In a solution of a solute in benzene with a molality of $x \ m$,the mole fraction of the solute is $0.2$. The value of $x$ is ...... .

$125 \, cm^3$ of isopropyl alcohol is added to water to make a solution of volume $175 \, cm^3$. Find the volume fraction and volume percentage of isopropyl alcohol in the solution.

For the solution formed by dissolving a solid in water,choose the correct option regarding the following statements: Statement-$1$: $A$ $1$ molal aqueous glucose solution contains $180 \ g$ of glucose in $1000 \ g$ of water. Statement-$2$: $A$ solution containing $1$ mole of solute in $1000 \ g$ of water is called a $1$ molal solution.

$250 \, mL$ of a sodium carbonate solution contains $2.65 \, g$ of $Na_2CO_3$. If $10 \, mL$ of this solution is diluted to $1 \, L$,what is the concentration of the resultant solution? (Molecular weight of $Na_2CO_3 = 106$)

What will be the molality of $10\%$ w/w aqueous solution of $NaOH$ (in $m$)? (Molecular mass of $NaOH = 40 \ g \ mol^{-1}$)

Molarity of a solution prepared by dissolving $75.5 \ g$ of pure $KOH$ in $540 \ mL$ solution is .......... $M$