The vapour pressure of ethanol $(C_2H_5OH)$ and methanol $(CH_3OH)$ at $298 \ K$ is $44.5 \ mm \ Hg$ and $88.7 \ mm \ Hg$ respectively. At the same temperature,an ideal solution is prepared by mixing $60 \ g$ of ethanol and $40 \ g$ of methanol. Find the mole fraction of methanol in the vapour state.

At $30^\circ C$,liquid $A$ and $B$ form an ideal solution. The total vapor pressure of a solution containing $1 \ mol$ of $A$ and $2 \ mol$ of $B$ is $250 \ mm \ Hg$. The total vapor pressure becomes $300 \ mm \ Hg$ when $1 \ mol$ more of $A$ is added to the first solution. What are the vapor pressures of pure $A$ and $B$ at the same temperature?

What is the vapour pressure of a solution containing $1 \ mol$ of a non-volatile solute in $36 \ g$ of water (in $mm \ Hg$)? $(P_1^0 = 400 \ mm \ Hg)$

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 .......... $torr$.

When a solute is added to a solvent having a vapor pressure of $0.80 \ atm$,the vapor pressure decreases to $0.60 \ atm$. The mole fraction of the solute is .........

At $298 \ K$,$0.714$ moles of liquid $A$ is dissolved in $5.555$ moles of liquid $B$. The vapour pressure of the resultant solution is $475 \ torr$. The vapour pressure of pure liquid $A$ at the same temperature is $280.7 \ torr$. What is the vapour pressure of pure liquid $B$ in $torr$?