Sample calculations of ionic transference numbers

Some reported values of cationic transference numbers are listed in Table 20.3. Conductivity data from Table 20.1 can be used to calculate transference numbers for protons in aqueous nitric acid, for example, from equations (20.1.2-9) and (20.1.2-12)  

The composition of the anode compartment following electrolysis was 1.366 wt% of barium chloride, where the compartment contained 120.37 g of solution. The product of 

Selected limiting ionic conductivities in aqueous solution at 298 K. The values are tabulated with cations (left-hand half of table) and anions (right-hand half of table) listed separately. Elemental ions are listed first, in order of increasing atomic mass, with molecular ions following, also in order of increasing mass  

The advance of the moving boundary marking the denser, less mobile KCl solution allows the transference number of the potassium ion to be found from equation (20.2.1-3). For a capillary of 0.209 cm inner radius, the displacement of the boundary after 200, 400 and 600 sec was found to be 6.4, 12.9 and 19.2 cm. A constant current of 36.4 mA was maintained. Using the first pair of data, the volume displaced (the cross-sectional area multiplied by the distance the boundary has moved through) is 0.88 cm  

The measured cell potential was -3.0 mV. Re-arrangement of equation (20.2.1-9) gives 

---