For a solution formed by mixing liquids $L$ and $M$,the vapour pressure of $L$ plotted against the mole fraction of $M$ in solution is shown in the following figure. Here $x_L$ and $x_M$ represent mole fractions of $L$ and $M$,respectively,in the solution. The correct statement$(s)$ applicable to this system is(are)
$A$. Attractive intermolecular interactions between $L-L$ in pure liquid $L$ and $M-M$ in pure liquid $M$ are stronger than those between $L-M$ when mixed in solution
$B$. The point $Z$ represents vapour pressure of pure liquid $M$ and Raoult's law is obeyed when $x_L \rightarrow 0$
$C$. The point $Z$ represents vapour pressure of pure liquid $L$ and Raoult's law is obeyed when $x_L \rightarrow 1$
$D$. The point $Z$ represents vapour pressure of pure liquid $M$ and Raoult's law is obeyed from $x_L=0$ to $x_L=1$

$PbCl_2$ is dissolved in water to make its saturated solution. What will be the freezing point of this solution?
Given: $K_f (H_2O) = 2 \ K \ kg \ mol^{-1}$,$K_{sp} (PbCl_2) = 4 \times 10^{-6}$
(Assume molarity to be equal to molality) $..... ^oC$

Properties such as boiling point,freezing point,and vapour pressure of a pure solvent change when solute molecules are added to get a homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of an ethylene glycol and water mixture as an anti-freezing liquid in the radiator of automobiles.
$A$ solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is $0.9$.
Given: Freezing point depression constant of water $(K_{f}^{\text{water}}) = 1.86 \ K \ kg \ mol^{-1}$
Freezing point depression constant of ethanol $(K_{f}^{\text{ethanol}}) = 2.0 \ K \ kg \ mol^{-1}$
Boiling point elevation constant of water $(K_{b}^{\text{water}}) = 0.52 \ K \ kg \ mol^{-1}$
Boiling point elevation constant of ethanol $(K_{b}^{\text{ethanol}}) = 1.2 \ K \ kg \ mol^{-1}$
Standard freezing point of water $= 273 \ K$
Standard freezing point of ethanol $= 155.7 \ K$
Standard boiling point of water $= 373 \ K$
Standard boiling point of ethanol $= 351.5 \ K$
Vapour pressure of pure water $= 32.8 \ mm \ Hg$
Vapour pressure of pure ethanol $= 40 \ mm \ Hg$
Molecular weight of water $= 18 \ g \ mol^{-1}$
Molecular weight of ethanol $= 46 \ g \ mol^{-1}$
In answering the following questions,consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.
$1.$ The freezing point of the solution $M$ is
$(A) \ 268.7 \ K \ (B) \ 268.5 \ K$
$(C) \ 234.2 \ K \ (D) \ 150.9 \ K$
$2.$ The vapour pressure of the solution $M$ is
$(A) \ 39.3 \ mm \ Hg \ (B) \ 36.0 \ mm \ Hg$
$(C) \ 29.5 \ mm \ Hg \ (D) \ 28.8 \ mm \ Hg$
$3.$ Water is added to the solution $M$ such that the mole fraction of water in the solution becomes $0.9$. The boiling point of this solution is
$(A) \ 380.4 \ K \ (B) \ 376.2 \ K$
$(C) \ 375.5 \ K \ (D) \ 354.7 \ K$
Give the answer for questions $1, 2$ and $3.$

Match List-$I$ with List-$II$

List-$I$	List-$II$
$A$. Solution of chloroform and acetone	$I$. Minimum boiling azeotrope
$B$. Solution of ethanol and water	$II$. Dimerizes
$C$. Solution of benzene and toluene	$III$. Maximum boiling azeotrope
$D$. Solution of acetic acid in benzene	$IV$. $\Delta V_{mix}=0$

Choose the correct answer from the options given below $:$

When $1.685 \ g$ of an alkali metal chloride is dissolved in $200 \ g$ water,the boiling point of the solution is measured to be $100.051 \ ^\circ C$. If the ionic solid has a crystal lattice with cation and anion radius $1.70 \ \mathring{A}$ and $1.80 \ \mathring{A}$ respectively,find the edge length of the solid assuming no defect in the crystal. Given: $K_b(H_2O) = 0.51 \ K \ kg \ mol^{-1}$,$N_A = 6 \times 10^{23}$,atomic masses: $[Li = 7, Na = 23, K = 39, Rb = 85.5, Cs = 133, Cl = 35.5]$.

Consider the following aqueous solutions.
$I$. $2.2 \ g$ Glucose in $125 \ mL$ of solution.
$II$. $1.9 \ g$ Calcium chloride in $250 \ mL$ of solution.
$III$. $9.0 \ g$ Urea in $500 \ mL$ of solution.
$IV$. $20.5 \ g$ Aluminium sulphate in $750 \ mL$ of solution.
The correct increasing order of boiling point of these solutions will be:
[Given: Molar mass in $g \ mol^{-1}$: $H=1, C=12, N=14, O=16, Cl=35.5, Ca=40, Al=27, S=32$]