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 :

  • A
    $(1)$ $A$, $B$ and $C$ only
  • B
    $(2)$ $A$, $D$ and $E$ only
  • C
    $(3)$ $A$ and $B$ only
  • D
    $(4)$ $A$ and $C$ only

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The number of pairs of solutions having the same value of osmotic pressure from the following is:
(Assume $100\%$ ionization)
$A.$ $0.500 \ M \ C_2H_5OH \ (aq)$ and $0.25 \ M \ KBr \ (aq)$
$B.$ $0.100 \ M \ K_4[Fe(CN)_6] \ (aq)$ and $0.100 \ M \ FeSO_4(NH_4)_2SO_4 \ (aq)$
$C.$ $0.05 \ M \ K_4[Fe(CN)_6] \ (aq)$ and $0.25 \ M \ NaCl \ (aq)$
$D.$ $0.15 \ M \ NaCl \ (aq)$ and $0.1 \ M \ BaCl_2 \ (aq)$
$E.$ $0.02 \ M \ KCl \cdot MgCl_2 \cdot 6H_2O \ (aq)$ and $0.05 \ M \ KCl \ (aq)$

Match the following.
List-$I$ List-$II$
$(A)$ Azeotrope $(I)$ $\Delta T_b = i K_b m$
$(B)$ Henry's law $(II)$ $p = K_H x$
$(C)$ Cryoscopic constant $(III)$ $\Delta T_f / m$
$(D)$ Van't Hoff factor $(IV)$ Deviation from Raoult's law
$(V)$ $\pi = CRT$

The correct answer is

An aqueous solution freezes at $-0.186 \ ^\circ C$ ($K_f = 1.86 \ ^\circ C \ kg \ mol^{-1}$; $K_b = 0.512 \ ^\circ C \ kg \ mol^{-1}$). What is the elevation in boiling point of the same solution?

The osmotic pressure of a solution of $NaCl$ is $0.10 \ atm$ and that of a glucose solution is $0.20 \ atm.$ The osmotic pressure of a solution formed by mixing $1 \ L$ of the sodium chloride solution with $2 \ L$ of the glucose solution is $x \times 10^{-3} \ atm.$ $x$ is.......... (nearest integer)

The solution of sugar in water contains

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