(b) The atomic radius of lithium is (23 A^circ. when the outermost 25 electrons is ionised off. The ionic radii of Lit is 0.76 A^circ . Assuming that the difference in radii relate to the space occupied by the 25 electrons, calculate the percentage of the volume of the lithium atom that is occupied by the valence electron. (c) The density of the anhydrous aluminium chloride was measured at 200^circ mathrm(C), 600^circ mathrm(C) and 800^circ mathrm(C) at atmospheric pressure and results are given below. Temperature in ( )^circ mathrm(C) & 200 & 600 & 800 Density in mathrm(g) / mathrm(cm)^3 & 6.9 & 2.7 & 1.5 i. Calculate the relative molecular mass of anhydrous aluminium chloride vapour at each temperature. [ R=8.31 mathrm(~J) / mathrm(K) (. ) ] ii. What is the probable molecular formula of aluminium chloride vapour at 200^circ mathrm(C) and 800^circ mathrm(C) . (mathrm(AL)=27.0, mathrm(CL)=35) iii. Outline the laboratory preparation of anhydrous Aluminium chloride from aluminium (d) Explain why the conductivity of the Lit (ion) is atomically to water. Question two a) Describe in details the extraction process of Aluminium from its principal or outlining the role of each chemical used.

## Step 1: Calculate the volume occupied by the valence electrons<br />### The atomic radius of lithium when the outermost 25 electrons are ionized off is $23 \, \text{Å}$. The ionic radius of $\text{Li}^+$ is $0.76 \, \text{Å}$. The difference in radii is due to the space occupied by the 25 electrons. To find the percentage of the volume occupied by these electrons, we first calculate the volumes using the formula for the volume of a sphere, $V = \frac{4}{3}\pi r^3$.<br /><br />- Volume of lithium atom: <br /> \[<br /> V_{\text{Li}} = \frac{4}{3}\pi (23)^3<br /> \]<br /><br />- Volume of $\text{Li}^+$ ion:<br /> \[<br /> V_{\text{Li}^+} = \frac{4}{3}\pi (0.76)^3<br /> \]<br /><br />- Volume occupied by valence electrons:<br /> \[<br /> V_{\text{electrons}} = V_{\text{Li}} - V_{\text{Li}^+}<br /> \]<br /><br />- Percentage of volume occupied by valence electrons:<br /> \[<br /> \text{Percentage} = \left(\frac{V_{\text{electrons}}}{V_{\text{Li}}}\right) \times 100<br /> \]<br /><br />## Step 2: Calculate the relative molecular mass of anhydrous aluminium chloride vapour<br />### Using the ideal gas law, $PV = nRT$, where $n = \frac{m}{M}$ (mass over molar mass), and rearranging gives $M = \frac{mRT}{PV}$. Given the densities at different temperatures, we can find the molar mass at each temperature.<br /><br />- At $200^\circ C$: Use density $6.9 \, \text{g/cm}^3$<br />- At $600^\circ C$: Use density $2.7 \, \text{g/cm}^3$<br />- At $800^\circ C$: Use density $1.5 \, \text{g/cm}^3$<br /><br />Convert densities to kg/m³ and use $R = 8.31 \, \text{J/K/mol}$.<br /><br />## Step 3: Determine the probable molecular formula of aluminium chloride vapour<br />### Compare the calculated molar masses with known values for possible molecular formulas like $\text{AlCl}_3$, $\text{Al}_2\text{Cl}_6$, etc., to determine the most likely formula at each temperature.<br /><br />## Step 4: Outline the laboratory preparation of anhydrous Aluminium chloride<br />### Describe the reaction between aluminium metal and chlorine gas or hydrogen chloride gas under controlled conditions to produce anhydrous aluminium chloride.<br /><br />## Step 5: Explain the conductivity of $\text{Li}^+$ ions in water<br />### Discuss how $\text{Li}^+$ ions interact with water molecules, leading to their high mobility and conductivity in aqueous solutions.<br /><br />## Step 6: Describe the extraction process of Aluminium<br />### Detail the Bayer process for refining bauxite to obtain alumina, followed by the Hall-Héroult process for electrolytic reduction of alumina to aluminium metal. Include the role of chemicals like sodium hydroxide and cryolite.