Relative lowering of vapour pressure of a dilute solution is $0.5$. What is the mole fraction of the non-volatile solute?

What is the mole ratio of benzene $(P_B^o = 150\, torr)$ and toluene $(P_T^o = 50\, torr)$ in the vapour phase if the given solution has a vapour pressure of $120\, torr$?

The vapour pressure of benzene at $90\,^oC$ is $1020 \, \text{torr}$. $5 \, g$ of a solute is dissolved in $58.5 \, g$ of benzene. The vapour pressure of the solution is $990 \, \text{torr}$. What is the molar mass of the solute?

In an experiment,$1 \ g$ of a non-volatile solute was dissolved in $100 \ g$ of acetone (molar mass $= 58 \ g/mol$) at $298 \ K$. The vapour pressure of the solution was found to be $192.5 \ mm \ Hg$. The molecular weight of the solute is (vapour pressure of pure acetone $= 195 \ mm \ Hg$). (in $.24$)

The mass of glucose that should be dissolved in $100 \ g$ of water in order to produce the same relative lowering of vapour pressure as is produced by dissolving $1 \ g$ of urea (molar mass $= 60 \ g/mol$) in $50 \ g$ of water is ........... $g$. (Assume dilute solution in both cases):-

The vapor pressures of two pure liquids $(A)$ and $(B)$ are $100 \ Torr$ and $80 \ Torr$ respectively. What is the total vapor pressure of the solution formed by mixing $2 \ moles$ of $(A)$ and $3 \ moles$ of $(B)$ (in $Torr$)?