A) 32
B) 16
C) 64
D) 48
Correct Answer: B
Solution :
Step I Calculation of number of moles \[{{p}_{solution}}={{p}_{benzene}}\times {{\chi }_{benzene}}\] \[{{P}_{\text{solution}}}=0.8\,bar\] \[{{p}_{{{C}_{6}}{{H}_{6}}}}=1\text{bar}\] \[{{\chi }_{{{C}_{6}}{{H}_{6}}}}=\frac{{{p}_{\text{solution}}}}{{{p}_{{{C}_{6}}{{H}_{6}}}}}=\frac{0.8\,\text{bar}}{1\,\text{bar}}\] \[{{\chi }_{{{C}_{6}}{{H}_{6}}}}=0.8\] \[{{\chi }_{{{C}_{6}}{{H}_{6}}}}=\frac{\text{Moles}\,\text{of}\,{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{6}}}}{\text{Moles}\,\text{of}\,{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{6}}}\text{+}\,\text{Moles}\,\text{of}\,\text{solute}}\] \[{{\chi }_{{{C}_{6}}{{H}_{6}}}}=\frac{(39\,g)/78\,g\,mo{{l}^{-1}}}{(39\,g)/(78\,mo{{l}^{-1}})+{{n}_{\text{solute}}}}\] \[0.8=\frac{0.5}{0.5+{{n}_{\text{solute}}}}\] \[0.4+0.8\,n\,\text{solute}=0.5\] \[0.8\,n\,\text{solute}=0.5-0.4\] \[n\,solute=0.1/0.8\] \[n\,solute=\frac{1}{8}\,\text{mol}\] Step II Calculation of molecular mass of solute \[\text{Molecular}\,\text{mass}\,\text{=}\frac{\text{Mass}\,\text{of}\,\text{solute}}{\text{Number}\,\text{of}\,\text{moles}\,\text{of}\,\text{solute}}\]\[\text{Molecular}\,\text{mass}=\frac{2.g}{(1/8)\,mol}\] \[=\,16g\,mo{{l}^{-1}}\]
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