319171
The boiling point of water \(\left( {{\rm{10}}{{\rm{0}}^{\rm{^\circ }}}{\rm{C}}} \right)\) becomes \({\rm{100}}{\rm{.5}}{{\rm{2}}^{\rm{^\circ }}}{\rm{C}}\) if 3 g of a nonvolatile solute is dissolved in 200 g of water. The molecular weight of solute is: (\({{\rm{K}}_{\rm{b}}}\) for water is \({\rm{0}}{\rm{.6}}{\mkern 1mu} {\mkern 1mu} {\rm{K}}{\mkern 1mu} {\mkern 1mu} {\rm{mola}}{{\rm{l}}^{{\rm{ - 1}}}}\))
1 12.1 g/mol
2 15.4 g/mol
3 17.3 g/mol
4 20.4 g/mol
Explanation:
First boiling point of water \({\rm{ = 10}}{{\rm{0}}^{\rm{^\circ }}}{\rm{C = T}}_{\rm{b}}^{\rm{0}}\) Final boiling point of water \({\rm{ = 100}}{\rm{.5}}{{\rm{2}}^{\rm{^\circ }}}{\rm{C = }}{{\rm{T}}_{\rm{b}}}\) \({\rm{w = 3g,W = 200g,}}{{\rm{K}}_{\rm{b}}}{\rm{ = 0}}{\rm{.6K}}{\mkern 1mu} {\mkern 1mu} {\rm{kg}}{\mkern 1mu} {\mkern 1mu} {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\) \({\rm{\Delta }}{{\rm{T}}_{\rm{b}}}{\rm{ = 100}}{\rm{.52 - 100 = 0}}{\rm{.5}}{{\rm{2}}^{\rm{^\circ }}}{\rm{C}}\) \({{\rm{M}}_{{\rm{solute}}}}{\rm{ = }}\frac{{{{\rm{K}}_{\rm{b}}}{\rm{ \times }}{{\rm{w}}_{{\rm{solvent}}}}{\rm{ \times 1000}}}}{{{\rm{\Delta }}{{\rm{T}}_{\rm{b}}}{\rm{ \times }}{{\rm{W}}_{{\rm{solvent}}}}}}{\rm{ = }}\frac{{{\rm{0}}{\rm{.6 \times 3 \times 1000}}}}{{{\rm{0}}{\rm{.52 \times 200}}}}\) \({\rm{ = }}\frac{{{\rm{1800}}}}{{{\rm{104}}}}{\rm{ = 17}}{\rm{.3}}{\mkern 1mu} {\mkern 1mu} {\rm{g/mol}}\).
