What is the mass in $g$ of a non-volatile solute with a molecular weight of $40$ that should be dissolved in $57 \ g$ of octane to reduce its vapour pressure to $80 \%$ of its original value?

The vapour pressure of a pure solvent is $0.70 \ atm.$ When a non-volatile solute $A$ is dissolved in it,the vapour pressure of the solution becomes $0.35 \ atm.$ The mole fraction of solute $A$ will be$:-$

$A$ mixture of volatile components $A$ and $B$ has a total vapour pressure (in $torr$) $P = 254 - 119 X_A$,where $X_A$ is the mole fraction of $A$ in the mixture. What are the values of $P_A^o$ and $P_B^o$ (in $torr$)?

Two liquids $X$ and $Y$ form an ideal solution. At a constant temperature of $300 \ K$,the vapor pressure of a solution containing $1 \ mol$ of $X$ and $3 \ mol$ of $Y$ is $550 \ mm \ Hg$. If $1 \ mol$ of $Y$ is added to this solution,the vapor pressure of the solution increases by $10 \ mm \ Hg$. What are the vapor pressures of $X$ and $Y$ in their pure states?

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 :

Derive an equation for a solution that shows the relation between total pressure and the mole fraction of a volatile solute and a volatile solvent,and explain it by plotting a graph.