# Ion Association Ion pair formation.

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Ion Association Ion pair formation

solvent-shared or solvent-separated
Ion Association Ion 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

Very difficult to bring the opposite ions so close!
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 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

Let 4F be passed through the cell; t+=3t-
4 Cl- -4e-  2 Cl2 4 H+ +4e-  2 H2 3 mol H+ 1 mol Cl-  3 mol H+ 1 mol Cl- 

For anodic region: Cresidual = Cinitial – Creact + C transfer 3 = – C transfer 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;

A solution of LiCl was electrolyzed in a Hittorf cell
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 g. Calculate the transport numbers of Li+ and Cl-. 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.x Charge carried by these moles: Q+=z+ F n+=z+ F c+ A x

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 × C mol-1 / 0.01 A × 200 S = 0.82

Independent migration
Kohlrausch’s Law of Independent migration Valid only at infinite dilution!

Experimentally determined
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Grotthuss Mechanism Explains 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 solvent
acetone Methyl alcohol Ethyl alcohol  / mPas 0.316 0.547 1.200 K+ 0.0082 0.0054 0.0022 Li+ 0.0075 0.0040 0.0015 Walden’s Rule L.h = constant