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  4. The mole fraction of methanol in its 4.5 molal aqueous solution is

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Q. The mole fraction of methanol in its $4.5$ molal aqueous solution is

KEAMKEAM 2012Solutions

Solution:

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 m} (\because$ Molality, m$=\frac{w \times 1000}{m \times W}) $

$ =1+\frac{1000}{18 \times 4.5} $

($\because.$ Molar mass of $H _{2} O =18 \,g \,mol ^{-1}$ )

$=1+\frac{1000}{81}$

$=\frac{1081}{81}=13.34$

$x=\frac{1}{13.34}=0.075$