$8$(a) (i) Why is boiling point of 1 M NaCl solution more than that of 1 M glucose solution ? $\displaystyle 1+2+2=5$

(ii)A non-volatile solute 'X' (molar mass $\displaystyle =50 \mathrm{~g} \mathrm{~mol}^{-1}$ ) when dissolved in 78g of benzene reduced its vapour pressure to 90%. Calculate the mass of X dissolved in the solution.(iii)Calculate the boiling point elevation for a solution prepared by adding 10g of $\displaystyle \mathrm{MgCl}_{2}$ to 200g of water assuming $\displaystyle \mathrm{MgCl}_{2}$ is completely dissociated. ( $\displaystyle \mathrm{K}_{\mathrm{b}}$ for Water $\displaystyle =0.512 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, Molar mass $\displaystyle \mathrm{MgCl}_{2}=95 \mathrm{~g} \mathrm{~mol}^{-1}$ )

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(b) (i) Why is the value of Van't Hoff factor for ethanoic acid in benzene close to 0.5 ? $\displaystyle 1+2+2=5$(ii)Determine the osmotic pressure of a solution prepared by dissolving $\displaystyle 2.32 \times 10^{-2} \mathrm{~g}$ of $\displaystyle \mathrm{K}_{2} \mathrm{SO}_{4}$ in 2L of solution at 25 °C, assuming that $\displaystyle \mathrm{K}_{2} \mathrm{SO}_{4}$ is completely dissociated. ( $\displaystyle \mathrm{R}=0.082 \mathrm{~L}$ atm $\displaystyle \mathrm{K}^{-1} \mathrm{~mol}^{-1}$, Molar mass $\displaystyle \mathrm{K}_{2} \mathrm{SO}_{4}=174 \mathrm{~g} \mathrm{~mol}^{-1}$ )(iii)When 25.6g of Sulphur was dissolved in 1000g of benzene, the freezing point lowered by 0.512 K. Calculate the formula of Sulphur $\displaystyle \left(\mathrm{S}_{\mathrm{x}}\right)$. $\displaystyle \left(\mathrm{K}_{\mathrm{f}}\right.$ for benzene $\displaystyle =5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, Atomic mass of Sulphur = 32g $\displaystyle \mathrm{mol}^{-1}$ )

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