CHƯƠNG 1 TÍNH CHẤT DẪN ĐIỆN CỦA DUNG DỊCH ĐIỆN LY

8/3/2019 CHNG 1 TNH CHT DN IN CA DUNG DCH IN LY

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Physical Chemistry II

7.3 conductivity of solution

Feb. 25, 2003

Chapter VII Electrolytic solution


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Conducting mechanism of electrolytic

solution

MzF

Qm


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Motion of ions in the solution:

Only the transfer can cause net electricity

1) diffusion: due to difference inconcentration

2) convection: due to the difference indensity or temperature

3) transfer: due to electric field


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7.3.1 conductance and its measurement

For metals:

Ohm s Law

I

UR

R: resistance

Dimension: Ohm,


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resistivity

A

l

R

Dimension: Ohm m, m


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For electrolytic solution:

conductivity () or spedific conductance:

Definition: = 1/

Dimension: S m-1

electric conductance (G) :

Definition: G = 1/R

Dimension:-1, mho, Siemens, S


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conductivity cell


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Type 206

conductance electrode


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WheatstoneBridge

Circuit

High-frequency alternative current, ca. 1000

Hertz


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R3 R2 = R4 R1

4

321

R

RRR

1

1

R

G

GKA

lG

cell

RKcell

Cell constant of a

conductivity cell


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The conductance cell is usually calibrated with

standard KCl (potassium chloride ) solution.

xxss RR RKcell

11.21.2890.14110.01470/S m-1

1.00.10.010.0010C/ mol dm-

3


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7.3.2 influential factors for conductivity

1) concentrationdependence of

conductance


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1. Acids and bases

have higherconductance

2. C < 5 mol dm-3

, increases with C

3. For CH3COOH conductance does

not depend on C


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(2) temperature-

dependence ofconductance


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1. 38 % H2SO4 was

used in acid-leadbattery;

2. Hot electrolytewas used for

electrolysis and

electroplating


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At room temperature, conductivity of

solution increases by 2% for per degreecentigrade.

)]25(')25('1[)( 25 TTT

PP TT


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7.3.3 Molar conductivity

Cm

V

V

m 11) Definition

V: degree of dilution

The conductivity of a solution is approximatelyproportional to the concentration

m is the conductivity contributed by 1 mole ofelectrolyte between electrodes of 1 m apart


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Dependence of molar conductivity

on concentration

m decreases withconcentration.

Kohlrausch replotted

m

against C1/2

Due to the interaction

between ions:

interionic attraction


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For 1:1

electrolytes:

C < 0.002~ 0.003

mol dm-3

Linear

relationship

between m

and

C1/2 can be

observed.


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Kohlrausch empirical formula

cAmm

To extrapolate the linear part ofm ~ C1/2

at low concentration to C = 0, m can be

obtained.m

the limiting value ofm at infinite

dilution: limiting molar conductivity


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7.3.4 Kohlrausch s law of independent

ionic mobilities

,, mmm

At infinite dilution, m should be

the sum of the separatecontributions of the ions


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limiting molar conductivity of

weak electrolyte

)()()( AcHHAc

mmm

)()()(

)()()(

ClNaAc

NaClH

mmm

mmm

)()()( NaClNaAcHClmmm


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7.3.5 ionic mobility and transference

number of ions

1) Ionic mobility

dl

dEr

dl

dEUr

Under unit potential gradient: dE/dl = 1

V m-1: U = R, ionic mobility


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I = I+ + I-

Q = Q+ + Q- Q

Qt

j

j

The fraction of the current transported by an ion

is its transference number or transport number

t = t+ + t- =

1

2) Transference number


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3) Relation between ionic mobility and

transference number

C-, Z-, U-; C+, Z+, U+;For time t: Q+ = A U+t C+ Z+ F

Q = A Ut CZF


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Q = Q+ + Q =AtF( U+C+ Z+ + U C

Z

)

C+ Z+ =C Z

Q =AtFC+ Z+ ( U+ + U

)

UU

Ut

UU

Ut


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4) Relation between transference

number and molar conductivity

I+ = AU+Z+C+F I = AUZ

C FI = I++ I =AC+Z+F(U++U

)

VUUFZACG )(


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)(

)(

)(

UUFZCl

VUUFZC

Al

VUUFZAC

AlG


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C

UUFZCm

)(

For uni-univalent electrolyte:

)(

UUFm

,, mmm

FUm ,

FUm

,


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t

FUU

FU

m

m

)(

,

mm t, mm t,

To measure m,+ orm,- , either t+ and t-or U+ and U- must be determined


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7.3.6 measurement of transference numbers

1) Hittorf method (1853)

Electrolysis of HCl solution

Anodic region cathodic regionBulk solution


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4 Cl-

-4e- 2 Cl2 4 H+ +4e- 2 H2

When 4 Faraday pass through the electrolytic cell

3 mol H+ 1 mol Cl-

3 mol H+ 1 mol Cl-


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Cresidual = Cinitial Creact + Ctransfer3 = 6 4 + Ctransfer

For anodic region:

t- = 1 / 4 = 0.25 t+ = 3 / 4 = 0.75


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Hittorf s

transference cell


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Example

Pt electrode, FeCl3 solution:

In cathodic compartment:

Initial: FeCl3 4.00 mol dm-3

Final: FeCl3 3.150 mol dm-3

FeCl2 1.000 mol dm-3

Calculate the transference number of Fe3+


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2) The moving-boundary

method

MA, MA have an ion in

common. The boundary,

rather difference in color,

refractivity, etc. is sharp.

In the steady state, the twoions move with the same

velocity.


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When Q coulomb passes, the

boundary moves x, the cross-sectional area of the tube is

A:

xACZ+F = t+Q


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Sample:

When A = 1.05 10-5 m2, C(HCl) = 10.0 molm-3, I = 0.01 A for 200 s, x was measured to be

0.17 m. Please calculate t (H+)

Solution:

t+ = 0.17 m 1.05 10-5 m2 10.0 mol m-3

1

96500 C mol-1 / 0.01 A 200 S

= 0.82


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7.3.7 factors on transference number

1) temperature

0.48850.48860.48870.488935

0.49010.49020.49030.490625

0.49240.49250.49260.492815

0.020.010.0050.000T / oC

Table Transference number of K+ in KCl solution

at different concentration and temperature


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2) co-existed ions

0.17490.50980.60800.6711t

HClKClNaClLiClelectrolyte

0.50840.48840.48330.4902t+

KNO3KIKBrKClelectrolyte

UU

Ut


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7.3.8 Influential factors for m

1) the nature of ions

(1) Charge

(4) Mechanism

(3) Electric character

(2) Radium


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2.091.04La3+

2.040.67Fe3+4.420--Fe(CN)6

4

1.890.57Al3+

3.030--Fe(CN)631.1891.04Sr2+

1.48--C2O42-1.1901.04Ca2+

1.66--CO32 1.0610.74Mg2+

0.7841.96Br0.7351.37K+

0.7631.81Cl0.5010.98Na+0.5541.23F0.3870.68Li+1.98--OH3.4982--H+

102

m

r / nmions102

m

r / nmions

Limiting molar conductivity of ions


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Mechanism of hydrogen and hydroxyl

ions

Grotthus mechanism (1805)


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2) Viscosity of the solvents

0.00150.00400.0075Li+

0.00220.00540.0082K+

1.2000.5470.316 /mPas

Ethyl

alcohol

Methyl

alcohol

acetone

Table. Viscosity of solvent on limiting molarconductivity of ions


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The Stokes s law

r

FeZ

m )300(6,


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Problems

1. Make comparison between Hittorf smethod and moving boundary method.

2. Why the limiting molar conductivity of

weak electrolyte can not be obtained by

extrapolating ofm ~ C1/2.

3. What experimental results back up theKohlrausch s Law of independent ionic

mobilities


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4. Summarize the effect of ionic nature on

limiting molar conductivity of ions


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Exercises

p. 573, ex. 4

ex. 7

ex. 9

ex. 13

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