Concise Physical Chemistry

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

210 COULOMETRY AND CONDUCTIVITY

+

HCl

LiCl

cathode

anode

FIGURE 13.4 Moving boundary determination of the mobility of H+.Li+is the follower

ion.

than its “share” of charge and less than 0.5 for an ion that carries less than its share

of the charge.

One way of measuring the mobility of a cation is to load a capillary tube with a

solution containing the ion in question on top of a second electrolyte solution that is

more dense than the measured ion solution. The cation of the more dense solution

is called afollower ionbecause when a field is applied to the tube, it moves upward

at the rate of the principal cation, H+in the case shown in Fig. 13.4. The follower

ion is drawn along by H+to prevent a charge gap from developing between the two

solutions.

Figure 13.4 shows a solution of HCl loaded into a capillary tube on top of a

solution of LiCl, where Li+is the follower ion. Upon applying a potential difference

across the cathode and anode, H+is attracted to the cathode (−) and Li+follows

along. The velocity of migration is determined by the faster of the two ions. The

interface between the HCl and LiCl solutions is maintained by the follower ion and

can be visually observed because of the difference in refractive indices of the two

solutions. The velocity isxms−^1 and the mobilityuis thespeed x/tper volt of

potential difference:

u=

x

tV

ms−^1

(

volt m−^1

)− 1

=

x

tV

m^2 volt−^1 s−^1

The rather odd-looking unit is meters per second per volt per meter of the resisting

medium. In the present case, this is unit voltage across the conducting solution. All

of the variables on the right are measurable quantities, hence the mobility can be

calculated.