For a dilute solution containing $2.5 \ g$ of a non-volatile non-electrolyte solute in $100 \ g$ of water,the elevation in boiling point at $1 \ atm$ pressure is $2 \ ^\circ C$. The concentration of the solute is very low compared to the solvent. What is the vapor pressure of the solution in $mm \ Hg$? $(K_b = 0.76 \ K \ kg \ mol^{-1})$

$1 \, \text{mole}$ of each of $A$ and $B$ form an ideal solution of vapour pressure $100 \, \text{mm Hg}$. Addition of $2 \, \text{moles}$ of $B$ to it decreases the vapour pressure by $20 \, \text{mm Hg}$. The vapour pressure of $A$ and $B$ in pure state are,respectively:

Which of the following pairs of solutions is isotonic?
$A$. $18 \ g/L$ of glucose solution and $6 \ g/L$ of urea solution
$B$. $10 \ g/L$ of glucose solution and $10 \ g/L$ of urea solution
$C$. $0.01 \ M \ NaOH$ solution and $0.02 \ M$ glucose solution
$D$. $0.01 \ M \ NaCl$ solution and $0.01 \ M$ glucose solution
(Assume that $NaCl$ undergoes complete dissociation)

Identify the correct statements :
$(A)$ The molality of $2.5 \text{ g}$ of ethanoic acid (Molar mass : $60 \text{ g mol}^{-1}$) in $75 \text{ g}$ of benzene solution is $0.556 \text{ m}$.
$(B)$ The molarity of a solution containing $5 \text{ g}$ of NaOH (molar mass : $40 \text{ g mol}^{-1}$) in $450 \text{ mL}$ of solution is $0.278 \text{ M}$ at $298 \text{ K}$.
$(C)$ Aquatic species are more comfortable in cold water.
$(D)$ The solubility of gas increases with decrease in pressure.
$(E)$ For a binary mixture of $A$ and $B$, the number of moles of $A$ and $B$ are $n_{A}$ and $n_{B}$ respectively. The mole fraction of $B$ will be $x_{B} = n_{A} / (n_{A} + n_{B})$.
Choose the correct answer from the options given below :

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 $= 4.2 \,J \,g^{-1} \,K^{-1}$]

On mixing urea, the boiling point of $H_{2}O$ changed to $100.5^{\circ}C$. Calculate the freezing point of the solution, if $K_{f}$ of water is $1.87 \ K \cdot kg \cdot mol^{-1}$ and $K_{b}$ of water is $0.52 \ K \cdot kg \cdot mol^{-1}$. (in $^{\circ}C$)