Physical Chemistry Third Edition

10.5 Electrical Conduction in Electrolyte Solutions 479

The mobility and friction coefficient of a given ion depend on the concentrations

of the other ions present. There are three important effects. The first effect is the

electrophoretic effect, due to the fact that ions of the opposite charge are moving in

the opposite direction from a given ion. Their attractive forces pull on a given ion in

the direction of their motion, slowing that ion. The second effect is therelaxation effect.

Every ion is surrounded by an “ion atmosphere” of excess charge of the opposite sign. If

an ion moves, it is no longer at the center of its ion atmosphere, which must then relax to

become centered on the new position of the ion. This effect also slows down the motion

of the ion. The third effect is thesolvation effect. In the limit of small concentration

each ion can attract its full complement of solvent molecules, but at high concentrations

ions compete with each other to attract solvent molecules. Since solvent molecules that

are strongly attracted to it can move with an ion, any change in the solvation can affect

the mobility of the ion. The electrophoretic effect and the relaxation effect vanish in

the limit of small concentration and the solvation effect approaches a concentration-

independent value. Therefore, ion mobilities and friction coefficients approach constant

values in the limit of infinite dilution. Equation (10.5-23) is correct only in the limit of

small concentrations. Table A.20 gives values of ion mobilities at infinite dilution in

water at 25◦C.

The ions with the largest mobilities in aqueous solutions are the hydrogen ion and

the hydroxide ion. The reason is that hydrogen and hydroxide ions can “exchange”

with water molecules. A hydrogen ion can attach itself to one or more water molecules,

making the H 3 O+ion or the H 5 O+ 2 ion, and so on. A hydrogen ion on the other side of

the H 3 O+can be released and attach itself to a second water molecule, after which a

different hydrogen ion is released, providing a rapid apparent motion of hydrogen ions.

The exchange of hydroxide ions is similar, with a hydrogen ion moving from a water

molecule to a hydroxide ion to form a “new” water molecule and a “new” hydroxide

ion in a different location, corresponding to effective radii smaller than actual ionic

radii.

EXAMPLE10.20

Calculate the apparent radii of the hydrogen and hydroxide ions from the ion mobilities.

Solution

ri(eff )

|zi|e

6 ρηui

For H+,

ri(eff )

1. 6022 × 10 −^19 C

6 π(8. 904 × 10 −^4 kg m−^1 s−^1 )(36. 25 × 10 −^8 m^2 s−^1 V−^1 )

 2. 63 × 10 −^11 CVkg−^1 m−^1 s−^2  2. 63 × 10 −^11 m 26 .3pm 0 .263 A

For OH−:

ri(eff )

1. 6022 × 10 −^19 C

6 π(8. 904 × 10 −^4 kg m−^1 s−^1 )(20. 5 × 10 −^8 m^2 s−^1 V−^1 )

 4. 66 × 10 −^11 CVkg−^1 m−^1 s−^2  4. 66 × 10 −^11 m 46 .6pm 0 .466 A