Atkins & de Paula: Atkins & de Paula: Elements of Physical Chemistry: Elements of Physical Chemistry:

5e5e

Chapter 9: Chemical Equilibrium: Electrochemistry

End of chapter 9 assignments

Discussion questions:• 1, 4

Exercises:• 1, 3, 9, 12, 13 (include last 3?)

Use Excel if data needs to be graphed

Homework assignmentsHomework assignments

• Did you:– Read the chapter?– Work through the example problems?– Connect to the publisher’s website &

access the “Living Graphs”?– Examine the “Checklist of Key Ideas”?– Work assigned end-of-chapter

exercises?

• Review terms and concepts that you should recall from previous courses

Build Yourself a Table…Build Yourself a Table…

TERM UNITS SYMBOLPotential volts V

Resistance ohms

Current amp I

Siemens -1 (ohm-1) S

Resistivity ohm meter

Conductivity ohm-1 meter-1

Molar conductivity

S m2 mol-1 m

Ionic conductivity

mol/dm3

mS m2 mol-1 + –T

erm

s, U

nits

, & S

ymbo

ls

is an uppercase

Foundational conceptsFoundational concepts

• What is the most important difference between solutions of electrolytes and solutions of non-electrolytes?

• Long-range (Coulombic) interactions among ions in solutions of electrolytes

The Debye-Hückel theoryThe Debye-Hückel theory

• Activity, a, is roughly “effective molar concentration”

• 9.1a aJ = JbJ/b b = 1 mol/kg

• 9.1b aJ = JbJ = activity

coefficient– treating b as the numerical value of molality

• If a is known, you can calculate chemical potential: μJ = μJ + RT ln aJ (9.2)

The mean activity coefficientThe mean activity coefficient

Mean activity coefficient = (+ –)½

For MX, = (+ –)½

• For MpXq, = (+p

–q)1/s s = p+q

• So for Ca3(PO4)2, = (+3

–2)1/5

Debye-Hückel theoryDebye-Hückel theory

• Fig 9.1 (203)• A depiction of the

“ionic atmosphere” surrounding an ion

• The energy of the central ion is lowered by this ionic atmosphere

Debye-Hückel theoryDebye-Hückel theory

• Debye-Hückel limiting law:log = –A|z+z–| I ½

is the mean activity coefficient

– I = ionic strength of the solutionI = ½(z+

2 b+ + z–

2 b– ) [b =

molality]

– A is a constant; A = 0.509 for water– z is the charge numbers of the ions

p.203

The extended Debye-Hückel The extended Debye-Hückel lawlaw

• log = – + C.I

is the mean activity coefficient

– I = ionic strength of the solutionI = ½(z+

2 b+ + z–

2 b– )

– A is a constant; A = 0.509 for water– B & C = empirically determined

constants– z = the charge numbers of the ions

A |z+z–| I ½

1 + B. I ½

p.203

Debye-Hückel theoryDebye-Hückel theory

• Fig 9.2 (203)• (a) the limiting law

for a 1,1-electrolyte(B & C = 1)

• (b) the extended law for B = 0.5

• (c) the extended law extended further by the addition of the C I term

[in the graph, C=0.2]

The migration of ionsThe migration of ions

• Ions move• Their rate of motion indicates:

– Size, effect of solvation, the type of motion

• Ion migration can be studied by measuring the electrical resistance in a conductivity cell

• V = IR

The migration of ionsThe migration of ions

• V = IR• Resistivity () and conductivity ()• And = 1/ and = 1/• Drift velocity, s = uE • Where u (mobility) depends

on a, the radius of the ion and , the viscosity of the solution

Conductivity cellConductivity cell

• Fig 9.3 (204)• The resistance is

typically compared to that of a solution of known conductivity

• AC is used to avoid decomposition products at the electrodes

Conductivity bridge

Do you see any trends?Do you see any trends?T

9.1

Ioni

c co

nduc

tivi

ties

, /(

mS

m2/

mol

)*

T9.

2 Io

nic

mob

ilit

ies

in w

ater

at 2

98 K

, u/

(10-

8 m

2 s-

1 V

-1)

Do you see any trends?Do you see any trends?

The hydrodynamic radiusThe hydrodynamic radius

• The equation for drift velocity (s) and the equation for mobility (u) together indicate that the smaller the ion, the faster it should move…

• But the Group 1A cations increase in radius and increase in mobility! The hydrodynamic radius can explain this phenomenon.

• Small ions are more extensively hydrated.

s = uE

Proton conduction through Proton conduction through waterwater

• Fig 9.4 (207) The Grotthus mechanism• The proton leaving on the right side is not

the same as the proton entering on the left side

Determining the Isoelectric Determining the Isoelectric PointPoint

• Fig 9.5 (207)• Speed of a

macro-molecule vs pH

• Commonly measured on peptides and proteins (why?)

• Cf “isoelectric focusing”

Types of electrochemical Types of electrochemical rxnsrxns

• Galvanic cell—a spontaneous chemical rxn produces an electric current

• Electrolytic cell—a nonspontaneous chemical rxn is “driven” by an electric current (DC)

Anatomy of electrochemical cellsAnatomy of electrochemical cells

Fig 9.6 (209) Fig 9.7 (209) The salt bridge overcomes difficulties that the liquid junction introduces into interpreting measurements

Half-reactionsHalf-reactions

• For the purpose of understanding and study, we separate redox rxns into two half rxns: the oxidation rxn (anode) and the reduction rxn (cathode)

• Oxidation, lose e–, increase in oxid #• Reduction, gain e–, decrease in oxid #• Half rxns are conceptual; the e– is

never really free

Dir

ect

ion

of

e– flow

in

ele

ctro

chem

ical

cells

Fig

9.8

(21

3)

Reactions at electrodesReactions at electrodes

• Fig 9.9 (213)• An electrolytic cell• Terms:

– Electrode – Anode– Cathode

• Fig 9.10 (213) Standard Hydrogen Electrode

• Is this a good illustration of the SHE?

• Want to see a better one?

A gas electrodeA gas electrode

19.3

E0 = 0 V

2e- + 2H+ (1 M) 2H2 (1 atm)

Reduction Reaction

Standard hydrogen electrode (SHE)

SStandard tandard HHydrogen ydrogen EElectrodelectrode

19.3

E0 = 0 V

Standard hydrogen electrode (SHE)

Standard Hydrogen ElectrodeStandard Hydrogen Electrode

H2 (1 atm) 2H+ (1 M) + 2e-

Oxidation Reaction

H2 gas, 1 atm

Pt electrode

SHE acts as cathode SHE acts as anode

Standard Hydrogen ElectrodeStandard Hydrogen Electrode

Metal-insoluble-salt electrodeMetal-insoluble-salt electrode

• Fig 9.11 (214)• Silver-silver

chloride electrode• Metallic Ag coated

with AgCl in a solution of Cl–

• Q depends on aCl

ion

Variety of cellsVariety of cells

• Electrolyte concentration cell• Electrode concentration cell• Liquid junction potential

Redox electrode

• Fig 9.12 (215)• The same element in two non-

zero oxidation states

The Daniell cellThe Daniell cell

• Fig 9.13 (215)• Zn is the anode• Cu is the

cathode

The cell reactionThe cell reaction

• Anode on the left; cathode on the right

Cell Diagram

Zn (s) + Cu2+ (aq) Cu (s) + Zn2+ (aq)

[Cu2+] = 1 M & [Zn2+] = 1 M

Zn (s) | Zn2+ (1 M) || Cu2+ (1 M) | Cu (s)

anode cathode

Measuring cell emfMeasuring cell emf

Fig 9.13 (217) Cell emf is measured by balancing the cell against an opposing external potential. When there is no current flow, the opposing external potential equals the cell emf.

The electromotive forceThe electromotive force

• The maximum non-expansion work (w’max) equals G [T,p=K] (9.12)

• Measure the potential difference (V) and convert it to work to calculate G

rG = –FE (F = 96.485 kC/mol)

• E = – rGF

The electromotive forceThe electromotive force

rG = –FE

rG = rG + RT ln Q

• E = E – ln Q

• E =

• At 25°C, = 25.693 mV

• E is independent of how the rxn is balanced

RTRTFF

rGrGFF

RTRTFF

Cells at equilibriumCells at equilibrium

ln K = FERT

• At equilibrium, Q = K and a rxn at equilibrium can do no work, so E = 0

• So when Q = K and E = 0, the Nernst equation

E = E – ln Q , becomes….

RTF

Cells at equilibriumCells at equilibrium

ln K = FERT

Is simply an electrochemical expression of

rG = – RT ln K

Cells at equilibriumCells at equilibrium

• If E > 0, then K > 1 and at equilibrium the cell rxn favors products

• If E < 0, then K < 1 and at equilibrium the cell rxn favors reactants

218218

Standard potentialsStandard potentials

• SHE is arbitrarily assigned E = 0 at all temperatures, and the standard emf of a cell formed from any pair of electrodes is their difference:

• E = Ecathode – Eanode OR

• E = Eright – Eleft

• Ex 9.6: Measure E, then calculate K

The variation of potential The variation of potential with pHwith pH

If a redox couple involves H3O+, then the potential varies with pH

Table 9.3 Table 9.3 Standard reduction potentials at 25°C Standard reduction potentials at 25°C

(1)(1) Reduction half-reaction Eo/V

Oxidizing agent Reducing agent

Strongly oxidizing

F2 2 e 2 F 2.87

S2O 82– 2 e 2 SO

42– 2.05

Au e Au 1.69

Pb4 2 e Pb2 1.67

Ce4 e Ce3 1.61

MnO 4– 8 H 5 e Mn2 4 H2O 1.51

Cl2 2 e 2 Cl 1.36

Cr2O 72– 14 H 6 e 2 Cr3 7 H2O 1.33

O2 4 H 4 e 2 H2O 1.23, 0.81 at pH 7

Br2 2 e 2 Br 1.09

Ag e Ag 0.80

Hg22 2 e 2 Hg 0.79

Fe3 e Fe2 0.77

I2 e 2 I 0.54

O2 2 H2O 4 e 4 OH 0.40, 0.81 at pH 7

Table 9.3 Table 9.3 Standard reduction potentials at 25°C Standard reduction potentials at 25°C

(2)(2) Reduction half-reaction Eo/V

Oxidizing agent Reducing agent

Cu2 2 e Cu 0.34

AgCl e Ag Cl 0.22

2H 2 e H2 0, by definition

Fe3 3 e Fe 0.04

O2 H2O 2 e HO 2– OH 0.08

Pb2 2 e Pb 0.13

Sn2 2 e Sn 0.14

Fe2 2 e Fe 0.44

Zn2 2 e Zn 0.76

2 H2O 2 e H2 2 OH 0.83, 0.42 at pH 7

Al3 3 e Al 1.66

Mg2 2 e Mg 2.36

Na e Na 2.71

Ca2 2 e Ca 2.87

K e K 2.93

Li e Li 3.05

Strongly reducing

For a more extensive table, see the Data section.

The determination of pHThe determination of pH

• The potential of the SHE is proportional to the pH of the solution

• In practice, the SHE is replaced by a glass electrode (Why?)

• The potential of the glass electrode depends on the pH (linearly)

A glass electrodeA glass electrode

• Fig 9.15 (222) • The potential of a

glass electrode varies with [H+]

• This gives us a way to measue pKa electrically, since pH = pKa when [acid] = [conjugate base]

The electrochemical seriesThe electrochemical series

• A couple with a low standard potential has a thermodynamic tendency to reduce a couple with a higher standard potential

• A couple with a high standard potential has a thermodynamic tendency to oxidize a couple with a lower standard potential

• E0 is for the reaction as written

• The more positive E0 the greater the tendency for the substance to be reduced

• The more negative E0 the greater the tendency for the substance to be oxidized

• Under standard-state condi-tions, any species on the left of a given half-reaction will react spontaneously with a species that appears on the right of any half-reaction located below it in the table (the diagonal rule)

• The half-cell reactions are reversible

• The sign of E0 changes when the reaction is reversed

• Changing the stoichio-metric coefficients of a half-cell reaction does not change the value of E0

• The SHE acts as a cath-ode with metals below it, and as an anode with metals above it

The determination of thermodynamic The determination of thermodynamic functionsfunctions

• By measuring std emf of a cell, we can calculate Gibbs energy

• We can use thermodynamic data to calculate other properties (e.g., rS)

rS =

F(E – E’)T – T ’

Determining thermodynamic Determining thermodynamic functionsfunctions

• Fig 9.16 (223)

• Variation of emf with temperature depends on the standard entropy of the cell rxn

Key Key IdeasIdeas

Key Key IdeasIdeas

Key Key IdeasIdeas

The EndThe End…of this chapter…”

Box 9.1 pp207ff

Ion channel

s and pumps