$A$ solution of glucose in water is labelled as $10 \% \ w/w$. What would be the molality and mole fraction of each component in the solution? If the density of the solution is $1.2 \ g \ mL^{-1}$,then what shall be the molarity of the solution?

(N/A) $10 \%$ $w/w$ solution of glucose in water means $10 \ g$ of glucose and $90 \ g$ of water.
$10 \ g$ of glucose $= \frac{10}{180} = 0.0555 \ mol$
$90 \ g$ of $H_2O = \frac{90}{18} = 5 \ mol$
$\text{Molality} = \frac{\text{Moles of solute} \times 1000}{\text{Mass of solvent in grams}} = \frac{0.0555}{90} \times 1000 = 0.617 \ m$
$\text{Mole fraction of glucose } (X_g) = \frac{0.0555}{5 + 0.0555} = 0.01$
$\text{Mole fraction of water } (X_w) = \frac{5}{5 + 0.0555} = 0.99$
$\text{Volume of } 100 \ g \text{ solution} = \frac{100}{1.2} = 83.33 \ mL$
$\text{Molarity} = \frac{0.0555}{83.33} \times 1000 = 0.67 \ M$