The solubility product of a sparingly soluble $AB_2$ salt is $2.56 \times 10^{-4} \ M^3$ at $25^{\circ} C$. The $K_f$ of water is $1.8 \ K \ kg \ mol^{-1}$. The depression in freezing point of a saturated solution of $AB_2$ is (in $K$)

$A$ solution of urea (molar mass $60 \, g \, mol^{-1}$) boils at $100.18 \, ^oC$ at atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512 \, K \, kg \, mol^{-1}$ respectively,the above solution will freeze at ........... $^oC$.

If the mole fraction of the solvent in a solution decreases,then:

The $pH$ of a $0.1 \ M$ monobasic acid solution is $2$. Its osmotic pressure at $T$ Kelvin temperature is ............. $RT$.

$A$ Beckmann thermometer is used to measure:

$P$ 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 $Q$.