Calculate the mole fraction of urea in an aqueous solution of $1 \ m$ urea $(NH_2CONH_2)$.

What is the mole fraction of water in $10\%$ by weight $(w/w)$ of aqueous urea solution? [Given: Molar mass of $H, O, C$ and $N$ are $1, 16, 12$ and $14 \text{ g mol}^{-1}$ respectively.]

Calculate the mass percentage of aspirin $(C_{9}H_{8}O_{4})$ in acetonitrile $(CH_{3}CN)$ when $6.5 \ g$ of $C_{9}H_{8}O_{4}$ is dissolved in $450 \ g$ of $CH_{3}CN$.

$A$ solution is prepared by dissolving $24.5 \ g$ of sodium hydroxide in distilled water to give $1 \ L$ solution. The molarity of $NaOH$ in the solution is (Given that molar mass of $NaOH = 40.0 \ g \ mol^{-1}$) (in $M$)

If the density of a $5 \ M$ solution of $KCl$ is $1.26 \ g \ mL^{-1}$,then find the molality of the solution. (molecular mass of $KCl = 74.55 \ g \ mol^{-1}$) (in $m$)

Calculate the concentration of sugar $(C_{12}H_{22}O_{11})$ in $mol \ L^{-1}$ if $20 \ g$ of sugar is dissolved in sufficient water to make the final volume $2 \ L$.