The vapor pressure of water at a certain temperature is $3000 \ N \ m^{-2}$. When a non-electrolyte solute is added,it decreases by $300 \ N \ m^{-2}$. The molality of the solution is ............. $m$.

Using Raoult's law,explain how the total vapour pressure over the solution is related to the mole fraction of components in the following solutions:
$(a)$ $CHCl_{3(l)}$ and $CH_{2}Cl_{2(l)}$
$(b)$ $NaCl_{(s)}$ and $H_{2}O_{(l)}$

$A$ set of solutions is prepared using $180 \ g$ of water as a solvent and $10 \ g$ of different non-volatile solutes $A, B$ and $C$. The relative lowering of vapour pressure in the presence of these solutes are in the order
[Given,molar mass of $A = 100 \ g \ mol^{-1}; B = 200 \ g \ mol^{-1}; C = 10,000 \ g \ mol^{-1}]$

Consider a binary solution of two volatile liquid components $1$ and $2$. $x_1$ and $y_1$ are the mole fractions of component $1$ in liquid and vapour phase,respectively. The slope and intercept of the linear plot of $\frac{1}{x_1}$ vs $\frac{1}{y_1}$ are given respectively as :

Calculate the mole fraction of solute in a solution if the vapour pressure of the solution and the pure solvent are $27 \text{ mm Hg}$ and $30 \text{ mm Hg}$ respectively at $298 \text{ K}$.

The vapour pressure of acetone at $20\,^{\circ}C$ is $185\,torr.$ When $1.2\,g$ of a non-volatile substance was dissolved in $100\,g$ of acetone at $20\,^{\circ}C,$ its vapour pressure was $183\,torr.$ The molar mass $(g\,mol^{-1})$ of the substance is: