$A$ $40 \%$ by mass sucrose solution is heated till it becomes $50 \%$ by mass. Calculate the mass of water lost from $100 \ g$ of the solution. (in $g$)

How are $0.50 \, mol$ $Na_{2}CO_{3}$ and $0.50 \, M$ $Na_{2}CO_{3}$ different?

$A$ solution is $0.25 \%$ by mass. What is the weight of solvent containing $1.25 \ g$ solute (in $g$)?

$3.1 \ g$ of a compound,'$X$' (molar mass $= 62 \ g \ mol^{-1}$) is dissolved in $19.5 \ g$ of other compound,$Y$ (molar mass $= 78 \ g \ mol^{-1}$). The ratio of mole fractions of $X$ and $Y$ in the solution is

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 .......... $mL$.

$300 \ g$ of $25\%$ solution and $400 \ g$ of $40\%$ solution are mixed by weight. Calculate the percentage of the solute by weight in the final mixture. (in $\%$)