Ion Association

Ion AssociationIon pair formation

Ion AssociationIon pair formation

fully solvated solvent-shared or solvent-separated

Ion pair

contact ion pair

Ion pairs formed when opposite ions come close enough to be separated by a distance < r*

Bjerrum

As-Charge of ions increases (zi): r* increases, probability of ion pair formation increases.

-Temperature increases, r* decreases, probability of IP formation decreases. Kinetic energy acts against attraction.

-Polarity of solvent increases (er), attraction decreases, probability of IP formation decreases

Electrostatic potential energy for inter-action between two univalent ions:

Substitute r = r*

For univalent electrolyte in water at 25oC, IP formation is negligible

r* is only 0.358 nm.

Very difficult to bring the opposite ions so close!

Ionic Mobilities

Transport Numbers

c = 1 M c+= a M c-= b M

Electroneutrality condition

c = 1 M c+= a M c-= b M

Let 4F be passed through the cell; t+=3t-

Before electrolysis

On electrolysis

After electrolysis

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

3 mol H+ 1 mol Cl-

3 mol H+ 1 mol Cl-

Let 4F be passed through the cell; t+=3t-

Cresidual = Cinitial – Creact + C transfer

3 = 6 – 4 + C transfer

For anodic region:

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

measurement of transport numbers by Hittorf method

The method of Hittorf is based on concentration changes in the anodic region and cathodic region in an electrolytic cell, caused by the passage of current through the electrolyte.

Let 1F be passed through the cell;

lostamounttotaltcompartmenanodeinlostamountt

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A solution of LiCl was electrolyzed in a Hittorf cell. After a current of 0.79 A had been passed for 2 h, the mass of LiCl in the anode compartment has decreased by 0.793 g.

a. Calculate the transport numbers of Li+ and Cl-.

b. If Lo(LiCl) is 115 W-1cm2mol-1, what are the molar ionic

conductivities and the ionic mobilities?

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 two ions move with the same velocity.

When Q coulomb passes, the boundary moves x, the cross-sectional area of the tube is A:

No. of mole of H+ that passed from AA’ to BB’

n=c.V=c+.A.xCharge carried by these moles:

Q+=z+ F n+=z+ F c+ A x

tIxAcFz

QQt

Sample:

When A = 1.05×10-5 m2, c(HCl) = 10.0 mol m-3, I = 0.01 A for 200 s, x was measured to be 0.17 m. 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

Kohlrausch’s Law ofIndependent migration

Valid only at infinite dilution!

NaClCOONaCHHClCOOHCH oooo LLLL 33

Experimentally determined

- - -

NaClCOONaCHHClCOOHCH oooo LLLL 33

Grotthuss MechanismExplains the high conductivity of H+ and OH- in water

Ion Solvation

Size

But larger size means slower motion, the conductivity should drop?!!!!

•Smaller size, •larger interaction with water molecule,• hydrate shell larger on Li+,• moving species larger,•Lower conductivity

Viscosity of the solventacetone Methyl

alcoholEthyl

alcohol /

mPas0.316 0.547 1.200

K+ 0.0082 0.0054 0.0022

Li+ 0.0075 0.0040 0.0015

Walden’s Rule L. = constant