Chapter 7 Electrochemistry

§7.5 Theories for strong electrolyte

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Self reading:

Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002.

pp. 300-304

Section 10.8 the Debye-Hückel theory of electrolyte solutions

IAlnm m A c

Stationary propertyDynamic property

For ideal solution:

( ) lni i iT RT m y

For nonideal solution:

( ) ln lni i i iT RT m RT y

'ln)( , riPT WRTG

RT

Wri

'ln

Theoretical evaluation of Wr’Before 1894: treated solution as ideal gas

1918-1920: Ghosh – crystal structure

1923: Debye-Hückel: ionic atmosphere

Empirical formula for electrolyte solution

1. The Debye-Hückel theory

Ionic atmosphere

Radius:1~100 nm

Basic assumptions

1) Point charge

2) Only coulombic attraction

3) Dielectric constant keep unchanged

4) Boltzmann distribution, Poisson equation

Peter J. W. Debye

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(1) Simplified Model

Germany, Netherlands1884/03/24~ 1966/11/02Studies on dipole moments and the diffraction of X rays

Shielded Coulombic potential04j

r

Z e

r

/

0

e4

j b r

r

Z e

r

1

20

2A 04rkTb

N Ie

kTb

eZ

r

ii

0

22

8ln

1 13 2 2

2A 01

20

ln

4 ( )i i

r

e NZ I

kT

Debye length

RT

Wri

'ln

IAZ ii2ln

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(2) Theoretical treatment

IAZ ii2ln

IZZA ln Lewis’s empirical equation

Group exercise:

Deduce

from

for aqueous solution at 298 K

IZZ 172.1ln

IZZ 509.0lg

(3) Experimental verification

Debye-Hückel limiting law holds quite well for dilute solutions (I< 0.01 m), but must be modified to account for the drastic deviations that occur at high concentrations.

I

IZZA

I

IZZA

11

lg

Valid for c < 0.1 mol·kg-1

bII

IZZA

1lg

Valid for c < 1 mol·kg-1

(4) Modification

(1) Simplified Model

(2) Theoretical treatment

(3) Experimental verification

(4) Modification

Process for establishment of a theory

2. Debye-Hückel-Onsage theory

1) Relaxation effect

2) Electrophoretic effect

In 1927, Onsager pointed out that as the ion moves across the solution, its ionic atmosphere is repeatedly be-

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ing destroyed and formed again. The time for formation of a new ionic atmosphere (relaxation time) is ca. 10-

7 s in an 0.01 mol·kg-1 solution.

Under normal conditions, the velocity of an ion is sufficiently slow so that the electrostatic force exerted by the atmosphere on the ion tends to retard its motion and hence to decrease the conductance.

6

3

2

2.08 10 41.25( )

( ) (1 )

Z Z q Z ZI

TT q

( ) I

Valid for 310-5 ~ 10-3 mol·kg-1

Fuoss: valid for < 0.1 mol·kg-1

Falkenhagen: valid for < 5 mol·kg-1, f

or LiCl: valid until 9 mol·kg-1

Lars Onsager1968 Noble PrizeUSA, Norway1903/11/27~1976/10/05Studies on the thermodynamics of irreversible processes

Progress of the theories for electrolyte

1800: Nicholson and Carlisle: electrolysis of water

1805: Grotthuss: orientation of molecules

1857: Clausius: embryo of dissociation

1886: vant’ Hoff: colligative property

1887: Arrhenius: dissociation and ionization

1918: Ghosh: crystalline structure

1923: Debye-Hückel: Debye-Hückel theory

1926: Bjerrum: conjugation theory

1927: Onsager: Debye-Hückel-Onsager theory

1948: Robinson and Stokes: solvation theory

Question:

Compare the solubility of AgCl(s) in NaCl solution, pure water, and concentrated KNO3 solution using that in pure water as standard.

AgCl(s) = Ag+(aq) + Cl¯(aq)

Solubility equilibrium and the effect of co-ion.

ionic strength on solubility: salt effect