Chapter 19, Problem 31QRT

(a)

Interpretation Introduction

Interpretation:

The electrode at which magnesium is produced on electrolysis of molten ${\text{MgCl}}_{\text{2}}$ has to be given.

Explanation of Solution

Magnesium chloride undergoes electrolysis to form magnesium metal and chlorine gas.  This can be shown as given below,

    ${\text{MgCl}}_{\text{2}}\stackrel{\text{electrolysis}}{\to }\text{Mg}(\text{in melt})\text{+}{\text{Cl}}_{\text{2}}\text{(g)}$

Magnesium is a metal and hence magnesium cation is produced on electrolysis.  This magnesium cation gets oxidized at the cathode resulting in the formation of magnesium metal.

(b)

Interpretation Introduction

Interpretation:

On the anode the substance that is produced on electrolysis of molten ${\text{MgCl}}_{\text{2}}$ has to be given.

Explanation of Solution

Magnesium chloride undergoes electrolysis to form magnesium metal and chlorine gas.  This can be shown as given below,

    ${\text{MgCl}}_{\text{2}}\stackrel{\text{electrolysis}}{\to }\text{Mg}(\text{in melt})\text{+}{\text{Cl}}_{\text{2}}\text{(g)}$

Magnesium is a metal and hence magnesium cation is produced on electrolysis.  Chloride ion is produced in the melt and chlorine gas is liberated at the anode.

(c)

Interpretation Introduction

Interpretation:

Amount of electrons that is used in electrolysis of $\text{1000}\text{kg}$ of ${\text{MgCl}}_{\text{2}}$ has to be calculated.

Explanation of Solution

Magnesium chloride undergoes electrolysis to form magnesium metal and chlorine gas.  This can be shown as given below,

    ${\text{MgCl}}_{\text{2}}\stackrel{\text{electrolysis}}{\to }\text{Mg}(\text{in melt})\text{+}{\text{Cl}}_{\text{2}}\text{(g)}$

For each mol of $\text{Mg}$ and ${\text{Cl}}_{\text{2}}$ that is produced from one mole of ${\text{MgCl}}_{\text{2}}$, two mol of electrons are required.  One mol of electrons is equal to one Faraday.  Conversion factors are used to calculate the mol of electrons that is required.  This can be shown as,

$\begin{array}{l}\text{1000}\text{kg}{\text{MgCl}}_{\text{2}}\text{×}\frac{\text{1000}\text{g}}{\text{1}\text{kg}}\text{×}\frac{\text{1}\text{mol}{\text{MgCl}}_{\text{2}}}{\text{95}\text{.211}\text{g}{\text{MgCl}}_{\text{2}}}\text{×}\frac{\text{2}\text{mol}{\text{e}}^{\text{-}}}{\text{1}\text{mol}{\text{MgCl}}_{\text{2}}}=\frac{\text{2000000}}{\text{95}\text{.211}}\text{mol}{\text{e}}^{\text{-}}\\ \text{=}\text{21005}\text{mol}{\text{e}}^{\text{-}}\\ =2.1\times {10}^4\text{mol}{\text{e}}^{\text{-}}\end{array}$

Number of mol of electrons that is required is $2.1\times {10}^4\text{mol}$.

(d)

Interpretation Introduction

Interpretation:

Energy required per mole of magnesium has to be calculated if $\text{8}\text{.4}\text{kWh}$ is used per pound of magnesium.

Explanation of Solution

Magnesium chloride undergoes electrolysis to form magnesium metal and chlorine gas.  This can be shown as given below,

    ${\text{MgCl}}_{\text{2}}\stackrel{\text{electrolysis}}{\to }\text{Mg}(\text{in melt})\text{+}{\text{Cl}}_{\text{2}}\text{(g)}$

Conversion factors can be used to find the amount of energy required per mole of magnesium.  This can be done as shown below,

$\begin{array}{l}\frac{\text{8}\text{.4}\text{kWh}}{\text{1}\text{lb}\text{Mg}}\text{×}\frac{\text{3}\text{.6}\times {10}^6\text{J}}{\text{1}\text{kWh}}\text{×}\frac{\text{1}\text{kJ}}{\text{1000}\text{J}}\text{×}\frac{\text{1}\text{lb}\text{Mg}}{\text{453}\text{.6}\text{g}\text{Mg}}\text{×}\frac{\text{24}\text{.305}\text{g}\text{}\text{Mg}}{\text{1}\text{mol}\text{Mg}}=\frac{\text{734}\text{.9832}}{\text{453}\text{.6}}\times {\text{10}}^{\text{3}}\text{kJ}{\text{mol}}^{\text{-1}}\text{Mg}\\ \text{=}\text{1}\text{.620}\times {\text{10}}^{\text{3}}\text{kJ}{\text{mol}}^{\text{-1}}\text{Mg}\\ =1.6\times {\text{10}}^{\text{3}}\text{kJ}{\text{mol}}^{\text{-1}}\text{Mg}\end{array}$

Therefore, the energy required for per mole of magnesium is $1.6\times {\text{10}}^{\text{3}}\text{kJ}{\text{mol}}^{\text{-1}}$.