Harris: Quantitative Chemical Analysis, Eight Edition

CHAPTER 13:CHAPTER 13:

FUNDAMENTALS OF ELECTROCHEMISTRY

CHAPTER 13: Opener A

CHAPTER 13: Opener B

Fuel Cell provides an instrument with electricity from the ocean floor

* HS- in the sediment pore water is depleted adjacent to anodeis depleted adjacent to anode

1 O id i f lfid f h lf f h1.Oxidation of sulfide accounts for half of the power output.

2. Thus, sulfide (SH-) is the fuel which is depleted near the anode.

3. The other half is likely derived from oxidation of Acetate by microbes colonizing the anode, with direct transfer of e- to the anodewith direct transfer of e to the anode

Electrodes next to an adrenal cell measure release ofthe hormone epiphrinethe hormone epiphrine

Figure 13-7 Cell used to measure the standard potential of the reaction13-3. Standard Potentialsg p

Ag + + e- ___ Ag (s)

13-3. Standard Potentials

P t ti t (V lt t ) i d t th lt l t i l- Potentiometer (Voltameter) is used to measure the voltage, e.g., electrical

potential difference between two electrodes.

- Negative terminal (-) : “common” or “ground”

: color coded black

: narrow receptacle (reference electrode) in a pH meter

Positive terminal (+) : color coded red

: wide receptacle (glass pH electrode) in a pH meter

- Positive voltage (e- flow from – terminal to + terminal)g ( )

Negative voltage (e- flow the other way)

13-3. Standard Potentials

- Left Cell : standard hydrogen electrode (S.H.E)

12H

21

H+(aq, A = 1) + e- (g, A =1) Eo = 0

Ri ht C ll A + (A 1) + A ( ) Eo +0 799V- Right Cell : Ag+ (A = 1) + e- Ag(s) Eo = +0.799V

- Standard Potential : What would be measured if the activities of

all reactants and products were unity.

13-3. Standard Potentials

It is usually not possible to construct a cell in which all the activities are unity.

i) There may not be a salt soluble enough to give a 1M solution. Even if therewere we don’t have an accurate way to calculate the activity coefficient atwere, we don t have an accurate way to calculate the activity coefficient atsuch a high ionic strength.

ii) N b d b ild t d d h d l t d I t d kii) Nobody ever builds a standard hydrogen electrodes. Instead, knownhydrogen ion activities are obtained using National Bureau of StandardBuffers.

iii) In real life, activities less than 1 are used in both half-cells.

iv) The Nernst Equation can be used to extract the value Eo from the potentialmeasured under non-standard conditions.

13-4. Nernst Equation

D i i F f ii) Eo (unit activities)

Driving Force for reaction ii) Concentration of reactants and products(Le Châtelier’s principle)

Net Driving Force (Eo and concentration) is expressed by Nernst Equation.

aA + bB cC + dD

lnRTEE o AC

cADd

*Pure solids, liquids and solvents, A = 1lnnF

EE AA

aABb

Q (Reaction Quotient) = AC

cADd

Concentration of solute : mol/L

Concentration of gases : PatmQ ( Q )AA

aABb

* The Nernst Equation can be used to extract the value Eo from the potential measured under non-standard conditions.

13-4. Nernst Equation

*The more positive the voltage (E), the more favorable the reaction is.

RTRT

G = -nFE

xF

RTxF

RT log30.2ln

K298J/K314.8302 coulombs 96485

K298J/K314.830.2

= 0.05916 J/C 0.05916 J/C= 0.05916 V

( ° ) at T = 298K (25°C),

V059160 ACcAD

dlogV05916.0

nEE o

AC AD

AAaAB

b

13-5. E0 and the Equilibrium Constant

A l i ll d l t i it b th t ll ti i t- A galvanic cell produces electricity because the net cell reaction is notat equilibrium.If we replace the potentiometer (large ) with a wire (small ) much more- If we replace the potentiometer (large ) with a wire (small ) much morecurrent will flow until the equilibrium is reached.

QnFRTEE o lnnF

at Equilibrium

KnFRTEE o ln0 nF

continued

13-5. E0 and the Equilibrium Constant

nFEKKRTEo

o lnlnRT

KKnF

E ln , ln

nFEo

RTeK

)1ll(10 10l nFEnFE ooRTnFEo

)10ln1loglog( 10 10ln

RTnFEe

RTnFEKRT

nEo

1010ln

FRT

oE 298K8 314J/K10lRT05916.0n

10K 298.15K, Tat oE

coulomb 96485298K8.314J/K3.210ln

F

RT

0 05916VJ/C059160 0.05916VJ/C05916.0

13-6. Cells as Chemical Probes

Potentiometry : The use of electrodes to measure voltages that provide chemical

information.

(The cell voltage tells us the activity of one unknown species ( g y p

if the activities of the other species are known).

Indicator Electrode : It responds to analyte an electroactive speciesIndicator Electrode : It responds to analyte, an electroactive species

that can donate or accept electron at the electrode)

Reference Electrode : It maintains a fixed potential (a known, fixed composition)

How to use potentiometry :1) We connect two half-cells (indicator & reference electrodes) by a salt bridge.2) We measure the cell voltage which is the difference between the potential of

the indicator electrode and the constant potential of the reference electrodethe indicator electrode and the constant potential of the reference electrode.3) We make an equation of first degree to get the unknown concentration of analyte.

13-6. Cells as Chemical Probes

- It is essential to distinguish two classes of equilibria associatedwith galvanic cells :with galvanic cells :

1) Equilibrium between the two half-cells (zero voltage)) q ( g )

2) Equilibrium within each half-cell (even at nonzero voltage)

- Equilibrium within each half-cell : It i i l h i l ti It i t d tiIt is simply a chemical reaction. It is not a redox reaction

CHAPTER 13: Figure 13.9

2) Equilibrium within each half-cell (even at nonzero voltage)i) in the right hand half celli) in the right-hand half-cell,

AgCl(s) Ag+(aq) + Cl-(aq)ii) in the left-hand half-cell,

CH COOH CH3CO + H+CH3COOH CH3CO2- + H+

13-6. Cells as Chemical Probes

Th ll ti- The cell reaction :

Anode : H2(g) 2H+ + 2e- E o = 0VAnode : H2(g) 2H + 2e E- 0VCathode AgCl(s) + e- Ag(s) + Cl-(aq) E+

o = 0.222V2

2AgCl(s) + H2(g, 1atm) 2H+(xM) + 2Cl-(0.1M) + 2Ag(s)

22 ][Cl][Hlog2

005916222.0 E

22[0.10]][Hlog2

005916222.0503.0

M108.1]H[ 4 continued

13-6. Cells as Chemical Probes

4 )1081)(00500(]][HCOO[CH 54

3

3a 108.1

050.0)108.1)(0050.0(

COOH][CH]][HCOO[CH

K

•i) This particular cell behaves as a pH meter, a probe for H+ (activity).

ii) It allows us to evaluate the equilibrium constant the acid-base reaction.

iii) We can assume that the conc. of CH3COOH and CH3COO- are equalto their initial concentration. Is this assumption reasonable ?

Example: How to measure the formation constant for Hg(EDTA)2-

Example: How to measure the formation constant for Hg(EDTA)2-

< Fi 13 10 >< Figure 13-10 >

In the right half-cell,

Hg2+ + Y4- HgY2-Kf

Hg Y HgY

][HgY][HgY 22

K[EDTA]]α[Hg

][ g]][Y[Hg

][ g4Y

242f

K

1)-12 Table (From 6 pHat 108.1α 5Y4

K i t d t b l Vi t ll ll th H 2+ t t k H Y2Kf is expected to be large. Virtually all the Hg2+ react to make HgY2-

Example: How to measure the formation constant for Hg(EDTA)2-

01M)(50 0mL)(02 0.00500M100mL

.01M)(50.0mL)(0][HgY -2

0.0150M100mL

(0.50mmol)-(2.00mmol)[EDTA] remaining

[EDTA]]α[M][MY

]][Y[M][MY 4

4

4

f

n

n

n

n

K

(0.00500)f K

[EDTA]]α[M]][Y[M 4Y

very small unknown [Hg2+] = ?

)0150.0)(10](1.8[Hg 5-2f K

y g

continued

Example: How to measure the formation constant for Hg(EDTA)2-

[Hg2+] = ?

Anode : H2(g, 1.00atm) 2H+(1.00M) + 2e- Eo = 0VCathode Hg2+ + e- Hg(l) Eo = 0.852V

H2(g) +Hg2+ Hg(l) + 2H+ Eo = 0.852V

][Hg][Hlog

205916.0 2

2

H

o

PEE

2

][ g H

](1 00)[H(1.00)log

205916.0852.00.342 2

2

](1.00)[Hg

g2 2

[Hg2+] = 5.7 10-18 M Kf = 3 1021 Compare it inTable 11-2

13-7. Biochemist Use Eo’

- E 0 applies when pH =0 (e.g., {H+} = 1.0). Because the pH inside a plant or animal cell is about 7, E 0 that applies at pH 0 is not particularly appropriate.

- Many of the reactions in living organisms are redox reactions. It is the reducing strength at pH = 7, not at pH = 0, that is relevant to the chemistryof a living cell.

- Reduction potential E (not E 0) are pH-dependent

- Eo’ (formal potential) : the reduction potential that applies under a specified set of conditions (pH concentration ionic strength)specified set of conditions (pH, concentration, ionic strength)

Th bi h i t ll th f l t ti l t H 7 E0’ (E i )-The biochemists call the formal potential at pH 7, E0’ (E zero prime)

13-7. Biochemist Use Eo’

-Relation Between Eo and Eo’aA + ne- bB +mH+ Eo

A : oxidized speciesA : oxidized speciesB : reduced species

a

mb

[A]][H[B]log05916.0

n

EE o

[ ]

a

bB

FFlog05916.0sother term

nEE o

AFnEo’ when pH = 7

(FA, FB : formal concentrations of A and B)

13 -7. Biochemist Use Eo’

T t [A] [B] t F F f ti l iti tiTo convert [A], [B] to FA or FB, we use fractional composition equations .

For Monoprotic AcidFor Monoprotic Acid,

]F[HF[HA]

ao ][H

][Fα[HA]K

FK

a

a1

-

][HF

Fα][AK

K