A farmer uses underground water for its daily consumption.

This water contains $100$ mg KNO

$3$ per liter. The farmer wants to reduce this salt concentration to $20$ mg$/$L to be able

to use this water as drinking water, and needs each day $5$ m $3$ drinking water.

For that purpose, he uses a CED process with $2$ compartments. Each compartment has a volume equal to $5$ m

$3.$ This

process integrates $10$ elementary cells with a CEM as a central membrane in each compartment.

Each rectangular membrane is $100$m thick, has as dimensions: $50$

$20$ cm $2,$ and is separated from another

membrane or electrode by a distance equal to $1$ cm$.$ Its boundary layer has a thickness equal to $10$m$.$

The membrane material has the following properties: density: $2\mathrm{.}97$ g$/$cm

$3,$ hydration rate: $50\%,$ IEC: $1\mathrm{.}21$ meq $/$g

Other data:

D$($K

$++)=9\mathrm{.}0\mathrm{.}1011$ m $2/$s

D$($K

$++)=1\mathrm{.}95\mathrm{.}108$ m $2/$s

D$($NO

$3--)=8\mathrm{.}8\mathrm{.}1011$ m $2/$s

D$($NO

$3--)=1\mathrm{.}90\mathrm{.}108$ m $2/$s

$\backslash$Lambda

$\backslash$deg $\backslash$deg $($K $++)=7\mathrm{.}35$ mS$.$m $2$ mol

$\backslash$Lambda

$\backslash$deg $\backslash$deg $($NO $3--)=7\mathrm{.}14$ mS$.$m $2$ mol Calculate:

$1)$

The concentration of functional sites $($W$),$ counter ions $($C$($K $++)),$ and co ions C$($NO $3--)),$ in each membrane

$2)$

The transport numbers of both K and NO $3$ in the solution and in the membrane

$3)$

The conductivities of the solution and of the membrane $($and also the specific resistance of the membrane$)$

$4)$

The limiting current density and the most suitable current density and current to operate the process

$5)$

The maximum and real concentrate concentrations

$6)$

The faradic yield, quantity of charge, duration and energetic consumption of the process