The density of '$x$' $M$ solution ('$x$' molar) of $NaOH$ is $1.12 \ g \ mL^{-1}$. While in molality,the concentration of the solution is $3 \ m$ $(3 \ molal)$. Then '$x$' is.
(Given: Molar mass of $NaOH$ is $40 \ g \ mol^{-1}$)

The correct relationship between molality $(m)$ and molarity $(M)$ of a solution is ($d = $ density in $g/mL$ and $M_{solute} = $ molar mass of solute in $g/mol$)

Two solutions labeled as $3\,M\,HCl$ and $1\,M\,HCl$ are mixed in the ratio of $x : y$ by volume and the molarity of the resulting solution is $1.5\,M$. The molarity of the resulting solution if they are mixed in the ratio $y : x$ by volume is ....... $M$.

In $500 \ mL$ of $0.2 \ M \ NaCl$ solution,$1500 \ mL$ of $0.4 \ M \ MgCl_2$ solution is mixed. The only incorrect final concentration of ion is (assume volume to be additive)

$1000 \ g$ aqueous solution of $CaCO_3$ contains $10 \ g$ of carbonate. Concentration of the solution is .......... $ppm$.

Nalorphene $(C_{19}H_{21}NO_{3})$,similar to morphine,is used to combat withdrawal symptoms in narcotic users. The dose of nalorphene generally given is $1.5 \, mg$. Calculate the mass of $1.5 \times 10^{-3} \, m$ aqueous solution required for the above dose.