8 Calculate the ionic strength and the
mean activity coefficient of 1.00 mmol kg-1 CaCl2
(aq) at 25°C.
Answer: [3.00 mmol kg-1, 0.880]
migration of ions
V = IR
R = ρL/A
κ = 1/ρ : conductivity
Λm = κ/c : molar conductivity
Λm = Λmo – Kc1/2
Λmo : limiting molar
conductivity
Λmo : = λ+ + λ−
Ionic conductivities
Table 9.1 Ionic conductivities, λ/(mS m2 mol−1)
Ionic mobilities in water
Ionic mobilities in water at 298 K, u/(10−8 m2 s−1 V−1)
Grotthus mechanism
Electrochemical cells
two electrodes share a
common electrolyte.
Figure 9.6 When the electrolytes in the
electrode compartments of a cell are
different, they need to be joined so that
ions can travel from one compartment to
another. One device for joining the two
compartments is a salt bridge.
a galvanic cell
Figure 9.7 The flow of electrons in
the external circuit is from the
anode of a galvanic cell, where
they have been lost in the
oxidation reaction, to the cathode,
where they are used in the
reduction reaction. Electrical
neutrality is preserved in the
electrolytes by the flow of cations
and anions in opposite directions
through the salt bridge.
an electrolytic cell
Figure 9.8 The flow of electrons
and ions in an electrolytic cell. An
external supply forces electrons
into the cathode, where they are
used to bring about a reduction,
and withdraws them from the
anode, which results in an
oxidation reaction at that electrode.
Cations migrate towards the
negatively charged cathode and
anions migrate towards the
positively charged anode. An
electrolytic cell usually consists of a
single compartment, but a number
of industrial versions have two
compartments.
The Standard Hydrogen Electrode
• Eo (H+/H2) half-cell = 0.000 V
ef{H2(g)} = 1.00
H2 (g)
a (H+) = 1.00
Pt gauze
a silver–silver-chloride electrode
Figure 9.10 The schematic
structure of a silver–silverchloride electrode (as an
example of an insoluble-salt
electrode). The electrode
consists of metallic silver
coated with a layer of silver
chloride in contact with a
solution containing Cl− ions.
a redox electrode
Figure 9.11 The schematic
structure of a redox electrode.
The platinum metal acts as a
source or sink for electrons
required for the
interconversion of (in this
case) Fe2+ and Fe3+ ions in the
surrounding solution.
A Daniell cell
Figure 9.12 A Daniell cell
consists of copper in
contact with copper(II)
sulfate solution and zinc in
contact with zinc sulfate
solution; the two
compartments are in
contact through the porous
pot that contains the zinc
sulfate solution. The
copper electrode is the
cathode and the zinc
electrode is the anode.
measurement of cell potential
Figure 9.13 The
potential of a cell is
measured by balancing
the cell against an
external potential that
opposes the reaction in
the cell. When there is
no current flow, the
external potential
difference is equal to
the cell potential.
The Nernst Equation
At 25.00°C,
Example 9.5
Calculating an equilibrium
constant
Calculate the equilibrium constant for the disproportionation reaction 2 Cu+(aq) ⇄ Cu(s) +
Cu2+(aq) at 298 K.
0
Strategy The aim is to find the values of 𝐸𝑐𝑒𝑙𝑙
corresponding to the reaction, for then we can use
eqn 9.16. To do so, we express the equation as the difference of two reduction half-reactions. The
stoichiometric number of the electron in these matching halfreactions is the value of V we require.
We then look up the standard potentials for the couples corresponding to the half-reactions and
0
calculate their difference to find 𝐸𝑐𝑒𝑙𝑙
. Use RT/F = 25.69 mV (written as 2.569 × 10−2 V).
Solution The two half-reactions are
The difference is
It then follows from eqn 9.16 with ν= 1, that
Therefore, because K = elnKK,
K = e37/2.569 = 1.8 × 106
Because the value of K is so large, the equilibrium lies strongly in favour of products, and Cu+
disproportionates almost totally in aqueous solution
A glass electrode
Figure 9.14 A glass electrode has
a potential that varies with the
hydrogen ion concentration in the
medium in which it is immersed.
It consists of a thin glass
membrane containing an
electrolyte and a silver chloride
electrode. The electrode is used in
conjunction with a calomel
(Hg2Cl2) electrode that makes
contact with the test solution
through a salt bridge; the
electrodes are normally combined
into a single unit.
Silver/Silver Chloride Electrode
m
0.00100
0.00322
0.00450
0.00562
0.00600
0.00750
0.00914
0.02563
0.04000
0.06000
0.08000
0.10000
0.12380
E
0.5788
0.5205
0.5037
0.4926
0.4894
0.4784
0.4686
0.4182
0.3965
0.3770
0.3630
0.3525
0.3420
m1/2
E+C
0.03162
0.05670
0.06708
0.07496
0.07746
0.08660
0.09559
0.16009
0.20000
0.24495
0.28284
0.31623
0.35185
0.22404
0.22575
0.22619
0.22646
0.22666
0.22712
0.22747
0.23007
0.23119
0.23251
0.23329
0.23425
0.23470
Temperature dependence of the
standard potential of a cell
Figure 9.15 The variation of the standard potential of a cell with
temperature depends on the standard entropy of the cell reaction.
Silver/Silver Chloride Electrode
Ag/AgCl Electrode
E0(V vs SHE)
25
0.22233
60
0.1968
125
0.1330
150
0.1032
175
0.0708
200
0.0348
225
-0.0051
250
-0.054
275
-0.090
E0(T) Ag/AgCl
0.30
0.20
Eo/V
T (°C)
E0(V) = 0.23735 - 5.3783x10-4t - 2.3728x10-6t2 2.2671x10-9(t+273) for 25 < t < 275 °C
0.10
0.00
-0.10
0
50
100
150
T/( oC)
200
250
300
Thermodynamic properties
Δ𝑟 𝐺 0 = −𝜈𝐹𝐸 0
and
𝜕𝐺 0 /𝜕𝑇 = −𝑆 0
Δ𝑟 𝐺 0 = −𝜈𝐹𝐸 0
𝑑𝐸 0 Δ𝑟 𝑆 0
=
𝑑𝑇
𝜈𝐹
Δ𝑟
𝐻0
= Δ𝑟
𝐺0
or
+ 𝑇Δ𝑟
𝑆0
Δ𝑟
=
𝑆0
𝑑𝐸 0
= 𝜈𝐹
𝑑𝑇
−𝜈𝐹(𝐸 0
−
𝑑𝐸 0
𝑇 𝑑𝑇 )
Thermodynamic properties
E0 = 0.22232 V
F = 96486 C mol-1