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 $\text{ K}$)

$A$ 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 ........... $^oC$.

$P$ 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 specific heat of a certain substance is $0.86 \,J \,g^{-1} \,K^{-1}$. Assuming ideal solution behaviour,the energy required (in $J$) to heat $10 \,g$ of $1 \,molal$ of its aqueous solution from $300 \,K$ to $310 \,K$ is closest to $.... \,J$
[Given: Molar mass of the substance $= 58 \,g \,mol^{-1}$; specific heat of water $= 4.2 \,J \,g^{-1} \,K^{-1}$]

The $pH$ of a $0.1 \ M$ monobasic acid is $2$. Its osmotic pressure at a given temperature $T \ (K)$ is: (Given that the effective concentration for osmotic pressure is $(1+\alpha) \times$ concentration of acid, where $\alpha$ is the degree of dissociation)

$6 \ g$ of a mixture of naphthalene $(C_{10}H_8)$ and anthracene $(C_{14}H_{10})$ is dissolved in $300 \ g$ of benzene. If the depression in freezing point is $0.70 \ K$,the composition of naphthalene and anthracene in the mixture respectively in $g$ are (molal depression constant of benzene is $5.1 \ K \ kg \ mol^{-1}$)