The molarity of pure water at $4\,^{\circ}C$ is ............... $M$.

Some amount of dichloromethane $(CH_2Cl_2)$ is added to $671.141 \ mL$ of chloroform $(CHCl_3)$ to prepare a $2.6 \times 10^{-3} \ M$ solution of $CH_2Cl_2$ $(DCM)$. The concentration of $DCM$ is $......... \ ppm$ (by mass). Given: Atomic mass: $C = 12, H = 1, Cl = 35.5$; density of $CHCl_3 = 1.49 \ g \ cm^{-3}$.

Calculate the mole fraction of $C_2H_6O_2$ (ethylene glycol) in an aqueous solution containing $28 \%$ by mass of $C_2H_6O_2$.

What is the mole fraction of the solute in a $2.5 \, m$ aqueous solution?

Calculate the concentration of fluorine in $ppm$ in $500 \ g$ of toothpaste containing $0.2 \ g$ of fluorine.

The concentration of $1 \ L$ of $CaCO_3$ solution is $1000 \ ppm$. What is its concentration in $mol \ L^{-1}$ ?
$(Ca=40 \ u, O=16 \ u, C=12 \ u)$