Weak electrolyte• Weak electrolytes are not fully ionized in solution, such as weak

acids and bases.

• Degree of ionization (α): defined as the ratio of the amount of ions being formed in the solution and the amount of electrolyte added to the solution.

• For the acid HA at a molar concentration c,

[H3O+] = αc, [A-] = αc , [HA] = c –αc

• Since only fraction, α, of electrolyte is actually presents as ions, the measure conductivity Λm, is given by:

Λm = αΛ0m

14

12

21 /

a

a

K

c

c

Ka

Ostwald’s dilution law

200

11

ma

m

mm K

c

24.7 The mobility of ions

• Drift speed: the terminal speed reached when the accelerating force is balanced by the viscous drag.

• Accelerating force induced by a uniform electric field (E = Δø/l):

F = z e E = z e Δø/l

• Friction force Ffric = (6πηa)s, a is the hydrodynamic radius

• Mobility of an ion:

a

zeEs

6

a

zeu

6

Mobility and conductivity

• For the solution:

Λ0m = (z+u+v+ + z-u-v-) F

Transport numbers

• The fraction of total current carried by the ions of a specified type.

• The limiting transport number, t0±,

I

It

I

It

uvzuvz

uvzt0

Conductivities and ion-ion interactions

24.8 The thermodynamic view of diffusion

• The maximum amount of work can be done when moving a substance from local x to x+dx is:

• When expressed with an opposite force:

dw = - F dx

Then one gets:

Therefore: The slope of the chemical potential can be interpreted as an effect force, thermodynamic force. This force represents the spontaneous tendency of the molecules to disperse.

dxx

ddwTp,

TpxF

,

• Since μ = μө + RTlnα

• One get

• Using concentrations to replace the activity:

• Recall Fick’s first law of diffusion:

TpTp x

aRT

x

aRTuF

,,

ln}

)ln({

Connections between the thermodynamic force and the

concentration gradient

Tpx

c

c

RTF

,

24.9 The diffusion equation

2

2

x

cD

t

c

Derivation of the diffusion equation

• The amount of particles enter the slab in the time interval dt equals: JAdt, where J is the matter flux

• The increase in molar concentration inside the slab is: JAdt / (Al t) = J/l

• Consider the outflow through the right-hand side:

-JAdt / (Al t) = J/l

• The net change is:

• Then

l

JJ

t

c '

2

2

x

cDlJJ

x

clc

xD

x

cD

x

cD

x

cDJJ

'

''

Designing electrochemical cells

• Example 1: 5Zn + 2MnO4- + 16H+ → 5Zn2+ + 2Mn2+ + 8H2O

• Example 2: Pt | H2(g) | HCl (aq), AgCl(s) | Ag(s)

• Example 3: Zn(s) | ZnCl2(aq) | KCl(aq) | CuCl2 | Cu(s)

Highlights of Chapter 9

• Extent of the reaction.• Reaction Gibbs energy.• The relationship between the reaction Gibbs energy and chemical

potential.• The relationship between the reaction Gibbs energy and chemical

equilibrium.• Expressing equilibrium constant in terms of the standard reaction

Gibbs energy.• Calculations of the reaction Gibbs energy.• Le Chatelier’s principle.• Van’t Hoff equation.• Changes of pH during the titration of weak acids (at the beginning,

in the process, at the stoichiometric point, beyond the ending point).

Highlights from Chapter 10

• Standard enthalpy and Gibbs energy of formation for ions.• Thermodynamic cycle.• The standard enthalpy and Gibbs energy of formation of H+ is used

as the reference for other ions.• Activity coefficient.• Debye-Huckel theory to calculate the mean activity coefficient.• Galvanic cell and electrolytic cell.• Electrodes and half reactions.• Cell potentials.• Calculations of the standard cell potential.• Applications of the standard potential.• Temperature coefficient of cell potential.

Highlights from Chapter 24

• Kinetic theory.• Flux of matter.• Flux of energy.• Flux of momentum.• Effusion.• Collision flux, collision frequency, and their connection with the

measurement of vapor pressure.• Molar conductivity for electrolytes.• Molar conductivity of individual ions.• Kohlrausch’s law.• Ostwald’s dilution law.• Thermodynamic view of diffusion.