Question

The mole fraction of methanol in $4.5$ molal aqueous solution is:

• A. $0.250$
• B. $0.125$
• C. $0.100$
• D. $0.075$
• E. $0.055$

Answer 1

The correct option is D $0.075$

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.)

$\frac{1}{x}=\frac{\frac{w}{m}+\frac{W}{M}}{\frac{w}{m}}$

$\frac{1}{x}=1+\frac{W\times m}{M\times w}\times \frac{1000}{1000}$

$\frac{1}{x}=1+\frac{1000}{M\times m}$ $(\because Molality,m=\frac{w\times 1000}{m\times W})$

$=1+\frac{1000}{18\times 4.5}$ $(\because Molarmassof{H}_{2}O=18g{mol}^{-1})$

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

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

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

Hence, option D is correct.