Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

ION MOBILITIES 209

whereαruns from 0 (the trivial case of no ionization) through small numbers at most

concentrations only rising toα=1 for complete ionization.

The only trouble with this plan is evident from Fig 13.3. Accurate data are difficult

to obtain at very low concentrations; and even if they could be found,◦is at the

intersection of two nearly parallel lines. A way out of this dilemma is through

Kohlrausch’s law of independent ion migration at infinite dilution. Figure 13.3 shows

that, although we cannot find an accurate value for◦HOAcdirectly, we can find

accurate values for◦HCland◦NaOAc. These, in combination with◦NaCl, yield

◦HCl+◦NaOAc−◦NaCl

=λ◦H++λ◦Cl−+λ◦Na++λ◦OAc−−λ◦Na+−λ◦Cl−

=λ◦H++λ◦OAc−

=◦m(HOAc)

Armed with this new piece of information, we can calculateα=/◦. The disso-

ciation reaction is

HOAc+

(1−α)c

←→H+

αc

+OAc−

αc

where the concentrations of the individual ions at overall concentrationcare con-

trolled by the degree of dissociationαc. The undissociated HOAc (1−α)cis what

is left of the original HOAc after dissociation has taken place. Typical values might

be 17% dissociated and 83% undissociated forα= 0 .17. The equilibrium constant

for thisaciddissociation reaction is

Ka=

[H+][OAc−]

[HOAc]

=

(αc)(αc)

(1−α)c

=

0. 170 (. 170 )

0. 83

c= 0. 035 c

If these dissociation data are observed for a 5. 0 × 10 −^4 molar solution,Ka(HOAc)

is found to be about 1. 7 × 10 −^5 (accurate value 1. 754 × 10 −^5 (CRC Handbook of

Chemistry and Physics, 2008–2009)). This is theacidity constantof acetic acid

familiar from general chemistry.

There are now computational methods of obtaining or at least approximating

quantum mechanical gas-phase free energies for the components of the dissociation

reaction along with the necessary computed free energies of solvent interactions.

13.5 ION MOBILITIES

Inion mobilitystudies we wish to know how fast an ion migrates in an electrical field.

This is related to the charge fluxJ=dQ/dtand to thetransport numbers t+andt−,

theproportionof charge carried through the solution by each ion. Transport numbers,

which are fractions, add up to 1 and are larger than 0.5 for an ion that carries more