The number of moles of a solute in its solution is $20$ and the total number of moles is $80$. The mole fraction of the solute is:

Which of the following statements is correct?
$(1)$ Molarity is the number of moles of solute in one liter of solution.
$(2)$ The normality and molarity of a sodium carbonate solution are the same.
$(3)$ The number of moles of solute dissolved in $1000 \ g$ of solvent is defined as molality $(m)$.
$(4)$ The ratio of the mole fractions of solute and solvent is equal to the ratio of their respective moles.

$A$ sample of drinking water is severely contaminated with chloroform $(CHCl_3)$. $CHCl_3$ is considered carcinogenic in nature. The level of contamination was $15 \ ppm$ (by mass).
$(i)$ Express this in percent by mass.
$(ii)$ Determine the molality of chloroform in the water sample.

The density of a $1.0 \ M$ aqueous solution of glucose is $1.1 \ g/mL$. What is the molality of the solution in $m$ (in $m$)?

Calculate the mass of urea $(NH_2CONH_2)$ required in making $2.5 \, kg$ of $0.25 \, \text{molal}$ aqueous solution.

An aqueous solution of glucose is $10\%$ in strength. The volume in which $1 \, \text{g-mole}$ of it is dissolved will be ........... $L$.