The elevation in boiling point for $1 \ m$ solution of non-volatile solute $A$ is $3 \ K$. The depression in freezing point for $2 \ m$ solution of $A$ in the same solvent is $6 \ K$. The ratio of $K_{b}$ and $K_{f}$ i.e.,$K_{b} / K_{f}$ is $1 : X$. The value of $X$ is [nearest integer].

The osmotic pressure of a $0.5 \ M$ aqueous solution of $CH_3COOH$ having a $pH$ of $2$ at temperature $T$ is . . . . . . . (in $RT$)

The difference between the boiling point and freezing point of an aqueous solution of urea containing $10.0 \ kg$ of water is $100.2372 \ ^oC$. How many grams of urea are dissolved in the solution? (Given: $K_b = 0.513 \ K \ kg \ mol^{-1}$,$K_f = 1.86 \ K \ kg \ mol^{-1}$)

$P$ and $Q$ combine to form two compounds $PQ_2$ and $PQ_3$. If $1 \ g$ of $PQ_2$ is dissolved in $51 \ g$ of benzene,the depression of freezing point is $0.8^{\circ} C$. If $1 \ g$ of $PQ_3$ is dissolved in $51 \ g$ of benzene,the depression of freezing point is $0.625^{\circ} C$. Given $K_f$ of benzene $= 5.1 \ K \ kg \ mol^{-1}$,calculate the atomic masses of $P$ and $Q$.

The $pH$ of a $0.1 \, M$ monobasic acid is measured to be $2$. Its osmotic pressure at a given temperature $T \, K$ is (in $, RT$)

$1 \, \text{mole}$ of liquid $A$ and $2 \, \text{moles}$ of liquid $B$ make a solution having an observed vapour pressure of $42 \, \text{torr}$. The vapour pressures of pure $A$ and pure $B$ are $45 \, \text{torr}$ and $36 \, \text{torr}$ respectively. The described solution: