Transference numbers are often measured by Hittorf method as illustrated in this

Question

Transference numbers are often measured by Hittorf method as illustrated in this problem. Consider the three-compartment cell: (-)Ag/AgNO_3(0.100 M)//AgNO_3(0.100 M)//AgNO_3(0.100 M)/Ag(+) where the "//" signify sintered glass disks that divide the compartments and prevent mixing, but not ionic movement. The volume of AgNO_3 so in each compartment (L, C, R) is 25.00 mL. An external power supply is connected to the cell with the polarity shown, and current is applied until 96.5 C have passed, causing Ag to deposit on the left Ag electrode and Ag to dissolve from the right Ag electrode. How many grams of Ag have deposited on the left electrode? If the transference number for Ag+ were 1.00. what would the conc of Ag" be in the three compartments after electrolysis? Suppose the transference number for Ag4 were 0.00, what would the con of Ag- be in the three compartments after electrolysis? In an actual experiment like this, it is found experimentally that the conc of Ag+ in the anode compartment R has increased to 0.121 M. Calculate t(Ag+).

Explanation / Answer

Increase in mass of silver around anode after electrolysis=0.121 M

If Ag+ had not migrated from the anode ,then the mass of silver had been 0.100M .Hence the decrease in the concentration around the anode as a result of migration of Ag+ ions is (0.121M-0.100M=0.021M

The decrease is proportional to the speed of Ag+ ions and the speed is proportional to the fraction of current carried by Ag+ ions.

therefore transport number of Ag+ ion is given by=t(Ag+)=fall in concentration around anode/total current passed=0.021 /0.100=0.21

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