$2\, \text{moles}$ of liquid $A$ is mixed with $3\, \text{moles}$ of liquid $B$. Calculate the mole fraction of $A$ in the vapour phase if $P_A^o = 100\, \text{mm}$ and $P_B^o = 200\, \text{mm}$.

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?

When $18 \ g$ of glucose $(C_6H_{12}O_6)$ is added to $178.2 \ g$ of water,the vapour pressure of the aqueous solution at $100 \ ^\circ C$ is .......... $torr$.

Select the correct option using $T$ (True) or $F$ (False) for the following statements: $(1)$ The decrease in vapour pressure is equal to the mole fraction of the solute. $(2)$ The relative lowering of vapour pressure is directly proportional to the amount of solute. $(3)$ The relative lowering of vapour pressure is equal to the mole fraction of the solute. $(4)$ The vapour pressure of the solution is equal to the mole fraction of the solvent.

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

The vapour pressure of a given liquid decreases if?