Elevation in boiling point for $1.5 \, m$ solution of glucose in water is $4 \, K$. The depression in freezing point for $4.5 \, m$ solution of glucose in water is $4 \, K$. The ratio of molal elevation constant to molal depression constant $(K_{b} / K_{f})$ is $....$

$A$ substance '$X$' $(1.5 \ g)$ dissolved in $150 \ g$ of a solvent '$Y$' (molar mass $= 300 \ g \ mol^{-1}$) led to an elevation of the boiling point by $0.5 \ K$. The relative lowering in the vapour pressure of the solvent '$Y$' is . . . . . . $\times 10^{-2}$. (Nearest integer)
[Given : $K_{b}$ of the solvent $= 5.0 \ K \ kg \ mol^{-1}$]
Assume the solution to be dilute and no association or dissociation of $X$ takes place in solution.

$A$ cylinder containing an ideal gas ($0.1 \; mol$ in $1.0 \; dm^{3}$) is in thermal equilibrium with a large volume of $0.5 \; m$ (molal) aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn,the volume of the gas in litres after equilibrium is achieved will be ............ $litre$.
(Given: $K_{f}$ (water) $= 2.0 \; K \; kg \; mol^{-1}$,$R = 0.08 \; dm^{3} \; atm \; K^{-1} \; mol^{-1}$,freezing point of water $= 273 \; K$)

At $T(K)$,the vapour pressure of pure benzene (molar mass $= 78 \ g \ mol^{-1}$) is $0.85 \ bar$. When $2.0 \ g$ of a non-volatile,non-electrolyte solute is added to $39 \ g$ of benzene,the vapour pressure of the solution at $T(K)$ is $0.83 \ bar$. The elevation in boiling point (in $K$) of the same solution is: ($K_b$ of benzene is $2.6 \ K \ kg \ mol^{-1}$)

Match the following.

$A$. Ebullioscopic constant	$I$. Depression of freezing point
$B$. Cryoscopic constant	$II$. Total pressure is the sum of partial pressures of the components
$C$. Henry's law	$III$. Elevation of boiling point
$D$. Dalton's law	$IV$. Solubility of a gas in liquid

The correct match is

The ionization constant of a monobasic acid $HA$ is to be determined. If a $0.025 \ m$ aqueous solution of the acid freezes at $-0.060 \ ^{\circ}C$,calculate the ionization constant $K_a$. (Assume molality = molarity and $K_f(H_2O) = 1.86 \ K \ kg \ mol^{-1}$).