KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    The mole fraction of methanol in its 4.5 molal aqueous solution is

    A) \[0.250\]                       

    B) \[0.125\]

    C) \[0.100\]                       

    D) \[0.075\]

    Correct Answer: D

    Solution :

    [d]
    Mole fraction, \[X=\frac{\frac{w}{m}}{\frac{w}{m}+\frac{W}{M}}\]
    (Where w and m represent the mass and molar mass of solute and W and M represent the mass and molar mass of solvent)   
    \[\frac{1}{x}=\frac{\frac{w}{m}+\frac{W}{M}}{\frac{w}{m}}\]
    \[\frac{1}{x}=1+\frac{W\times m}{M\times w}\times \frac{1000}{1000}\]
    \[\frac{1}{x}=1+\frac{1000}{M\times w}\left( \therefore MOlarity,m=\frac{w\times 1000}{m\times W} \right)\]
    \[=1+\frac{1000}{18\times 4.5}\]
    (\[\therefore \]molar mass of \[{{H}_{2}}O=18\]\[mo{{l}^{-1}}\])\[=1+\frac{1000}{81}=13.34\]
    \[x=\frac{1}{13.34}=0.075\]


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