1

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

6

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

7

∞ 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)

9

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

12

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( )

12

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