A village of $100$ inhabitants consumes on average $200m3$ of water per day. The treatment station mainly includes an ultrafiltration system

which feeds an electrodialyzer. The water to be treated contains $70m\frac{g}{L}$ of nitrate ions, mainly in the form of KNO$3.$ The aim is to reduce

the nitrate content to $25m\frac{g}{L}($European standard$).$ The electrodialysis module has $25$ elementary cells with $2$ compartments. Each

membrane has a unit surface area of $0\mathrm{.}5m2$ and is separated by $1cm$ from its neighbor. The applied current density is $10m\frac{A}{c}m2$ and

the farada efficiency is $97\%.$

$1-$ What is the function of the ultrafiltration system positioned upstream of the electrodialyzer?

$2-$ Calculate the KNO$3$ salt content in the concentrate leaving the electrodialyzer.

$3-$ Calculate for one day the quantity of current used then the operating time of the electrodialyzer.

$4-$ Assuming that the electrical resistance of an elementary cell of the electrodialyzer is equivalent to that of the solution constituting the

diluate $($due to its low concentration$),$ calculate this electrical resistance $R$ according to:

$R=\frac{e}{y^{}.S}$ with $e$ : inter$-$membrane distance $(m),y^{}$ : conductivity of the solution $(\frac{S}{m}),S$ : membrane surface $(m2).\frac{?}{\text{b}\text{a}\text{r}}(y)$ being otherwise equal

to: $FC(uK++$uNO$3-)$ with $F$ : Faraday constant $(96500\frac{C}{m}ol),C$ : concentration of the solution $($mol$/$m$3),$ u: ionic electrophoretic mobility

$(7\mathrm{.}62\mathrm{.}10-8$ m$2.$V$-1.$s$-1$ for K$+$ and $7\mathrm{.}40\mathrm{.}10-8$ m$2.$V $-1.s-1$ for $NO3-).$

Deduce the power dissipated by an elementary cell, then by the electrodialyzer as a whole.

Data :

Atomic masses: K: $39$; N: $14$; O: $161$ year $=$

$365\mathrm{.}25$ days