The density of a $2.05 \ M$ solution of acetic acid $(CH_3COOH)$ in water is $1.02 \ g \ mL^{-1}$. The molality of the solution is ......... $mol \ kg^{-1}$.

Which of the following factors affect the molarity of a solution?

If $100 \ g$ of a $0.2 \ m$ aqueous solution is diluted by adding $200 \ g$ of water, what will be the molality of the resulting solution?

If $80 \ g$ of copper sulphate $CuSO_{4} \cdot 5H_{2}O$ is dissolved in deionised water to make $5 \ L$ of solution. The concentration of the copper sulphate solution is $x \times 10^{-3} \ mol \ L^{-1}$. The value of $x$ is .... .
[Atomic masses: $Cu = 63.54 \ u, S = 32 \ u, O = 16 \ u, H = 1 \ u$]

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.

Which of the following modes of expressing concentration is independent of temperature?