The vapor pressures of two liquids $P$ and $Q$ are $80 \ torr$ and $60 \ torr$,respectively. The total vapor pressure of a solution formed by mixing $3 \ moles$ of $P$ and $2 \ moles$ of $Q$ is .......... $torr$.

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 $H_{2}O_{(l)}$

Two liquids $A$ and $B$ form a solution at $306 \ K$ that follows the equation $P \ (\text{in } atm) = 0.172X_A + 0.215$,where $P$ is the total vapor pressure of the solution and $X_A$ is the mole fraction of $A$. The vapor pressure of pure $B$ is ............ . (in $atm$)

Relative lowering of vapour pressure of a dilute solution of glucose dissolved in $1 \ kg$ of water is $0.002$. The molality of the solution is (in $m$)

The vapour pressure of water at $23^{\circ} C$ is $19.8 \ mm$. If $0.1 \ mole$ of glucose is dissolved in $178.2 \ g$ of water, what is the vapour pressure (in $mm$) of the resultant solution?

$A$ solution containing $30 \,g$ of non-volatile solute in $90 \,g$ of water has a vapour pressure of $2.8 \,kPa$ at $298 \,K$. Further,$18 \,g$ of water is added to the solution and the new vapour pressure becomes $2.9 \,kPa$ at $298 \,K$. Calculate:
$i$. Molar mass of the solute
$ii$. Vapour pressure of water at $298 \,K$