At $80\,^oC$,the vapour pressure of pure liquid $A$ is $520\, mm\,Hg$ and that of pure liquid $B$ is $1000\, mm\,Hg$. If a mixture of $A$ and $B$ boils at $80\,^oC$ and $1\, atm$ pressure,the amount of $A$ in the mixture is ........... $mol\,\%$.

On dissolving $0.5 \ g$ of a non-volatile non-ionic solute to $39 \ g$ of benzene,its vapor pressure decreases from $650 \ mm \ Hg$ to $640 \ mm \ Hg$. The depression of freezing point of benzene (in $K$) upon addition of the solute is. . . . .
(Given data : Molar mass and the molal freezing point depression constant of benzene are $78 \ g \ mol^{-1}$ and $5.12 \ K \ kg \ mol^{-1}$,respectively)

At $35^{\circ} C$,the vapour pressure of $CS_{2}$ is $512 \; mm \; Hg$ and that of acetone is $344 \; mm \; Hg$. $A$ solution of $CS_{2}$ in acetone has a total vapour pressure of $600 \; mm \; Hg$. The false statement amongst the following is

At $40\,^oC$,the vapour pressure (in torr) of a solution of methyl alcohol $(A)$ and ethyl alcohol $(B)$ is represented by: $P_s = 120 X_A + 138$,where $X_A$ is the mole fraction of methyl alcohol. The values of $\lim_{X_A \to 0} (P_B^0)$ and $\lim_{X_B \to 0} (P_A^0)$ are:

Solid Lead nitrate is dissolved in $1 \, L$ of water. The solution was found to boil at $100.15^{\circ}C$. When $0.2 \, mol$ of $NaCl$ is added to the resulting solution,it was observed that the solution froze at $-0.8^{\circ}C$. The solubility product of $PbCl_2$ formed is $........... \times 10^{-6}$ at $298 \, K$. (Nearest integer) Given: $K_b = 0.5 \, K \, kg \, mol^{-1}$ and $K_f = 1.8 \, K \, kg \, mol^{-1}$. Assume molality to be equal to molarity in all cases.

After adding a non-volatile solute, the freezing point of water decreases to $-0.186^{\circ} C$. Calculate $\Delta T_b$ if $K_f = 1.86 \text{ K kg mol}^{-1}$ and $K_b = 0.521 \text{ K kg mol}^{-1}$. (in $\text{ K}$)