lecture #10 of 17ardo/echem/uci-chem248-2019s_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... a...
TRANSCRIPT
![Page 1: Lecture #10 of 17ardo/echem/UCI-CHEM248-2019S_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... A detailed review of Section 4.4.2 and Chapter 5 Fick’s Second Law of Diffusion Linear](https://reader034.vdocuments.mx/reader034/viewer/2022042112/5e8e6dbd686ba260181a7a89/html5/thumbnails/1.jpg)
691
Lecture #10 of 17
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692
Q: What’s in this set of lectures?
A: B&F Chapters 4 & 5 main concepts:
● Section 4.4.2: Fick’s Second Law of Diffusion
● Section 5.1: Overview of step experiments
● Section 5.2: Potential step under diffusion controlled
● Sections 5.3 & 5.9: Ultramicroelectrodes
● Sections 5.7 – 5.8: Chronoamperometry/Chronocoulometry
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693
693Wightman, Anal. Chem., 1981, 53, 1125A
… scanning is “often” steady-state at a UME
… steady-state occurs when v << RTD/(nFr02)
… v (mV s-1) << 26 mV x (D/r02)… for a BASi UME with r0 = 5 𝜇m…
… (1 x 10-5 cm2 s-1) / (0.5 x 10-3 cm)2 = 26 x 40 mV s-1s
… v << 1 V s-1… Wow!
RECALL FROM LAST TIME…
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694… additional/final points to address about UMEs:
1) You can buy them; how do you make them?
2) UME arrays and ensembles
3) Potential step experiments with UMEs…
4) How rapidly is steady-state attained?
![Page 5: Lecture #10 of 17ardo/echem/UCI-CHEM248-2019S_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... A detailed review of Section 4.4.2 and Chapter 5 Fick’s Second Law of Diffusion Linear](https://reader034.vdocuments.mx/reader034/viewer/2022042112/5e8e6dbd686ba260181a7a89/html5/thumbnails/5.jpg)
695… arrays of UMEs (from B&F)…
Semi-infinite linear diffusion
Semi-infinite mixed diffusion
Semi-infinite linear diffusion, again
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696
macroscopic planar electrode: 𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2
… this is because a UME must behave like a macroscopic
electrode at sufficiently small times, right?... Right!
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697
macroscopic planar electrode:
disk UME:
hemispherical UME:
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 4𝑛𝐹𝐷𝐶∗𝑟0
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 2𝜋𝑛𝐹𝐷𝐶∗𝑟0
… this is because a UME must behave like a macroscopic
electrode at sufficiently small times, right?... Right!
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698
Cottrell eq. steady-state
current eq.
macroscopic planar electrode:
disk UME:
hemispherical UME:
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 4𝑛𝐹𝐷𝐶∗𝑟0
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 2𝜋𝑛𝐹𝐷𝐶∗𝑟0
… this is because a UME must behave like a macroscopic
electrode at sufficiently small times, right?... Right!
![Page 9: Lecture #10 of 17ardo/echem/UCI-CHEM248-2019S_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... A detailed review of Section 4.4.2 and Chapter 5 Fick’s Second Law of Diffusion Linear](https://reader034.vdocuments.mx/reader034/viewer/2022042112/5e8e6dbd686ba260181a7a89/html5/thumbnails/9.jpg)
699… additional/final points to address about UMEs:
1) You can buy them; how do you make them?
2) UME arrays and ensembles… GOT IT!
3) Potential step experiments with UMEs…
4) How rapidly is steady-state attained?
![Page 10: Lecture #10 of 17ardo/echem/UCI-CHEM248-2019S_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... A detailed review of Section 4.4.2 and Chapter 5 Fick’s Second Law of Diffusion Linear](https://reader034.vdocuments.mx/reader034/viewer/2022042112/5e8e6dbd686ba260181a7a89/html5/thumbnails/10.jpg)
700
r0 = 10 µm
5 µm
1 µm2 µm
… at early times, the current asymptotically approaches il...
C* = 1 x 10-6 moles cm-3
D = 10-5 cm2 s-1
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701
r0 = 10 µm
5 µm
1 µm2 µm
C* = 1 x 10-6 moles cm-3
D = 10-5 cm2 s-1
… at early times, the current asymptotically approaches il...
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702
i(t)
Time-1/2, s-1/2
note that the i(t) versus (1/t1/2) plot no longer intersects “0”…
… and D can be calculated without knowing C*… How?
2𝜋𝑛𝐹𝐷𝐶∗𝑟0
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 2𝜋𝑛𝐹𝐷𝐶∗𝑟0
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703
i(t)
Time-1/2, s-1/2
note that the i(t) versus (1/t1/2) plot no longer intersects “0”…
… and D can be calculated without knowing C*… How?
* Two equations!
… calculate D1/2C* from slope…
and DC* from y-intercept
2𝜋𝑛𝐹𝐷𝐶∗𝑟0
𝑖 𝑡 =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 2𝜋𝑛𝐹𝐷𝐶∗𝑟0
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704… how long does it take for UME’s to attain steady-state?
r0 = 10 µm
5 µm
1 µm2 µm
Error =𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2+ 2𝜋𝑛𝐹𝐷𝐶∗𝑟0
𝑛𝐹𝐴𝐷1/2𝐶∗
𝜋1/2𝑡1/2
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705
r0 = 10 µm
5 µm
1 µm2 µm
25 seconds6.31.00.2
** Recall that these diffusional
processes only occur in the
absence of stirring
… how long does it take for UME’s to attain steady-state?
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706
r0 r0 tsteady-state
10-3 cm 10 µm 25 s
10-4 cm 1 µm 0.25 s
10-5 cm 100 nm 2.5 ms
10-6 cm 10 nm 25 µs
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707the short time limit imposed by RuCd for a macroscopic
electrode is ~100 µs…
… but UMEs are much faster!
r0 r0 tsteady-state RuCd*
10-3 cm 10 µm 25 s 1.7 µs
10-4 cm 1 µm 0.25 s 170 ns
10-5 cm 100 nm 2.5 ms 17 ns
10-6 cm 10 nm 25 µs 1.7 ns
α r02 α r0
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708
r0 r0 tsteady-state RuCd*
10-3 cm 10 µm 25 s 1.7 µs
10-4 cm 1 µm 0.25 s 170 ns
10-5 cm 100 nm 2.5 ms 17 ns
10-6 cm 10 nm 25 µs 1.7 ns
… recall that Ru is nearly independent of
the WE–RE separation:
the short time limit imposed by RuCd for a macroscopic
electrode is ~100 µs…
… but UMEs are much faster!
1α r0
2 α r0 α r0-1
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709
needed for il < 10 nA: a Faraday cage…
http://www.columbia.edu/cu/physics/demo-images/
… and a Keithley 428 programmable
current amplifier grounded to the cage
http://www.keithley.com/products/
… and lastly, two things you’ll really want for these experiments…
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710
UMEa reference electrode
(no counter
electrode needed)
Keithley 428
Faraday cage
… there are also a few things you will not be needing…
ground the
Faraday
cage to the
Keithley
ground
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711UME take-home messages:
After rapid double-layer charging…
… operate UMEs at either short times
= linear diffusion…
Can determine effects of rapid catalysis without
complications from diffuse–double-layer charging
… or long times
= steady-state radial diffusion…
Can determine D without knowing C*
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712We only have time to look at techniques/publications by one
of these four UME pioneers… Guess who?
◆ Ralph “Buzz” Adams (d. Univ. Kansas)
◆ Mark Wightman (UNC Chapel Hill)
◆ Allen Bard (UT Austin)
◆ Henry White (Univ. Utah)
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713Bard and scanning electrochemical microscopy (SECM)…
http://electrochem.cwru.edu/ed/encycl/art-m04-microscopy.htm
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714
http://electrochem.cwru.edu/ed/encycl/art-m04-microscopy.htm
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715
http://electrochem.cwru.edu/ed/encycl/art-m04-microscopy.htm
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716
Fan & Bard, Science, 1995, 267, 871
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717
tip
su
rfa
ce
C(x)/C*
1
0
the magic of “thin layer electrochemistry”...
distance
… Recalling Section 1.4.2 (Semi-Empirical)
𝐽𝑖 𝑥 = −𝐷𝑖𝐶𝑂∗ − 𝐶𝑂 𝑥 = 0
𝜕𝑂
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718
tip
su
rfa
ce
su
rfa
ce
tip
distance
C(x)/C*
1
0
1
0
the magic of “thin layer electrochemistry”...
distance
𝐽𝑖 𝑥 = −𝐷𝑖𝐶𝑂∗ − 𝐶𝑂 𝑥 = 0
𝜕𝑂
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719
su
rfa
ce
tip
distance
?
0
A feasibility assessment… 1 molecule is trapped within
a 1 µm x 1 µm x 10 nm volume between an SECM tip
and a surface. What’s the value of the limiting current?
δ0
m𝑖 = −𝑛𝐹𝐴𝐷Δ𝐶
𝛿
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720
su
rfa
ce
tip
distance
?
0
δ0
m
A feasibility assessment… 1 molecule is trapped within
a 1 µm x 1 µm x 10 nm volume between an SECM tip
and a surface. What’s the value of the limiting current?
𝑖 = −𝑛𝐹𝐴𝐷Δ𝐶
𝛿
𝐶1molecule = 1molecule1 mol
6.022 x 1023 molecules
1
10 x 10−7 cm 1 x 10−4 cm 2
𝐶1molecule = 1.66 x 10−10 mol/cm3
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721
su
rfa
ce
tip
distance
?
0
δ0
m
A feasibility assessment… 1 molecule is trapped within
a 1 µm x 1 µm x 10 nm volume between an SECM tip
and a surface. What’s the value of the limiting current?
𝑖 = −𝑛𝐹𝐴𝐷Δ𝐶
𝛿
𝑖 = 1 eq/mol 96485 C/eq 1 x 10−4 cm 2 1 x 10−5 cm2/s1.66 x 10−10 mol/cm3
10 x 10−7 cm
= 1.6 x 10−12 A = 1.6 pA
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722
su
rfa
ce
tip
distance
?
0
δ0
m
… so we’re talking about pA's. We can measure that!
A feasibility assessment… 1 molecule is trapped within
a 1 µm x 1 µm x 10 nm volume between an SECM tip
and a surface. What’s the value of the limiting current?
𝑖 = −𝑛𝐹𝐴𝐷Δ𝐶
𝛿
𝑖 = 1 eq/mol 96485 C/eq 1 x 10−4 cm 2 1 x 10−5 cm2/s1.66 x 10−10 mol/cm3
10 x 10−7 cm
= 1.6 x 10−12 A = 1.6 pA
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723
Fan & Bard, Science, 1995, 267, 871
Reviewed in Bard & Fan, Acc. Chem. Res., 1996, 29, 572
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724
Q: What was in this set of lectures?
A: B&F Chapters 4 & 5 main concepts:
● Section 4.4.2: Fick’s Second Law of Diffusion
● Section 5.1: Overview of step experiments
● Section 5.2: Potential step under diffusion controlled
● Sections 5.3 & 5.9: Ultramicroelectrodes
● Sections 5.7 – 5.8: Chronoamperometry/Chronocoulometry
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725
A detailed review of Section 4.4.2 and Chapter 5
● Fick’s Second Law of Diffusion
● Linear Diffusion = time-dependent current (Cottrell Equation)
● Anson Plots for surface adsorbed species
● Radial Diffusion = time-independent current (at steady-state)
● Ultramicroelectrodes (UMEs), Scanning Electrochemical Microscopy (SECM), and single molecule electrochemistry
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726
Q: What’s in this set of lectures?
A: B&F Chapter 2 main concepts:
● “Section 2.1”: Salt; Activity; Underpotential deposition
● Section 2.3: Transference numbers; Liquid-junction
potentials
● Sections 2.2 & 2.4: Donnan potential; Membrane potentials;
pH meter; Ion-selective electrodes
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727Refresher… the equilibrium potential and the Nernst Equation
O + ne– ⇌ R
the standard potential
(look it up in the back of your book or in the CRC table)
activity of R
activity of O𝐸 = 𝐸0 −
𝑅𝑇
𝑛𝐹ln𝑎𝑅𝑎𝑂
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728
… write the activity as the product of the activity coefficient and concentration…
Refresher… the equilibrium potential and the Nernst Equation
O + ne– ⇌ R
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅𝐶𝑅γ𝑂𝐶𝑂
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹ln𝑎𝑅𝑎𝑂
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729Refresher… the equilibrium potential and the Nernst Equation
E0'
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
𝐸 = 𝐸0′ −𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
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730Refresher… the equilibrium potential and the Nernst Equation
the formal potential… this depends on the identity and
concentration of all ionizable species present in solution
E0'
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
𝐸 = 𝐸0′ −𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
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731
Fig. 10-1, p. 268 in Skoog & West
BaSO4
CH3COOH
H2O
However, equilibrium “constants” are not… constants…
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732
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
A (activity) = 1.0 for any pure solid compound
in its standard state at room temperature
… let’s focus on the solubility of BaSO4…
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733
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
… let’s focus on the solubility of BaSO4…
the activity coefficient
for SO42-
the concentration
of SO42-
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734
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
… let’s focus on the solubility of BaSO4…
the thermodynamic equilibrium constant
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735
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
… let’s focus on the solubility of BaSO4…
the concentration equilibrium constant
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736
𝐼
Fig. 10-3, p. 272 in Skoog & West
Ionic strength, I = 0.5(zA2[A] + zB
2[B] + zC2[C] + …)
… the more charge on an ion, the greater the depression of its activity
coefficient by an inert salt…
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737
Fig. 10-3, p. 272 in Skoog & West
𝐼
Ionic strength, I = 0.5(zA2[A] + zB
2[B] + zC2[C] + …)
… the more charge on an ion, the greater the depression of its activity
coefficient by an inert salt…
… so, for NaCl, what is I?
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𝐼
Ionic strength, I = 0.5(zA2[A] + zB
2[B] + zC2[C] + …)
… the more charge on an ion, the greater the depression of its activity
coefficient by an inert salt…
738
Fig. 10-3, p. 272 in Skoog & West… so, for NaCl, what is I? [NaCl]!
(~10 mM) ~100 mM
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739
Bockris & Reddy, Fig. 2.18
… the more charge on an ion, the greater the depression of its activity
coefficient by an inert salt… but at high concentration, this trend flips!
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740
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
… let’s focus on the solubility of BaSO4…
… but what are these, how do we calculate them…
… and why do they depend on the concentration of salt?
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741
BaSO4(s) ⇌ SO42-(aq) + Ba2+(aq)
2H2O ⇌ H3O+ + OH–
CH3COOH + H2O ⇌ H3O+ + CH3COO–
… in all three of these cases, K' > K, at not too large of an ionic strength
general observation: K' always shifts (from K) to favor
the most ionic state of the equilibrium
more ionicless ionic
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742Refresher… the equilibrium potential and the Nernst Equation
𝐸 = 𝐸0′ −𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
Fe3+ + 1e– ⇌ Fe2+
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
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743
Fe3+ + 1e– ⇌ Fe2+
Refresher… the equilibrium potential and the Nernst Equation
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
𝐸 = 𝐸0′ −𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
![Page 54: Lecture #10 of 17ardo/echem/UCI-CHEM248-2019S_lecture10.pdf10-5 cm 100 nm 2.5 ms 17 ns ... A detailed review of Section 4.4.2 and Chapter 5 Fick’s Second Law of Diffusion Linear](https://reader034.vdocuments.mx/reader034/viewer/2022042112/5e8e6dbd686ba260181a7a89/html5/thumbnails/54.jpg)
744Refresher… the equilibrium potential and the Nernst Equation
… now, γFe3+ < γFe2+, agreed?
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
𝐸 = 𝐸0′ −𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
Fe3+ + 1e– ⇌ Fe2+
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
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745
Table 10-2, p. 274 in Skoog & West
Debye–Hückel equation
(in water at 25 °C)
α = effective diameter of hydrated ion (nm)
− log γ𝑥 =0.51𝑧𝑥
2 𝐼
1 + 3.3α𝑥 𝐼
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746Debye–Hückel equation
(in water at 25 °C)
α = effective diameter of hydrated ion (nm)
− log γ𝑥 =0.51𝑧𝑥
2 𝐼
1 + 3.3α𝑥 𝐼
… the derivation is long and the main idea is that you balance
thermal motion (Boltzmann) with electrostatics (Poisson/Gauss)
from Wiki
Physicist & P-Chemist
Peter Joseph William Debye
(1884–1966)
Physicist & P-Chemist
Erich Armand Arthur Joseph Hückel
(1896–1980)
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747Debye–Hückel equation
(in water at 25 °C)
α = effective diameter of hydrated ion (nm)
… the “limiting law” is when I 0 (< 10 mM),
and then the D-H eq. simplifies
to just the numerator:
− log γ𝑥 =0.51𝑧𝑥
2 𝐼
1 + 3.3α𝑥 𝐼
Bockris & Reddy, Fig. 3.23
− log γ𝑥 = 0.51𝑧𝑥2 𝐼
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748
Fe3+ + 1e– ⇌ Fe2+
… now, γFe3+ < γFe2+, agreed? So…
and
… and we conclude that in the presence of added salt…
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
lnγ𝑅γ𝑂
> 0γ𝑅γ𝑂
> 1.0
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
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749
no added salt…
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
γ𝑂 ≈ γ𝑅 ≈ 1.0
lnγ𝑅γ𝑂
≈ 0
Fe3+ + 1e– ⇌ Fe2+
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
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750
no added salt…
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
γ𝑂 ≈ γ𝑅 ≈ 1.0
lnγ𝑅γ𝑂
≈ 0
with added salt…
ANSWER: E0' shifts to more negative potentials
Fe3+ + 1e– ⇌ Fe2+
Question: How, qualitatively, is the equilibrium potential for
Fe2+/Fe3+ affected by the addition of a supporting electrolyte, KF,
at a concentration of 0.1 M?
and lnγ𝑅γ𝑂
> 0γ𝑅γ𝑂
> 1.0
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751Question: What if the redox species were negatively charged,
like [FeIII(CN)6]3–/[FeII(CN)6]
4–, and we increased the concentration
of supporting electrolyte to ~0.1 M?
[FeIII]3– + 1e– ⇌ [FeII]4–
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
with added salt…Fe(CN)6
3-/Fe(CN)64-
No added salt(note ipc and iR)
and 𝒍𝒏𝜸𝑹𝜸𝑶
< 𝟎𝜸𝑹𝜸𝑶
< 𝟏. 𝟎
ANSWER: E0' shifts to more positive potentials
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increasing
supporting
electrolyte
Im-Tl+, to bring Tl+
to the electrode
Id-Tl+, to bring Tl+
to the electrode
cathodic reaction
752Question: What if the redox species were positive/neutral
charged, like Tl+/0, and we increased the concentration of
supporting electrolyte to ~0.1 M?
Tl+ + 1e– ⇌ Tl0
𝐸 = 𝐸0 −𝑅𝑇
𝑛𝐹lnγ𝑅γ𝑂
−𝑅𝑇
𝑛𝐹ln𝐶𝑅𝐶𝑂
with added salt…
and 𝒍𝒏𝜸𝑹𝜸𝑶
> 𝟎𝜸𝑹𝜸𝑶
> 𝟏. 𝟎
ANSWER: E0', again, shifts to more negative potentials
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753
Co0 ⇌ Co2+ + 2e–
Eeq
Underpotential deposition (UPD)… practical “activity”… even of solids!
Co2+ + 2e– ⇌ Co0
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754
Co0 ⇌ Co2+ + 2e–
Eeq
Co2+ + 2e– ⇌ Co0
Underpotential deposition (UPD)… practical “activity”… even of solids!
… but what are these
small cathodic current "bumps"
that occur at Eapp > Eeq?
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755
Co0 ⇌ Co2+ + 2e–
Eeq
B&F, pg. 420
… aCo < 1… because the
activity of a solid is proportional
to its surface coverage!
Co2+ + 2e– ⇌ Co0
Underpotential deposition (UPD)… practical “activity”… even of solids!
… but what are these
small cathodic current "bumps"
that occur at Eapp > Eeq?
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756
Co0 ⇌ Co2+ + 2e–
Co2+ + 2e– ⇌ Co0
Eeq
Coδ+
gold
OPD of cobalt
gold
cobalt UPD of cobalt
Mendoza-Huizar, Robles, & Palomar-Pardavé, J. Electroanal. Chem., 2003, 545, 39
Underpotential deposition (UPD)… practical “activity”… even of solids!
… aCo < 1… because the
activity of a solid is proportional
to its surface coverage!
B&F, pg. 420
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757
an ISE (for nitrate ions)an SCE
Now on to two general liquid junctions that we care about (the most)…
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758
when two ionic solutions are separated across an interface that
prevents bulk mixing of the ions, but has ionic permeability, a
potential (drop) develops called the liquid junction potential.
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 2.3.2
same salt;
different conc.
one ion in common;
same conc.everything else.
… liquid junctions: