a$.$ In the electrolytic winning of Zn the cell voltage, V$,$ and current efficiency, C$.$E$,$ vary with the current density as given below:

A$/$cm$3$ V C$.$E$.(\%)$

$0\mathrm{.}012\mathrm{.}580$

$0\mathrm{.}022\mathrm{.}790$

$0\mathrm{.}053\mathrm{.}094$

$0\mathrm{.}103\mathrm{.}596$

i$.$ Calculate the electric energy consumption in killowatthours per kilogram of Zn for the four current densities. $[10$ Marks$]$

ii$.$ In practice also capital investments must be considered. Indicate which investment must be considered. Indicate which current density you would choose to give the lowest overall cost of electrolysis. $[5$ Marks$]$