Post on 26-Mar-2021
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Chemistry 163B
Electrochemistry
2
activity coefficients for ions (HW8 #58)
2
2
2
2 2
22
2
( ) ( )
( )
( )
2( )
( )
( ) ( ) 2 ( )
1
Ba aq Cl aqsp
BaCl s
BaCl s
Ba aq Ba
Cl aq Cl
BaCl s Ba aq Cl aq
a aK
a
a
a Ba
a Cl
determine and independently
but only
2
2
Ba Cl
Ba Cl
cannot
223
23 2
11
1 (1)sp
sp
MMBa ClK
K Ba Cl
3
work of expansion
H2 (10 bar) ö H2(1 bar)
10bar
10bar
pfft
1 bar 1 bar
4
hydrogen pressure [‘concentration’] cell (reaction I of III)
H2 (10 bar) ö H2(1bar)
reactionRT Q ln
2
15 706
10P
RT kJ per mole HP
)
ln .( )
bar
bar
2 2 is for reaction H ( 1 ba0 r) H ( 1 bar) P P
5
d and work-other (did before for dG)
0 by 2nd law
(very general)- -
-,
other
T P other
d dH TdS SdTd d q TdS SdT VdP d w
d d w
for a spontaneous process at constant T,P the MAXIMUM work done ON SURROUNDINGSis || and this occurs when the process approaches
REVERSIBILITY
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responsible for 3 redox reactions; here’s II (HW8, prob #60)
oxidation anodereduction cathode
2e + H2 (g, 1 bar) + 2AgCl(s) ö 2H+ [1M] +2Cl- [1M] +2Ag(s) + 2e
e
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∞ for the reaction (see Appendix A, Table 4.1 for data; additional decimal places from other tables)
2e +H2 (g, 1atm) + 2AgCl(s) ö 2H+ [1M] + 2Cl- [1M] + 2Ag(s) +2e
f± ºGf± (kJ) 0 -109.79 0 -131.23 0
± ºG± = - (0) -2 (-109.79) + 2(0) + 2(-131.23) + 2 (0) = -42.88 kJ
e + ½ H2 (g, 1atm) + AgCl(s) ö H+ [1M] + Cl- [1M] + Ag(s) + e
± =for 2 moles e transferred
± ºG±=-21.44 kJ per ½ mole H2
± for 1 mole e transferred
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and FINALLY wother !!! (p. 20 [18]2nd)
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wother (p. 260 [255]2nd)
electricald w dQ -
electric potential charge transfer
dQ dn F moles of e’s transferred
from negativecharge on e
F is Faraday constant96,458 coulomb (mole e)1
(n moles electrons transferred)
&
electrical
electrical
rev
d w dn
w n
w n
E R
F
F
F
p260 z -n
-
electromotive force=
UNITS: [w] = [Q] [F]joule= coulomb volt
p. 260 vs is overcomplicated
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sign of F and spontaneity
,
,
,
for irreversible for reversible
T P other
irrev irrevT P cell cell
T P cell cell
w
nn
F
F
T,P < 0 spontaneous F > 0 spontaneous
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vs F
reactionRT Q n ln F
ln
reactionRT Q
n nF F
ln
2980.02569 ln
reaction
reaction
RT Qn
T K
Qn
F
1
n = moles electrons transferredn =mol
n= n moln unitless
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responsible for 3 redox reactions; here’s II (HW8, prob #60)
F00
0.22233oxidation anodereduction cathode
2e + H2 (g, 1bar) + 2AgCl(s) ö 2H+ [1M] +2Cl- [1M] +2Ag(s) + 2e 0.22233
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example incorporating activities
2e +H2 (g, 1bar ) + 2AgCl(s) ö 2H+ [1M] + 2Cl- [1M] + 2Ag(s) +2e
( )
2
2 2 2
2( )
0.02569 ln
Ag sH Cl
H AgCl s
a a a
n a a
2 2
4 2 2[ ] [ ]0.02569 ln
H H
H Cln P
1
[ ] [ ]
can't independently meansure and
AgCl Ag
H H Cl Cl
H Cl
H Cl
a a
a H a Cl
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example incorporating activities
2 2
4 2 2[ ] [ ]0.02569 ln
H H
H Cln P
2 e’s0.22233 V
2
4 2 2
unitless; have dropped standard state concs and pressure from denominators
[1 ] [1 ]0.025690.22233 ln2 (1 bar)
H
M M
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example incorporating activities
2
4 2 2[1 ] [1 ]0.025690.22233 ln2 (1 bar)
H
M M
• Calculate ’s from observed F (HW8, prob 60)• If ’s =1
1
4
0.025690.22233 ln 1 0.222332
2 96,485 0.22233
4.290 10 42.90
n
mol C mol V
CV kJ
F
= -42.88 kJ for 2 moles e transferred [from f earlier ]
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intensive F vs extensive F = - ( /nF)
2e +H2 (g, 1 bar) + 2AgCl(s) ö 2H+ [1M] + 2Cl- [1M] + 2Ag(s) +2e
Fcell= 0.22233 V = -42.88 kJ for 2 moles e transferred
( )
2
2 2 2
2 ' 2( )
0.02569 ln2
Ag sH Clcell e s cell
H AgCl s
a a a
a a
H2 (g, 1 bar) ö 2H+ [1M] +2e F= 0 V
2e + 2AgCl(s) ö 2Cl- [1M] + 2Ag(s) F= 0.22233 V
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intensive F vs extensive F = - ( /nF)
e +½H2 (g, 1 bar) + AgCl(s) ö H+ [1M] + Cl- [1M] + Ag(s) +e
Fcell= 0.22233 V = -21.44 kJ for 1 moles e transferred
½H2 (g, 1 bar) ö H+ [1M] +e F= 0 V
e + AgCl(s) ö Cl- [1M] + Ag(s) F= 0.22233 V
F intensivesame as for 2 mole e’sF is oomph per electron( )
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2
1 1 1
1 1( )
0.02569 ln1
Al s
H
H Clcell e cell
AgCl s
a a a
a a
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intensive F vs extensive F = - ( /nF)
= -21.44 kJ for 1 moles e transferred
( )1
2
2
1 1 1
1 1( )
0.02569 ln1
Ag s
H
H Clcell e cell
AgCl s
a a a
a a
( )
2
2 2 2
2 ' 2( )
0.02569 ln2
Ag sH Clcell e s cell
H AgCl s
a a a
a a
= -42.88 kJ for 2 moles e transferred
2 1
cell e cell e
same
2 12e e
two times greater
n F extensive: depends on stoichiometry
F intensive: independent of ‘how reaction is written’ooomph PER electron
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biological example: cytochrome C iron containing enzyme (reaction III)
CytC=cytochrome Cstandard state pH=7, [H+]=107
2e + 2CytC(Fe3+ ) ö 2CytC(Fe2+ )
2e + ½O2(g) + 2H+(aq) ö H2O ({)
Fred(V)pH70.25
0.816
standard REDUCTION potentials
reaction: the oxidation of CytC(Fe2+ )
2CytC(Fe2+ ) ö 2CytC(Fe3+ ) + 2e
2e + ½O2(g) + 2H+(aq) ö H2O ({)
½O2(g) + 2H+(aq) +2CytC(Fe2+ ) ö 2CytC(Fe3+ ) + H2O ({)
F(V)
0.25
0.816
standard state [H+]=10-7
oxidation
reduction
-
?= Fcell
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biological example (redox equation III)
½O2(g) + 2H+(aq) +2CytC(Fe2+ ) ö 2CytC(Fe3+ ) + H2O ({)
2 2
' '12 2
7
ln ln[ ]
10 1
cell cell cell
O O
RT RTQn n PH
M bar
F F
what’s º′ ?what’s Q ?what’s n ?
standard state ′
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F and thermodynamic derivatives, etc. (HW8, prob #59)
n
n
F
F
ln ln eq eq
RTRT K KnF
P P
SST T nF
2 2
P P
H HT TT T T n TF
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ΔCp from Φ
P
H T S
H T S n T nT
F F
P P
SST T nF
2
2
2
2
pP PP P
pP
H C n n n TT T T T
C n TT
F F F
F
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relationships on final
Electrochemistry:
reaction =nF cell
ln
0.02569 ln 298
FRT Qn
Q at T Kn
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End of Lecture