$8 \ g$ of $NaOH$ is dissolved in $18 \ g$ of $H_2O$. Mole fraction of $NaOH$ in solution and molality (in $mol \ kg^{-1}$) of the solution respectively are

Calculate $(a)$ molality,$(b)$ molarity,and $(c)$ mole fraction of $KI$ if the density of $20 \%$ (mass/mass) aqueous $KI$ solution is $1.202 \, g \, mL^{-1}$.

The mole fraction of a solute in a solution is $0.1$. At $298 \ K$,molarity of the solution is the same as its molality. The density of this solution at $298 \ K$ is $2.0 \ g \ cm^{-3}$. The ratio of the molecular weights of the solute and solvent,$\left(\frac{MW_{solute}}{MW_{solvent}}\right)$,is

The concentration of an aqueous solution of $0.01 \ M \ CH_3OH$ is very nearly equal to which of the following?

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.

$A$ solution of two components containing $n_{1}$ moles of the $1^{st}$ component and $n_{2}$ moles of the $2^{nd}$ component is prepared. $M_{1}$ and $M_{2}$ are the molecular weights of component $1$ and $2$ respectively. If $d$ is the density of the solution in $g \ mL^{-1}$, $C_{2}$ is the molarity and $x_{2}$ is the mole fraction of the $2^{nd}$ component, then $C_{2}$ can be expressed as