Question

How long will it take to produce $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathit{K}\mathit{g}$ of magnesium metal by the electrolysis of molten magnesium chloride using a current of $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathit{A}$ ?

Short answer

t = 44.1 hours will it take to produce $1.00\times {10}^{3}Kg$ of magnesium metal by the electrolysis of molten magnesium chloride using a current of $5.00\times {10}^{4}A$ .

Step-by-step solution

Definition of Electrolysis of molten

Electrolysis is a chemical reaction that causes any molten ion to disintegrate into its constituent elements. Lead ions are reduced to lead atoms in the electrolysis of molten lead (II) bromide, whereas bromide ions are oxidized to bromine gas. The method can be applied to a variety of industrial operations.

Electrical current is electrical charge transferred at a particular time

These three properties can be calculated using the equation shown below. If we find the charge; we can use the equation shown above for calculating the time needed for the production of $1.00\times {10}^{3}Kg$of magnesium metal by electrolysis of molten magnesium chloride.

 Calculate the moles of magnesium, and we can do that from the mass of the magnesium

Moles of magnesium are calculated by dividing the mass of magnesium by the molar mass of magnesium.

$\text{n(Mg) =}\frac{\text{mass}}{\text{Molar mass}}\text{=}\frac{1.00\times {10}^{6}g}{24.301g/mol}{\text{=4.11×10}}^2\text{mol}$

Relate the moles of magnesium with the moles of electrons

If you look, at the figure below, you can see that the mole ratio is 1 to 2.
$\text{n}\left({\text{c}}^{\text{-}}\right){\text{= 2×n(Mg) = 2×411×10}}^4\text{mol}$
$n\left(e^{-}\right)=8.22\times {10}^{4}mol$
${\text{MgCl}}_2(\text{s})\stackrel{▴}{\to }{\text{Me}}^{2+}+2\text{Cl}$

${\text{Cathode: Mg}}^{2+}+2e^{-2}\to \text{Mg}$

$\text{Anode:}2{\text{Cl}}^{-}\to {\text{Cl}}_2+2e^2$

${\text{Mg}}^{2+}+2\text{Cl}\to \text{Mg}+{\text{Cl}}_2$

Calculating of magnesium metal by the electrolysis of molten magnesium chloride

The charge on 1 mole of electrons is called the Faraday 96,485 coulombs of charge pet mole of electrons. Thus q equals the number of moles of electrons times the charge per mole of electrons.

${\text{q}}^{\text{*}}\text{n}\left({\text{e}}^{\text{-}}\right){\text{×F = 8.22×10}}^4{\text{molee}}^{\text{-}}{\text{×96,485c/mole}}^{\text{-}}$

${\text{q = 7.93×10}}^9\text{C}$

Express time from the equation for current

Now, evaluating,

$\text{t =}\frac{\text{q}}{\text{I}}\text{=}\frac{{\text{7.93×10}}^4\text{C}}{{\text{5.00×10}}^4\text{- 4}}{\text{= 1.59×10}}^{5}s$

t=44.1 hours

t=44.1 hours will it take to produce $1.00\times {10}^{3}Kg$of magnesium metal by the electrolysis of molten magnesium chloride using a current of $5.00\times {10}^{4}A$.

Therefore, magnesium metal takes t=44.1 hours by electrolysis of molten magnesium chloride with a current of $5.00\times {10}^{4}A$.