If $80 \ g$ of $NaOH$ is mixed with $54 \ g$ of water to form a solution,calculate the mole fraction of water.

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 $2 \ L$.

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 molarity if $30 \, mL$ of $0.5 \, M$ $H_2SO_4$ is diluted to $500 \, mL$. (in $, M$)

The volume of water added to $500 \ mL$ of $0.5 \ M \ NaOH$ solution so that its strength becomes $10 \ mg \ mL^{-1}$ will be .......... $mL$.

The molarity of a solution of $Na_2CO_3$ having $10.6 \ g$ in $500 \ mL$ of solution is ......... $M$.